Chapter 1 (Chip-Scale Quantum Imaging and Spectroscopy)
Chapter 1 (Chip-Scale Quantum Imaging and Spectroscopy)
Chapter 1 (Chip-Scale Quantum Imaging and Spectroscopy)
Abstract:
This scholarly contribution delves into the forefront of chip-scale quantum
technologies, exploring the symbiotic integration of quantum principles within microchip
architectures. The chapter navigates the intricate landscape of quantum imaging and
spectroscopy, elucidating the unprecedented precision and computational efficacy afforded
by the marriage of quantum mechanics with microscale semiconductor devices. The
discourse commences with an exploration of the foundational principles underpinning chip-
scale quantum imaging, elucidating the intricate interplay of superposition and entanglement.
As the narrative unfolds, the discussion seamlessly transitions to the burgeoning trend of
hybrid quantum-classical architectures, where classical computing harmoniously
complements quantum processing, optimizing the strengths of both paradigms. Extending the
inquiry beyond theoretical realms, the chapter illuminates diverse applications across
scientific disciplines. From the realms of healthcare, drug discovery, environmental
monitoring, to real-time industrial analysis, chip-scale quantum technologies emerge as
transformative tools, promising to redefine the boundaries of scientific inquiry. Peering into
the future, predictions for exponential growth in quantum processing power on chips beckon
a paradigm shift, while the establishment of quantum communication networks hints at a
global quantum internet. The chapter concludes with a succinct summary of key findings and
a compelling call to action, urging continued research, interdisciplinary collaboration, and
educational initiatives to unlock the full potential of chip-scale quantum imaging and
spectroscopy. The narrative woven herein beckons researchers and enthusiasts alike to
embark on a journey towards unravelling the intricacies of quantum phenomena at the
microscale.
1. Introduction
1.1 Background
In recent years, quantum technologies have emerged as transformative tools in the
realm of imaging and spectroscopy. Traditional methods, while powerful, face limitations in
precision and computational efficiency. The integration of quantum capabilities into
microchips presents a ground-breaking solution to these challenges. This chapter explores the
profound implications of chip-scale quantum imaging and spectroscopy, aiming to
revolutionize scientific analyses at the microscopic level.
Quantum phenomena, when harnessed on a chip-scale platform, unlock unprecedented
sensitivity and computational power. The significance of this integration lies in its potential
to redefine the boundaries of what is achievable in imaging and spectroscopy. As we delve
into the principles and applications of chip-scale quantum technologies, it becomes evident
that this marriage of quantum capabilities with microchip technology is poised to usher in a
new era in scientific exploration.
1.2 Objectives
Provide a comprehensive review of fundamental principles underlying chip-scale
quantum imaging and spectroscopy. Explore unique characteristics of quantum sensors
integrated into microchips, emphasizing enhanced sensitivity and computational
efficiency. Uncover diverse applications across scientific disciplines, showcasing
transformative roles in healthcare, materials science, diagnostics, drug discovery,
environmental monitoring, and materials analysis through case studies. Outline future
directions and considerations, addressing potential advancements and challenges.
Emphasize the implications of chip-scale quantum technologies for the future of scientific
research and technological innovation.
1.3 Definitions:
Chip-Scale Quantum Imaging and Spectroscopy refers to an innovative field of
scientific inquiry where quantum principles are harnessed and integrated into microscale
semiconductor devices, commonly known as chips, for the purpose of imaging and
spectroscopic analysis.
Quantum Imaging:
Quantum imaging on a chip involves utilizing quantum properties, such as superposition and
entanglement, to enhance the precision and sensitivity of imaging techniques. This quantum-
enhanced imaging holds promise for applications ranging from medical diagnostics to
materials characterization, allowing for the visualization of objects with unprecedented detail
and accuracy.
Quantum Spectroscopy:
Chip-Scale Quantum Spectroscopy involves the use of quantum technologies for analysing
the interaction of matter with electromagnetic radiation. By leveraging quantum principles in
spectroscopic techniques, researchers aim to achieve higher levels of precision in identifying
and characterizing materials. This can have applications in fields like chemistry,
environmental monitoring, and industrial processes.
The integration of quantum principles onto microchips represents a significant advancement,
enabling the development of portable and efficient devices for imaging and spectroscopic
analysis. This emerging field holds the potential to revolutionize various scientific disciplines
by providing new tools for researchers to explore and understand the quantum nature of
matter at the microscale.
1.4 Brief history and evolution of quantum imaging and spectroscopy:
The field of quantum optics—concerned with the quantum mechanical properties of light—
begins with the start of quantum mechanics itself. Max Planck was investigating
electromagnetic radiation when he made his initial quantum conjecture; that light could only
be emitted with a quanta of energy E = hν [1, 2]. Einstein added to the beginnings of quantum
mechanics with his work on the photo-electric effect in which he again discussed the quanta
of light energy. Einstein’s work proposed the idea that the quantized energy of light was a
fundamental aspect of light itself, not just the emission process [3]. These quanta of light are
what modern physicists call “photons”—a term coined in the 1920’s.
The stellar interferometry experiment of Robert Hanbury Brown and Richard Q. Twiss, using
intensity correlations led to much debate and research that clarified aspects of quantum optics
[4]. As Brown and Twiss pointed out in response to the controversy, the predictions from
Maxwell’s equations for classical electrodynamics are identical to the predictions of quantum
optics with quantized photo-detections (i.e. detecting photons) [5]. Their experiment inspired
the formulation of a quantum mechanical theory of optical coherence and detection [6–10],
extending the earlier work in classical coherence to the quantum optical and single photon
domain [11].
More recently, the quantum mechanical properties of images and imaging techniques have
been investigated [12–14]. Imaging, a subfield of optics, deals primarily with the transverse
spatial degrees of freedom of an optical field. Research has included quantum ghost imaging
[15–17], quantum communication [18, 19], and quantum enhanced sensing and lithography
[20–23]. Two interesting features of quantum mechanics are entanglement and weak values.
These concepts are connected to quantum measurement theory and for this reason have the
potential for practical use in metrology or measurement-based communication technology.
1.4.1 Information Theory
Information theory is a relatively young field, beginning in the 1940’s with the
seminal work of Claude Shannon [26, 27]. It concerns itself with the communication
over a noisy channel and uses entropy to quantify information. Communication or
information transfer can be quantified in terms of mutual information, here I describe
the concept of mutual information for continuous
and discrete probabilities.
Discrete Probabilities
where H(X) is the marginal entropy. This is shown conceptually in Fig. 1.1. The
marginal entropy of X is given by
, (1.2)
the joint entropy of X and Y is given by
, (1.3)
Figure 1.1: The concept of mutual information is shown visually. The system defined
by the variable X is represented by the blue circle on the left, the system defined by the
variable Y is represented by the pink circle on the right. Marginal entropies for each
system H(X) and H(Y ), respectively, and the entropy of the joint system H(X,Y ) can be
calculated. The mutual information is the overlap of the marginal entropies of systems
X and Y . The sum of the marginal entropies for system X and system Y counts this
overlap region twice, and by subtracting off the joint system entropy we are left only
with the mutual information as described by Eq. 1.1.
Figure 1.2: An alternative concept of mutual information is shown visually. The system
defined by the variable X is again represented by the blue circle on the left and the
system defined by the variable Y is again represented by the pink circle on the right.
Non-overlapping conditional entropies for each system H(X|Y ) and H(Y |X),
respectively, can be calculated. The mutual information is the overlap of the entropies
of systems X and Y . The joint system entropy H(X,Y ) minus these conditional
entropies gives the mutual information as described by Eq. 1.4.
where the function P(x,y) is the joint probability which characterizes the corre-
lation between X and Y .
, (1.5)
conceptually in Fig. 1.2. This formulation of the mutual information can be useful
when the correlation between the random variables is known.
Continuous Probability Densities
(1.6)
(1.7)
and
(1.8)
where the subscript c indicates the quantity uses continuous probability distri-
butions.
The fact that the continuous probability distribution can exceed 1 indicates the
continuous and discrete entropic formulas may not converge in the limit of small
discretization widths. The probability density function is related to the discrete
probabilities in the following manner:
, (1.9)
where the region of x with significant probability is discretized into b bins of
width ∆x. We now compare the discrete formulas to the continuous ones:
(1.10)
The entropy formulas for discrete and continuous probabilities therefore do not
converge to the same value for small discretization width. They are offset by the
logarithm of the number of discretization bins b;
. (1.11)
This is not the case for the mutual information formula however; because the
mutual information involves adding and subtracting entropies I(X;Y ) = H(X) + H(Y ) −
H(X,Y ), the divergent offset terms cancel out, resulting in
Figure 3. The evolution of PIC bandwidth, power efficiency, and total power consumption
[22].
Therefore, quantum technology can affect the way we live due to its ability to
provide fascinating advances in both technology and fundamental science areas. The
most important aim of this technology is to pave the way for smaller, faster, and more
flexible electronics than ever before. Only during a few years, the development of
quantum technology was realized due to its potential for commercial applications and
strategic sectors and transferred from “blue sky” science to a field of technology
rapidly [22]. For instance, quantum computing as a feature of quantum technology—
processing a sufficient quantum volume with advantages in real-world applications—
can be employed to solve cryptanalytic or machine learning algorithm problems. It does
not mean that a quantum computer made with mechanisms and methods of quantum
technology and the precision, accuracy, speed, and endurance factors of the quantum
computer are determined to describe its performance. It seems that high-performance
computing with quantum computers can be obtained by the development of room
temperature superconducting materials. Many researchers believe that the use of
quantum technology in integrated silicon circuits can lead to quality improvement of
silicon-based photonics, and new devices are going to be built based on this integration
approach. For instance, using the integration of quantum technology in silicon
photonics, devices can be built to meet our technological needs in the field of
communications, information, and data processing [23]. Regarding the challenges that
need to be tackled for the maturation and scaling up of quantum photonic integrated
circuits (PICs), major areas such as components, platforms, and integration processes
must be developed. For example, several quantum elements such as grating couplers,
waveguides, phase shifters, cavities, resonators, single photon sources, light emitting
diodes, and detectors need to be matured and their operation optimized for a selected
wavelength range. In addition, for scalable quantum operation, the insertion loss of
quantum elements must be drastically reduced and their ability for integration into a
standardized platform must be improved. In regard to the integration challenges, it was
found that silicon integrated quantum photonics can be considered a promising
approach to generate and manipulate entangled states of light on-chip scale and realize
quantum integrated circuits. Among quantum technology subsections, quantum emitters
were selected as the case of study. With this approach, the newest findings and progress
obtained in recent years are highlighted to provide an extensive overview of recent
developments in quantum emitters.
3.1 Quantum Emitters
On the basis of lab-scale experimental results for the preparation, manipulation,
and read out of quantum states from a modest number of quantum bits (qubits), we
need to use different benchtop components, including tunable and narrow-line width
lasers and optical elements such as lenses, wave plates, and prisms. Therefore, to
realize photonic quantum systems, quantum scientists and engineers need to solve the
integration challenges of quantum system components. Analogous to integrated circuit
chips, the quantum circuits need to integrate thousands or millions of components and
quantum elements on one chip. These components must provide the required
functionality, high performance, and stability. Consequently, novel design architectures
and fabrication techniques with the ability to integrate the quantum elements into chip-
scale electronics are essential [24]. To exploit the quantum circuit technology, the
implementation of a scalable architecture must be established beyond the realm of
‘mere’ engineering and, therefore, a transformative approach is required [25]. For
example, superconducting qubits and superconducting nanowire single-photon
detectors operate in an RF regime [25]. Due to the power dissipation, footprint, limited
frequency, and accuracy of the CMOS standard devices used for control and readout,
the scale-up in the size of this kind of single-photon detector is limited when we
attempt to achieve the required performances in real-world applications [25,26]. Tasker
et al. believed that the classical interface hardware for integrated quantum photonics is
still being implemented with large-footprint discrete electronics that limit device
scalability and performance. Therefore, silicon quantum photonics is not able to be
integrated with monolithic complementary metal–oxide–semiconductor (CMOS)
electronics [27]. In Figure 4, key milestones for integrated quantum photonics in the
past decade are shown [28]. As can be found from this figure, in 2008, the fabricated
circuit contained a few components. However, a quantum device with more than 650
components was formed in 2018. The capability of these devices changed from
enabling two-photon quantum interference to two-qubit operations. This rapid
progression triggers enabling discoveries in foundational quantum mechanics,
computing, communications, and metrology [28]. Similar to the integration and
complexity level of conventional PICs, the integration and complexity level of QPICs
need to be developed significantly. Today, the most advanced PICs comprise ~5 × 103
components, which can be considered as the upper limit for what is currently
achievable for QPIC scalability with existing fabrication and packaging technologies
[28].
Figure 4. Key milestones for integrated quantum photonics in the past decade:
on-chip two-photon interference and integrated controlled not (CNOT) gate [28].
As mentioned above, since integrated quantum photonics (IQP) is a compelling
platform for the future of quantum technologies, many attempts have been made to
overcome the integration challenges at the chip scale. This technology originated from
quantum information theory and it has become a powerful research methods toolbox for
researchers from numerous fields to find answers to many of their scientific questions
today. To date, various quantum compounds have been exploited to promote the
realization of quantum integration technology. Quantum compounds that have been
developed for quantum technology integration consist of superconducting circuits,
nonlinear waveguides, ultracold atoms, trapped ions, cavities, solid-state spins, and
emitters [29]. Quantum emitters are one of the most important quantum compounds
that are needed to be prepared in the chip scale. Consequently, the exploitation of
wafer-scale fabricated single-photon sources is highly notable. As has been highlighted,
a large number of identical single photons are required for harnessing the power of
integrated quantum photonics IQP on the chip scale. Accordingly, different types of
quantum emitters with the ability of integration on the chip scale were introduced.
Usually, quantum emitters include parametric photon-pair sources and single-photon
sources (SPSs) [29]. Among them, single-photon sources play an important role in the
advancement of quantum technology, which means that installation of single-photon
sources (SPSs) on a chip that can deterministically emit indistinguishable single
photons is very critical for the scaling operation of single-photon-based quantum
photonic integrated circuits (QPICs). In Figure 5, the SPS timeline for developing
physical systems and materials is shown. To provide the right impression of integrated
quantum chips, a sample of the configured integrated quantum compounds is shown in
Figure 6 [29]. In Figure 6a, the first IQP circuit for CNOT entangling operation in
silica-on-insulator waveguides is illustrated. The control and target qubits are
represented by Ci and Ti (i = 0, 1) in this circuit. V A and VB are ancilla qubits. The
cladding layers of regions I and III are presented in the bottom left panel, and II is the
silica core layer [29]. In Figure 6b, a quantum circuit in silica, prepared by laser
writing, is shown. Complex three-dimensional integration can be produced using the
quantum circuit. Pure and identical photons can be generated by the integrated
spontaneous four-wave mixing (SFWM) SPS in Si photonic waveguides or
microresonators, which are shown in Figure 6c.
Here, the role of electrical connection was played by a thin gold layer—which acts as a strain
transfer structure—and broadband backside mirror for the QD micromesa that was prepared
by in situ electron-beam lithography [44]. Experimental results showed that the multiphoton
suppression had not been influenced by spectral tuning [44]. Besides the development in the
preparation of advanced materials such as the QD-based single photon emitter employed for
experimental demonstration of quantum technologies, the improvement in fabrication
techniques also continued. For example, to achieve cavity mode resonance with a great
enhancement of QD photoluminescence (PL) intensity, a precise calibration process of an
Al0.9Ga0.1As/GaAs DBR micropillar cavity, which matched the single InAs/GaAs quantum
dot (QD) exciton emission, was proposed [45]. Under a weak coupling regime, the light–
matter interaction of single QDs in a DBR micropillar cavity (Q∼3800) was investigated by
temperature-tuned PL spectra. In this study, a value of g (2)(0) = 0.070 was demonstrated using
the second-order autocorrelation measurement and highly pure single-photon emission at
high count rates was indicated by the estimated net count rate before the first objective lens
was reached (1.6 × 107 counts/s) under continuous wave excitation [45]. A heterogeneous
photonic integration platform was developed, allowing direct integration of GaAs
waveguides and cavities containing selfassembled InAs/GaAs quantum dots that provide
such capabilities in a scalable on-chip implementation [45]. In their experiments, a highly
efficient optical interface between Si 3N4 waveguides and single quantum dots in GaAs
geometries was achieved which included quantum dot radiative rate enhancement in
microcavities, and a path for reaching the nonperturbative strong-coupling regime [45].
Davanco et al. [46] indicated that robust implementation of single-photon sources can be
achieved through the use of systems that provide both strong light–matter interactions and a
low-loss interface between emitters and optical fields (Figure 7). Uppu et al. [47] reported a
coherent and stable single-photon source that simultaneously achieves high purity (g (2)(0) =
0.020 ± 0.005), high indistinguishability(V = 96 ± 2%), and >80% coupling efficiency with
the waveguide. Such a ‘plug-andplay’ single-photon source can be integrated with on-chip
optical networks implementing photonic quantum processors (Figure 8). As can be seen from
the figure, the taper section is responsible for the collection and guidance of the squeezed
emission out of the waveguide. The fundamental mode is reflected by a mirror prepared from
a photonic crystal and, therefore, the directional out-coupling of the QD signal becomes
available. The excitation and collection spots are highlighted with red and green spots. The
fundamental and first-order modes of the waveguide are excited by a Y-splitter.
The transmission of first-order mode into the emitter section was selectively performed by
the photonic crystal. To suppress the pump laser, a waveguide taper and two 90 ◦ bends were
coupled with the pump laser filter. The bottom-left grating is used to align in-coupling of the
laser beam by monitoring the reflected signal from the photonic crystal [47]. Another on-chip
waveguide-coupled single-photon source was proposed by Jiang et al. [48], in which the
waveguide was directly made by a quantum dot membrane (Figure 9). Grating output
couplers are made at both ends of the waveguide to scatter light out of the on-chip waveguide
plane into the detection apparatus [47]. The second-order correlation function g(2)(τ)
measurements were performed using a Hanbury Brown and Twiss interferometer to indicate
the photon statistics of the on-chip photon source. The obtained results showed an on-chip
single-photon source that is easily implemented and easily integrated into quantum photonic
circuits [48].
Figure 10. Prelocalization protocol for epitaxially grown QDs (real data shown) [49].
Part II shows how the alignment mask is imaged and where the crosses are located, and part
III indicates how the QD photoluminescence is pictured and spatially correlated with the
cross positions. A close-up image of the emission pattern of a single QD is shown in IV.
Progress was also made in the quantum integration platform by using the mechanical strain
engineering of low-dimensional semiconductors. It is well known that the unpredictable
transition energies of different QDs can be accounted for using randomness in strain, shape,
and composition in semiconductors [50]. One of the powerful methods for reshaping the
electronic states of semiconductors is strain engineering that can advance the development of
all-solid-state low-dimensional semiconductor-based single- and entangled-photon sources
with well-defined energies. The recent progress of employing a mechanical strain field to
control the electronic states and optical properties of low-dimensional semiconductors is
reviewed by Tao et al. [50]. They provided a comprehensive summary of diverse strain
engineered devices for engineering the exciton binding energy, the coherent coupling of
electronic states, and the optical properties of low-dimensional semiconductors including
single and entangled photons. In addition, a discussion of the prospects and challenges of
deploying the strain engineering technique for future scalable quantum networks and
photonic quantum circuits was also presented. Yang and co-workers [51] emphasized that
inability to grow perfectly identical quantum dots with ideal optical properties necessitates
the application of post-growth tuning techniques via, e.g., temperature, electric, magnetic, or
strain fields. They showed that the wavelength of single photons and entangled photon pairs
emitted by InGaAs/GaAs quantum dots can be reversibly tuned using piezoelectric crystals
such as PMN-PT [51]. For electrical triggering and tuning of the wavelength or the exciton’s
fine structure, they used quantum light-emitting diodes. Furthermore, the frequency even
feedback, which is verified by two-photon interference with photons from two stabilized
sources, was employed to compensate the wavelength drift caused by piezo creep and also to
ensure the indistinguishability of photons [51]. Nevertheless, by performing many attempts to
prepare a GaAs quantum dot single-photon source on the chip scale, considerable progress
was also made in the preparation of III-nitride QDs that can even operate at room
temperature. However, a reliable SPE platform with a high signal to noise ratio and relatively
low g(2)(0) must be achieved by the growth of high-quality material with a higher emission
energy of ~3 eV. Due to the large exciton binding energies of III-nitride semiconductor
quantum dots (QDs), they are promising candidates for single-photon emission at
noncryogenic temperatures [52].
It has been reported that GaN QD single-photon emitters can operate at 300 K and their
performance for the emission of single photons depends on the balance between the emission
line width and the biexciton binding energy [52]. It has been shown that when using GaN
QDs embedded in a planar AlN layer, grown on silicon, the brightness and single-photon
purity can be adjusted to improve the performance metrics [52]. Authors have described that
the large exciton binding energies lead to high brightness and, by the spectral overlap with
the biexcitonic emission, this can be used to affect the single-photon purity. They concluded
that small GaN QD single-photon emitters can play a significant role in future room
temperature applications [52]. Additionally, encouraging progress has been made in the
hybrid integration of solid-state SPSs based on InAs/GaAs quantum dots (QDs) [53].
However, to overcome a serious challenge in the scalable implementation of multiple
identical SPSs on silicon CMOS chips, the spectral and spatial randomness inherent in QDs
needs to be controlled. To overcome this challenge, a hybrid integration technique called
transfer printing based on a pick-and-place operation was introduced [53]. In this method, the
integration of desired QD SPSs in any position on the silicon CMOS chips is allowed.
Nevertheless, even in this scenario, to avoid interference with single photons different from
the sources, it is essential to have in situ fine tuning for perfect wavelength matching among
the integrated QD SPSs. Katsumi et al. [53] reported in situ wavelength tuning of QD SPSs
integrated on a CMOS silicon chip and in situ wavelength matching between two dissimilar
QD sources integrated on the same silicon chip had been demonstrated previously (Figure
11). In their experiments, optically driven heating pads were used to thermally tune the
emission wavelengths of the integrated QDs and, therefore, augment the QD SPSs. In their
investigations, the integration of all the necessary elements was performed using transfer
printing, which largely simplified the fabrication of the three-dimensional stack of
micro/nanophotonics structures. Their approach to employ the transfer printing method can
open the possibility for realizing large-scale QPICs that leverage CMOS technology [53].
Figure 11. Schematic of the investigated device structure. A QD SPS is placed above a glass-
cladded silicon waveguide. An optical heating pad is implemented on the marginal region of
the integrated SPS (inset: schematic of the device cross-section). Reprinted (adapted) with
permission from Ref. [53]. Copyright (2020) AIP Publishing.
Despite the excellent performance of QD-based quantum emitters, scalability of the
technology remains an open challenge. This is actually due to the natural growth of QDs at
random spatial positions. Both the natural and site-controlled localized QDs show
inhomogeneous spectral resonances spanning 2 to 10 MeV. Ollivier et al. [54] demonstrated
new techniques for identifying these optical transitions and discussed the physics that
determines the source characteristics. Finally, the remaining fabrication challenges of
identical sources on a large scale were outlined [54]. Other exciting areas that are promising
venues for integrating QD-based single-photon emitters into such quantum photonic circuits
have been introduced in [55,56].
Figure 12. Schematic presentation of carbon nanotube quantum emitter and its emission
wavelength band [57].
It should be noted that the underlying quantum decoherence resulted from exciton– bath
interaction, which led to coherence time (T 2), is the fundamental challenge in realizing
coherent SPEs. The coherence times (T2), which are typically much shorter than the
spontaneous emission (SE) lifetime (T 1), are far from the ideal Fourier transform limit of
T2/2T1 = 1. The possible solutions to overcome O-band emission limitations are the reduction
in phonon dephasing involved with cryogenic cooling and the enhancement of T 1 time via the
Purcell effect [57]. Luo et al. [59] indicated that SWCNT excitons coupled to plasmonic
nanocavity arrays reached deeply into the Purcell regime with Purcell factors (FP) up to FP =
180 (average FP = 57), Purcell-enhanced quantum yields of 62% (average 42%), and a
photon emission rate of 15 MHz into the first lens. Only one order of magnitude-enhanced
photophysical properties of every SWCNT were received due to the quasi-deterministic
cavity coupling [59]. It was demonstrated that a promising transform-limited single-photon
generation can be achieved using an ultranarrow exciton line width (18 µeV) which reached
the radiative lifetime limit [59]. Settele et al. [60] introduced a simple reaction protocol for
the creation of only one type of luminescent defect in polymer-sorted carbon nanotubes. In
comparison with the commonly obtained binding configurations, the mentioned defect
exhibits longer photoluminescence lifetimes. Their experiments confirmed the single-photon
emission at room temperature. The developed functionalization process can apply to other
polymer-wrapped nanotubes with further emissions in the near-infrared region [60]. Zheng et
al. [61] reported a novel chemical process involving interactions of photoexcited aromatic
compounds with SWCNT sidewalls. Due to irradiation of UV light of aqueous suspensions of
SWCNTs and exposure to organic aromatic compounds, fluorescent defects are formed in the
nanotubes at rates that depend on the aromatic ring substituents [61]. They found that the
generated dual fluorescent quantum defects in SWCNTs can provide emission lines? closer to
standard telecom wavelengths, advancing the prospects of applications as single-photon
sources in quantum information processing [61]. Berger and co-workers [62] reported that a
net spin can be carried out using the covalent functionalization of purified semiconducting
SWCNTs with stable organic radicals (perchlorotriphenylmethyl, PTM). Their results
confirmed the fact that the existence of the radical-enhanced intersystem crossing leads to an
increased triplet exciton population, which could provide access to elusive triplet manifold in
SWCNTs [62].
Figure 15. (a) Schematic sketch of the device structure with monolayer WSe2 over a step
(height h = 105 nm). The WSe2 flake is contacted by Ti/Au (5/200 nm) electrodes and
separated from the back-gate electrode by a 20 nm thick gate dielectric (Al2O3). (b) False-
color scanning electron image of the device (Scale bar, 5 µm). (c) Schematic band diagram of
a SQE photodiode for negative drain-source voltage (V DS). Following resonant optical
excitation, single electron-hole pairs are generated and dissociated at the junction, which
results in a PC [71].
In their experiments, the WSe2 flake is contacted by Ti/Au (5/200 nm) electrodes and
separated from the back-gate electrode by a 20 nm thick gate dielectric (Al 2O3). Figure 15b
shows a false-color scanning electron microscopic image of the sample. The band diagram of
SQE photodiodes for negative drain-source voltage (VDS) is schematically illustrated in
Figure 15c. Following resonant optical excitation, the photocurrent (PC) is generated by
dissociation of single electron–hole pairs at the junction. The single-photon nature of the
emission was demonstrated by the strong photon antibunching. The PC is highly dominated
by absorption at localized states, showing an exponential dependence with the applied
electric field [71]. Lu et al. [72] tried to bring about high-quality quantum light sources and
directly incorporated them into an AlN-based photonic integrated circuit platform (Figure
16).
They believed that the generated and directly integrated quantum emitters (QEs) in III-nitride
semiconductors are able to be used in different types of applications, such as optoelectronics,
high-voltage power transistors, and microwave amplifiers. They also believed that the
potential of high-quality QEs, monolithically integrated in a wide range of III-nitride device
technologies, results in new quantum device opportunities and industrial scalability. In Figure
16a, the scalable AlN-on-sapphire photonic integrated circuits with integrated quantum
emitters are shown. A wurtzite crystal structure of aluminum nitride (yellow: aluminum
atom, black: nitrogen atom) is illustrated in the black inset. Microscopic images of the
fabricated QE integrated waveguides and fiber edge coupling are shown in the blue inset. It
can be seen that the grating couplers are used for visual feedback [72]. Atomic force
microscopy images of a sample before and after annealing are presented in Figure 16b. After
annealing and slight coalescing of the AlN film, the maintenance of the hexagonal structure
of the nanocolumns can be seen. The close-up cross-section of the single-mode AlN-on-
sapphire waveguide can be found in Figure 16c [72]. A tunable hybrid device consisting of
lifetime-limited single emitters (line width ~40 MHz) and 2D materials at subwavelength
separation without degradation of the emission properties was reported by Schadler and co-
workers [73]. The tunability in the ultrabroadband range (>400 GHz) and fast modulation
(frequency ~100 MHz) of the emission energy were achieved by an integrated, ultracompact
tunable SPS (Figure 17). Figure 17a shows the schematic hybrid device. As can be found
from the figure, atomically thin layers of graphene and MoS 2, cover fluorescent molecules
embedded in a polyvinyl alcohol (PVA) film. The thickness of PVA is 300 nm and the
thickness of the SiO2 thin film is 285 nm. Red-shifted fluorescence of excited single
molecules (inset) is detected with a single-photon counting module (SPCM) [69]. An optical
micrograph, AFM topography, and DBT emission map for MoS 2 (left column) and bilayer
graphene (right column) devices are illustrated from the top to bottom of Figure 17b. The
fluorescence excitation spectrum of an ensemble of single molecules in an uncovered
nanocrystal at 3 K can be seen in the top panel of Figure 17c. Details of two emission peaks
with a Lorentzian line shape (solid line) can be observed in the bottom panel of Figure 17c.
The narrower peak shows an FWHM of 43 ± 7 MHz. Antibunching measurement of the
resonant excitation of a single peak, as shown in part c, is shown in Figure 17d [73].
Hexagonal boron nitride is another wide-bandgap van der Waals material that is considered
in this review. It has recently emerged as a promising platform for quantum photonic
experiments.
Figure 16. Quantum emitters in aluminum nitride integrated photonics. (a) Scalable AlN-on-
sapphire photonic integrated circuits with integrated quantum emitters. Black inset: Wurtzite
crystal structure of aluminum nitride (yellow: aluminum atom, black: nitrogen atom). Blue
inset: Microscope image of the fabricated QE-integrated waveguides, where the grating
couplers are used for visual feedback during fiber edge coupling. (b) Atomic force
microscopy of a sample before and after annealing. Cutout 1 indicates the hexagonal
structure of the nano-columns is maintained after annealing. Cutout 2 shows slight coalescing
of the AlN _lm columnar structure and improved orientation alignment to the c-axis,
indicating an improved crystallinity to the AlN _lm. (c) Close-up cross-section of the single-
mode AlN-on sapphire waveguide, which is 450 nm in width by 200 nm in height. The
quantum emitter is embedded within the AlN waveguide. Reprinted (adapted) with
permission from Ref. [72]. Copyright (2020) American Chemical Society.
Figure 17. Single molecules integrated with 2D materials. (a) Hybrid device schematic.
Atomically thin layers of graphene and MoS2 cover fluorescent molecules embedded in a
PVA film (hPVA = 300nm) on SiO2 (hSiO2 = 285 nm). Single molecules are resonantly excited
(inset) and their red-shifted fluorescence detected with a single-photon counting module
(SPCM). Electric fields are controlled by applying DC (V g) and AC (δVg) potentials to the Si+
+
back gate. (b) Top to bottom: optical micrograph, AFM topography, and DBT emission map
for MoS2 (left column) and bilayer graphene (right column) devices. White dashed lines
outline the flakes. Scale bars are 20 µm. (c) Top panel: fluorescence excitation spectrum of
an ensemble of single molecules in an uncovered nanocrystal at 3 K. Bottom panel: detail of
two emission peaks with Lorentzian line shape (solid line), the narrower peak shows a fwhm
of 43 ± 7 MHz. (d) Antibunching measurement for resonant excitation of a single peak as
shown in part c. The solid line is a fit to the data using a second-order correlation function.
Reprinted (adapted) with permission from Ref. [73]. Copyright (2019) American Chemical
Society.
Previously, the formation and localization of narrowband quantum emitters in large flakes
(up to tens of micrometers wide) of hexagonal boron nitride was studied by Choi et al. [74].
In their experiments, it was explained that electron irradiation or high-temperature annealing
can be used to activate as-grown hexagonal boron nitride emitters and ion implantation or
focused laser irradiation can be employed to increase the formation probability of emitters in
the as-grown material [74]. Interestingly, it was realized that the emitters are always localized
at the edges of the flakes, unlike most luminescent point defects in threedimensional
materials. The authors believed that their results constitute an important step in the roadmap
of deploying hexagonal boron nitride in nanophotonic applications [74]. Additionally, single-
photon emission from 2D hexagonal boron nitride (hBN) has been reported by others [75–
78]. In comparison with other SPEs, the brightness of hBN is in the range of MHz without
cavity enhancement, which is similar to what has been achieved previously in InAs QDs [79].
Stable and bright single-photon emitters (SPEs) which operate at room temperature have
emerged using color centers in two-dimensional hexagonal boron nitride (h-BN) [79].
Recently, Yim et al. [80] reported the selective formation of vacancy-based SPEs at
nanoscale wrinkles in h-BN. They showed that the optical dipole of SPEs preferentially
aligned to the wrinkle direction. Their density functional theory calculations confirmed that
in localizing vacancy-based SPE candidates, the wrinkle’s curvature and alignment of the
defect’s symmetry plane to the wrinkle direction play crucial roles [80]. The wrinkle-induced
generation of SPEs and their polarization alignment to the wrinkle direction were
experimentally confirmed by optical measurement methods. They concluded that a new route
to controlling the atomic position can be found in their results and the possible
crystallographic origin of the SPEs in h-BN was revealed by optical property measurements.
A microscopic image of the h-BN flake used in Yim et al. experiment is shown in Figure 18.
The recent advances in hBN quantum light emission compared with other 2D material-based
quantum sources and their performances were analyzed in [81]. In addition, state-of-the-art
fabrication techniques of stable single-photon emitters in the UV, visible, and near-IR
regions, their activation, characterization techniques, and photostability towards a wide range
of operating temperatures and harsh environments were discussed [81].
Figure 18. Microscopic image of the h-BN flake used in Yim et al.’s experiments. Reprinted
(adapted) with permission from Ref. [80]. Copyright (2020) American Chemical Society.
Using density functional theory, it has been predicted that the single-photon emission in UV
to IR regions can be obtained by defect structures in hBN [81]. In this study, emitting single
photons of different energies with unique applications in the field of quantum communication
and quantum photonic circuits was demonstrated. The schematic of three main quantum
emitters in hBN on Si/SiO2 substrate is represented in Figure 19. In this figure, boron and
nitrogen atoms in the h-BN monolayer are indicated by pink and gray colors [81].
Figure 19. Schematic representation of three main quantum emitter hosts in hBN on Si/SiO 2
substrate, emitting single photons of different energies and their unique applications [81]. The
NBVN defect (nitrogen vacancy and boron replaces nitrogen) supplied the single photons that
can emit the visible light and be used in quantum photonic circuits for quantum computing.
Additionally, VBO2 defect (boron vacancy with oxygen (yellow) atoms) can provide single
photons that can emit the near-IR light with potential for application in quantum
communication based on optical fiber.
The top view and side view of AA’ stacking can be found in Figure 20a,b. The top view and
side view of AB stacking can also be seen in Figure 20c,d. In Figure 20e,f, the direct and
indirect bandgaps of bulk h-BN and h-BN monolayers are, respectively, illustrated. The
general properties of monolayer, multilayer, and bulk hBN material are indicated in Figure
20g. Additionally, the Raman shifts (around values) for high-quality crystals are shown in
Figure 20g. In Figure 21a,b, the electronic structures of NBVN and VBO2 defects can be found.
Only spin-preserving transitions are assumed to experimentally determine the bandgaps.
Black and gray arrows indicate the occupied and unoccupied states [81].
In Figure 21c–e, a boron vacancy with two oxygen atoms (V BO2 defect) is shown in red and
boron and nitrogen atoms with dangling bonds passivated by hydrogen (white) are,
respectively, shown in green and grey colors [81]. Figure 21f shows the enhancement of
spontaneous emission (γsp/γsp0 ) due to defect coupling with gold nanospheres. The effect of
strain on the NBVN defect structure is presented in Figure 21g.
To transfer the 2D material from the growth substrate to the chip without contamination,
Glushkov et al. [82] grew a widely used 2D material (hexagonal boron nitride, hBN) on
silicon nitride chips directly, and performed the optical characterization of defects in the
intact as-grown material. In their investigation, the direct growth approach was compared
with the standard wet transfer method to confirm the clear advantages of the direct growth. It
was found that the method is easily extendable to other 2D materials. Direct growth of hBN
on silicon nitride photonic chips is shown in Figure 22. Figure 22a shows the furnace for
CVD growth of few-layer hBN with loaded silicon nitride substrates. A single 10 × 20 mm
chip with multiple silicon nitride waveguides, running horizontally across the whole chip, is
shown in Figure 22b. In Figure 22c, the optical micrograph of the zoomed-in region from (b)
is shown. A scanning electron microscopic (SEM) micrograph of a zoomed-in area next to
the imaging well (dashed rectangle in c) is presented in Figure 22d. An AFM image of the
directly grown few-layer hBN film on silicon nitride is shown in Figure 22e.
Figure 21. Simulated electronic structures of NBVN and VBO2 defects, schematic
representation of VBO2 defect in hBN monolayer, boron and nitrogen dangling bonds,
coupling of gold nanosphere to emitter in hBN multilayer flake, Strain directions and spectral
tuning of hBN quantum emitter. (a,b) Electronic structures of NBVN and VBO2 defect, in
which 1.95 eV transition (transition from a ground state at 1.95 eV to an excited state located
at 3.90 eV) and 1.85 eV transition (transition from a ground state at 0.98 eV to an excited
state located at 2.83 eV) were highlighted, consistent with experimental studies and Only
spin-preserving transitions are assumed and occupied and unoccupied states are represented
by black and grey arrows. (c–e) Schematic representation of VBO2 defect (Boron vacancy
with two oxygen atoms (red colour)), Boron (green) and Nitrogen (grey) dangling bonds with
hydrogen (white) passivated respectively. (f) Spontaneous emission enhancement (γsp/γsp0 )
due to defect coupling with gold nanospheres. (g) Effect of strain on NBVN defect structure
[81].
Figure 22. Direct growth of hBN on silicon nitride photonic chips. (a) Furnace for CVD
growth of few-layer hBN with loaded silicon nitride substrates. (b) Single 10 × 20 mm chip
with multiple silicon nitride waveguides, running horizontally across the whole chip. Scale
bar: 5 mm. (c) Optical micrograph of the zoomed-in region from b), showing a number of
imaging wells on waveguides. Scale bar: 100 µm. (d) Scanning electron microscope (SEM)
micrograph of a zoomed-in area next to the imaging well (dashed rectangle in c) after the
growth. Scale bar: 20 µm. (e) AFM image of the directly grown few-layer hBN film on
silicon nitride. Scale bar: 2 µm [82].
New insights on the various metrics of performance across multiple platforms of SPEs were
recently reviewed [83,84]. These reviews highlighted that the extraction of quantum light
from 2D materials is highly efficient due to the atomic thickness of 2D materials and their
surface dangling bond. Two-dimensional emitters in atomically hin host materials can easily
be accessed and be interfaced to judiciously designed electronic and photonic devices.
Quantum Spectroscopy:
Spectroscopic techniques employ light to interact with matter and thus probe
certain features of a sample to learn about its consistency or structure. Light is
electromagnetic radiation, a phenomenon exhibiting different energies, and dependent
on that energy, different molecular features can be probed. The basic principles of
interaction of electromagnetic radiation with matter are treated in this chapter. There is
no obvious logical dividing point to split the applications of electromagnetic radiation
into parts treated separately. The justification for the split presented in this text is
purely pragmatic and based on ‘common practice’. The applications considered in this
chapter use visible or UV light to probe consistency and conformational structure of
biological molecules. Usually, these methods are the first analytical procedures used by
a biochemical scientist. The applications covered in Chapter 13 present a higher level
of complexity in undertaking and are employed at a later stage in biochemical or
biophysical characterization.
An understanding of the properties of electromagnetic radiation and its
interaction with matter leads to an appreciation of the variety of types of spectra and,
consequently, different spectroscopic techniques and their applications to the solution
of biological problems.
Wavelength
M vectors
E vectors Direction of
propagation
UV/Vis Microwavespectroscopy
X-ray absorption IR/ Raman NMR
absorption ESR
1017 1016 1015 1014 1013 1012 1011 1010 109 108 Frequency in s–1
6 5 4 3 2
10 10 10 10 10 101 1 10–1 10–2 –1
Wavenumber in cm
7 6 5 4 3
10 10 10 10 10 102 101 1 10–1
Energy in J mol–1
Fig. 12.2 The electromagnetic spectrum and its usage for spectroscopic
methods.
a particle, albeit having a mass of zero. As a particle, it interacts with matter by
transferring its energy E: hc
E¼ ¼h ð12:1Þ l where h is the Planck constant (h =6.63 1034 Js) and is
the frequency of the radiation as introduced above.
When considering a diatomic molecule (see Fig. 12.3), rotational and
vibrational levels possess discrete energies that only merge into a continuum at very
high energy. Each electronic state of a molecule possesses its own set of rotational and
vibrational levels. Since the kind of schematics shown in Fig. 12.3 is rather complex,
the Jablonski diagram is used instead, where electronic and vibrational states are
schematically drawn as horizontal lines, and vertical lines depict possible transitions
(see Fig. 12.8 below).
In order for a transition to occur in the system, energy must be absorbed. The
energy change DE needed is defined in quantum terms by the difference in absolute
energies between the final and the starting state as DE¼Efinal – Estart ¼h.
Electrons in either atoms or molecules may be distributed between several
energy levels but principally reside in the lowest levels (ground state). In order for an
electron to be promoted to a higher level (excited state), energy must be put into the
system. If this energy E¼h is derived from electromagnetic radiation, this gives rise to
an absorption spectrum, and an electron is transferred from the electronic ground state
(S0) into the first electronic excited state (S1). The molecule will also be in an excited
vibrational and rotational state. Subsequent relaxation of the molecule into the
vibrational ground state of the first electronic excited state will occur. The electron can
then revert back to the electronic ground state. For non-fluorescent molecules, this is
accompanied by the emission of heat (DH).
m m
DH
v= 6
v= 5
v= 4
v= 3
v= 2
v= 1
Electronic ground state (S0)
Fig. 12.3 Energy diagram for a diatomic molecule exhibiting rotation, vibration
as well as an electronic structure. The distance between two masses m1 and m2
(nuclear displacement) is described as a Lennard–Jones potential curve with different
equilibrium distances (Re) for each electronic state. Energetically lower states always
have lower equilibrium distances. The vibrational levels (horizontal lines) are
superimposed on the electronic levels. Rotational levels are superimposed on the
vibrational levels and not shown for reasons of clarity.
12.1 Introduction
E
s*
p* Anti-binding
n Non-binding
p
s Binding
Fig. 12.4 Energy scheme for molecular orbitals (not to scale). Arrows indicate
possible electronic transitions. The length of the arrows indicates the energy required to
be put into the system in order to enable the transition. Black arrows depict transitions
possible with energies from the UV/Vis spectrum for some biological molecules. The
transitions shown by grey arrows require higher energies (e.g. X-rays).
The plot of absorption probability against wavelength is called absorption
spectrum. In the simpler case of single atoms (as opposed to multi-atom molecules),
electronic transitions lead to the occurrence of line spectra (see Section 12.7). Because
of the existence of more different kinds of energy levels, molecular spectra are usually
observed as band spectra (for example Fig. 12.7 below) which are molecule-specific
due to the unique vibration states.
A commonly used classification of absorption transitions uses the spin states of
electrons. Quantum mechanically, the electronic states of atoms and molecules are
described by orbitals which define the different states of electrons by two parameters: a
geometrical function defining the space and a probability function. The combination of
both functions describes the localisation of an electron.
Electrons in binding orbitals are usually paired with antiparallel spin orientation
(Fig. 12.8). The total spin S is calculated from the individual electron spins. The
multiplicity M is obtained by M¼ 2Sþ1. For paired electrons in one orbital this yields:
S ¼ spinðelectron 1Þþ spinðelectron 2Þ ¼ ðþ1=2Þþð1=2Þ ¼ 0
The multiplicity is thus M¼2 0 þ 1 ¼ 1. Such a state is thus called a singlet state
and denotated as ‘S’. Usually, the ground state of a molecule is a singlet state, S0.
In case the spins of both electrons are oriented in a parallel fashion, the resulting
state is characterised by a total spin of S¼1, and a multiplicity of M=3. Such a state is
called a triplet state and usually exists only as one of the excited states of a molecule,
e.g. T1.
According to quantum mechanical transition rules, the multiplicity M and the
total spin S must not change during a transition. Thus, the S0!S1 transition is allowed
and possesses a high transition probability. In contrast, the S0!T1 is not allowed and
has a small transition probability. Note that the transition probability is proportional to
the intensity of the respective absorption bands.
Most biologically relevant molecules possess more than two atoms and,
therefore, the energy diagrams become more complex than the ones shown in Fig. 12.3.
Different orbitals combine to yield molecular orbitals that generally fall into one of five
different classes (Fig. 12.4): s orbitals combine to the binding s and the antibinding s*
orbitals. Some p orbitals combine to the binding p and the anti-binding p* orbitals.
Other p orbitals combine to form non-binding n orbitals. The population of binding
orbitals strengthens a chemical bond, and, vice versa, the population of anti-binding
orbitals weakens a chemical bond.
12.1.3 Lasers
Laser is an acronym for light amplification by stimulated emission of radiation.
ATPase assay Coupled enzyme assay with ATPase, pyruvate NADH: 340
kinase, lactate dehydrogenase:
ATP ! ADP (consumes ATP)
phosphoenolpyruvate!pyruvate(consumesADP)
pyruvate ! lactate (consumes NADH)
12.2.1 Chromophores in proteins
The electronic transitions of the peptide bond occur in the far UV. The intense
peak at 190 nm, and the weaker one at 210–220 nm is due to the p!p* and n!p*
transitions. A number of amino acids (Asp, Glu, Asn, Gln, Arg and His) have weak
electronic transitions at around 210 nm. Usually, these cannot be observed in proteins
because they are masked by the more intense peptide bond absorption. The most useful
range for proteins is above 230 nm, where there are absorptions from aromatic side
chains. While a very weak absorption maximum of phenylalanine occurs at 257 nm,
tyrosine and tryptophan dominate the typical protein spectrum with their absorption
maxima at 274 nm and 280 nm, respectively (Fig. 12.5). In praxi, the presence of these
two aromatic side chains gives rise to a band at 278 nm. Cystine (Cys2) possesses a
weak absorption maximum of similar strength as phenylalanine at 250 nm. This band
can play a role in rare cases in protein optical activity or protein fluorescence.
Proteins that contain prosthetic groups (e.g. haem, flavin, carotenoid) and some
metal–protein complexes, may have strong absorption bands in the UV/Vis range.
These bands are usually sensitive to local environment and can be used for physical
studies of enzyme action. Carotenoids, for instance, are a large class of red, yellow and
orange plant pigments composed of long carbon chains with many conjugated double
bonds. They contain three maxima in the visible region of the electromagnetic spectrum
(420 nm, 450 nm, 480 nm).
Porphyrins are the prosthetic groups of haemoglobin, myoglobin, catalase and
cytochromes. Electron delocalisation extends throughout the cyclic tetrapyrrole ring of
porphyrins and gives rise to an intense transition at 400 nm called the Soret band. The
spectrum of haemoglobin is very sensitive to changes in the iron-bound ligand.
These changes can be used for structure–function studies of haem proteins.
Absorbance
Fig. 12.5 The presence of larger aggregates in biological samples gives rise to
Rayleigh scatter visible by a considerable slope in the region from 500 to 350 nm. The
dashed line shows the correction to be applied to spectra with Rayleigh scatter which
increases with l4. Practically, linear extrapolation of the region from 500 to 350 nm is
performed to correct for the scatter. The corrected absorbance is indicated by the
double arrow.
Molecules such as FAD (flavin adenine dinucleotide), NADH and NADþ are
important coenzymes of proteins involved in electron transfer reactions (RedOx
reactions). They can be conveniently assayed by using their UV/Vis absorption: 438
nm (FAD), 340 nm (NADH) and 260 nm (NADþ).
Chromophores in genetic material
The absorption of UV light by nucleic acids arises from n!p* and p!p*
transitions of the purine (adenine, guanine) and pyrimidine (cytosine, thymine, uracil)
bases that occur between 260 nm and 275 nm. The absorption spectra of the bases in
polymers are sensitive to pH and greatly influenced by electronic interactions between
bases.
12.2.2 Principles
Quantification of light absorption
The chance for a photon to be absorbed by matter is given by an extinction
coefficient which itself is dependent on the wavelength l of the photon. If light with the
intensity I0 passes through a sample with appropriate transparency and the path length
(thickness) d, the intensity I drops along the pathway in an exponential manner. The
characteristic absorption parameter for the sample is the extinction coefficient a,
yielding the correlation I= I0 ead. The ratio T= I/I0 is called transmission.
Biochemical samples usually comprise aqueous solutions, where the substance
of interest is present at a molar concentration c. Algebraic transformation of the
exponential correlation into an expression based on the decadic logarithm yields the
law of Beer–Lambert:
I0 1
lg ¼ lg ¼ e c d ¼ A ð12:2Þ I T
where[d]¼1cm,[c]¼1moldm3,and[e]¼ 1dm3 mol1 cm1.e isthemolarabsorption
coefficient (also molar extinction coefficient) (a¼ 2.303 ce). A is the absorbance of the
sample, which is displayed on the spectrophotometer.
The Beer–Lambert law is valid for low concentrations only. Higher
concentrations might lead to association of molecules and therefore cause deviations
from the ideal behaviour. Absorbance and extinction coefficients are additive
parameters, which complicates determination of concentrations in samples with more
than one absorbing species. Note that in dispersive samples or suspensions scattering
effects increase the absorbance, since the scattered light is not reaching the detector for
readout. The absorbance recorded by the spectrophotometer is thus overestimated and
needs to be corrected (Fig. 12.5).
Deviations from the Beer–Lambert law
According to the Beer–Lambert law, absorbance is linearly proportional to the
concentration of chromophores. This might not be the case any more in samples with
high absorbance. Every spectrophotometer has a certain amount of stray light, which is
light received at the detector but not anticipated in the spectral band isolated by the
monochromator. In order to obtain reasonable signal-to-noise ratios, the intensity of
light at the chosen wavelength (Il) should be 10 times higher than the intensity of the
stray light (Istray).
Ifthestraylightgainsinintensity,theeffectsmeasuredatthedetectorhavenothingorlittle to do
with chromophore concentration. Secondly, molecular events might lead to deviations
from the Beer–Lambert law. For instance, chromophores might dimerise at high
concentrations and, as a result, might possess different spectroscopic parameters.
Absorption or light scattering – optical density
In some applications, for example measurement of turbidity of cell cultures
(determination of biomass concentration), it is not the absorption but the scattering of
light (see Section 12.6) that is actually measured with a spectrophotometer. Extremely
turbid samples like bacterial cultures do not absorb the incoming light. Instead, the light
is scattered and thus, the spectrometer will record an apparent absorbance (sometimes
also called attenuance). In this case, the observed parameter is called optical density
(OD). Instruments specifically designed to measure turbid samples are nephelometers
or Klett meters; however, most biochemical laboratories use the general UV/Vis
spectrometer for determination of optical densities of cell cultures.
Factors affecting UV/Vis absorption
Biochemical samples are usually buffered aqueous solutions, which has two
major advantages. Firstly, proteins and peptides are comfortable in water as a solvent,
which is also the ‘native’ solvent. Secondly, in the wavelength interval of UV/Vis
(700–200 nm) the water spectrum does not show any absorption bands and thus acts as
a silent component of the sample.
The absorption spectrum of a chromophore is only partly determined by its
chemical structure. The environment also affects the observed spectrum, which mainly
can be described by three parameters:
• protonation/deprotonation (pH, RedOx);
• solvent polarity (dielectric constant of the solvent); and
• orientation effects.
Vice versa, the immediate environment of chromophores can be probed by
assessing their absorption, which makes chromophores ideal reporter molecules for
environmental factors. Four effects, two each for wavelength and absorption changes,
have to be considered:
• a wavelength shift to higher values is called red shift or bathochromic
effect;
• similarly, a shift to lower wavelengths is called blue shift or
hypsochromic effect;
• an increase in absorption is called hyperchromicity (‘more colour’),
• while a decrease in absorption is called hypochromicity (‘less colour’).
Protonation/deprotonation arises either from changes in pH or
oxidation/reduction reactions, which makes chromophores pH- and RedOx-sensitive
reporters. As a rule of thumb, lmax and e increase, i.e. the sample displays a batho- and
hyperchromic shift, if a titratable group becomes charged.
Furthermore, solvent polarity affects the difference between the ground and
excited states. Generally, when shifting to a less polar environment one observes a
batho- and hyperchromic effect. Conversely, a solvent with higher polarity elicits a
hypso- and hypochromic effect.
Lastly, orientation effects, such as an increase in order of nucleic acids from
singlestranded to double-stranded DNA, lead to different absorption behaviour. A
sample of free nucleotides exhibits a higher absorption than a sample with identical
amounts of nucleotides but assembled into a single-stranded polynucleotide.
Accordingly, doublestranded polynucleotides exhibit an even smaller absorption than
two single-stranded polynucleotides. This phenomenon is called the hypochromicity of
polynucleotides. The increased exposure (and thus stronger absorption) of the
individual nucleotides in the less ordered states provides a simplified explanation for
this behaviour.
12.2.3 Instrumentation
UV/Vis spectrophotometers are usually dual-beam spectrometers where the first
channel contains the sample and the second channel holds the control (buffer) for
correction.
Alternatively, one can record the control spectrum first and use this as internal
reference for the sample spectrum. The latter approach has become very popular as
many spectrometers in the laboratories are computer-controlled, and baseline correction
can be carried out using the software by simply subtracting the control from the sample
spectrum.
The light source is a tungsten filament bulb for the visible part of the spectrum,
and a deuterium bulb for the UV region. Since the emitted light consists of many
different wavelengths, a monochromator, consisting of either a prism or a rotating
metal grid of high precision called grating, is placed between the light source and the
sample. Wavelength selection can also be achieved by using coloured filters as
monochromators that absorb all but a certain limited range of wavelengths. This limited
range is called the bandwidth of the filter. Filter-based wavelength selection is used in
colorimetry, a method with moderate accuracy, but best suited for specific colorimetric
assays where only certain wavelengths are of interest. If wavelengths are selected by
prisms or gratings, the technique is called spectrophotometry (Fig. 12.6).
Beam
Mirrors Grating selector
Sample
Slit Slit cuvette
Vis light
Detector
Computer
Prism
UV light
Half-mirrors Mirror
Reference
cuvette
Mirror Mirror
Absorbance
0
240 260 280 300 320
Absorbance
Fig. 12.7 Top: Absolute spectra of ubiquinone (solid curve)and ubiquinol (dotted curve).
Bottom: Difference spectrum.
Difference spectra have three distinct features as compared to absolute spectra:
• difference spectra may contain negative absorbance values;
• absorption maxima and minima may be displaced and the extinction coefficients are
different from those in peaks of absolute spectra;
• there are points of zero absorbance, usually accompanied by a change of sign of the
absorbance values. These points are observed at wavelengths where both species of related
molecules exhibit identical absorbances (isosbestic points), and which may be used for
checking for the presence of interfering substances.
Common applications for difference UV spectroscopy include the determination of the
number of aromatic amino acids exposed to solvent, detection of conformational changes
occurring in proteins, detection of aromatic amino acids in active sites of enzymes, and
monitoring of reactions involving ‘catalytic’ chromophores (prosthetic groups, coenzymes).
Derivative spectroscopy
Another way to resolve small changes in absorption spectra that otherwise would remain
invisible is the usage of derivative spectroscopy. Here, the absolute absorption spectrum of a
sample is differentiated and the differential dxA/dlx plotted against the wavelength. Since the
algebraic relationship between A and l is unknown, differentiation is carried out by numerical
methods using computer software. The usefulness of this approach depends on the individual
problem. Examples of successful applications include the binding of a monoclonal antibody
to its antigen with second-order derivatives and the quantification of tryptophan and tyrosine
residues in proteins using fourth-order derivatives.
Solvent perturbation
As we have mentioned above, aromatic amino acids are the main chromophores of proteins in
the UV region of the electromagnetic spectrum. Furthermore, the UV absorption of
chromophores depends largely on the polarity in its immediate environment. A change in the
polarity of the solvent changes the UV spectrum of a protein by bathochromic or
hypsochromic effects without changing its conformation. This phenomenon is called solvent
perturbation and can be used to probe the surface of a protein molecule. In order to be
accessible to the solvent, the chromophore has to be accessible on the protein surface.
Practically, solvents like dimethyl-sulfoxide, dioxane, glycerol, mannitol, sucrose and
polyethylene glycol are used for solvent perturbation experiments, because they are miscible
with water. The method of solvent perturbation is most commonly used for determination of
the number of aromatic residues that are exposed to solvent.
Spectrophotometric and colorimetric assays
For biochemical assays testing for time- or concentration-dependent responses of systems, an
appropriate read-out is required that is coupled tothe progress of the reaction (reaction
coordinate). Therefore, the biophysical parameter being monitored (read-out) needs to be
coupled to the biochemical parameter under investigation. Frequently, the monitored
parameter is the absorbance of a system at a given wavelength which is
monitoredthroughoutthecourseoftheexperiment.Preferably,oneshouldtrytomonitor the
changing species directly (e.g. protein absorption, starting product or generated product of a
reaction), but in many cases this is not possible and a secondary reaction has to be usedto
generatean appropriate signal formonitoring.A common applicationof the latter approach is
the determination of protein concentration by Lowry or Bradford assays, where a secondary
reaction is used to colour the protein. The more intense the colour, the more protein is
present. These assays are called colorimetric assays and a number of commonly used ones are
listed in Table 12.1.
12.3 FLUORESCENCE SPECTROSCOPY
12.3.1 Principles
Fluorescence is an emission phenomenon where an energy transition from a higher to a lower
state is accompanied by radiation. Only molecules in their excited forms are able to emit
fluorescence; thus, they have to be brought into a state of higher energy prior to the emission
phenomenon.
We have already seen in Section 12.1.2 that molecules possess discrete states of energy.
Potential energy levels of molecules have been depicted by different Lennard– Jones
potential curves with overlaid vibrational (and rotational) states (Fig. 12.3). Such diagrams
can be abstracted further to yield Jablonski diagrams (Fig. 12.8).
Fig. 12.8 Jablonski diagram. Shown are the electronic ground state (S0), two excited singlet
states (S1, S2) and a triplet state (T1). Vibrational levels (v) are only illustrated exemplarily.
Solid vertical lines indicate radiative transitions, dotted lines show non-radiative transitions.
The inset shows the relationship between electron configurations, total spin number S and
multiplicity M.
In these diagrams, energy transitions are indicated by vertical lines. Not all transitions are
possible; allowed transitions are defined by the selection rules of quantum mechanics. A
molecule in its electronic and vibrational ground state (S0v0) can absorb photons matching
the energy difference of its various discrete states. The required photon energy has to be
higher than that required to reach the vibrational ground state of the first electronic excited
state (S1v0). The excess energy is absorbed as vibrational energy (v> 0), and quickly
dissipated as heat by collision with solvent molecules. The molecule thus returns to the
vibrational ground state (S1v0). These relaxation processes are non-radiating transitions from
one energetic state to another with lower energy, and are called internal conversion (IC).
From the lowest level of the first electronic excited state, the molecule returns to the ground
state (S0) either by emitting light (fluorescence) or by a non-radiative transition. Upon
radiative transition, the molecule can end up in any of the vibrational states of the electronic
ground state (as per quantum mechanical rules).
If the vibrational levels of the ground state overlap with those of the electronic excited state,
the molecule will not emit fluorescence, but rather revert to the ground state by non-radiative
internal conversion. This is the most common way for excitation energy to be dissipated and
is why fluorescent molecules are rather rare. Most molecules are flexible and thus have very
high vibrational levels in the ground state. Indeed, most fluorescent molecules possess fairly
rigid aromatic rings or ring systems. The fluorescent group in a molecule is called a
fluorophore.
Since radiative energy is lost in fluorescence as compared to the absorption, the fluorescent
light is always at a longer wavelength than the exciting light (Stokes shift). The emitted
radiation appears as band spectrum, because there are many closely related wavelength
values dependent on the vibrational and rotational energy levels attained. The fluorescence
spectrum of a molecule is independent of the wavelength of the exciting radiation and has a
mirror image relationship with the absorption spectrum. The probability of the transition from
the electronic excited to the ground state is proportional to the intensity of the emitted light.
An associated phenomenon in this context is phosphorescence which arises from a transition
from a triplet state(T1) to the electronic(singlet) ground state(S0). The molecule gets into the
triplet state from an electronic excited singlet state by a process called intersystem crossing
(ISC). The transition from singlet to triplet is quantum-mechanically not allowed and thus
only happens with low probability in certain molecules where the electronic structure is
favourable. Such molecules usually contain heavy atoms. The rate constants for
phosphorescence are much longer and phosphorescence thus happens with a long delay and
persists even when the exciting energy is no longer applied.
The fluorescence properties of a molecule are determined by properties of the molecule itself
(internal factors), as well as the environment of the protein (external factors). The
fluorescence intensity emitted by a molecule is dependent on the lifetime of the excited state.
The transition from the excited to the ground state can be treated like a decay process of first
order, i.e. the number of molecules in the excited state decreases exponentially with time. In
analogy to kinetics, the exponential coefficient kr is called rate constant and is the reciprocal
of the lifetime: r = kr1. The lifetime is the time it takes to reduce the number of fluorescence
emitting molecules to N0/e, and is proportional to l3.
The effective lifetime of excited molecules, however, differs from the fluorescence lifetime r
since other, non-radiative processes also affect the number of molecules in the excited state.
is dependent on all processes that cause relaxation: fluorescence emission, internal
conversion, quenching, fluorescence resonance energy transfer, reactions of the excited state
and intersystem crossing.
The ratio of photons emitted and photons absorbed by a fluorophore is called quantum yield
F (equation 12.3). It equals the ratio of the rate constant for fluorescence emission kr and the
sum of the rate constants for all six processes mentioned above.
¼ NððemÞÞ ¼ kr ¼ þ þ þ kr þ ð Þþ ¼ ð12:3Þ
N abs k kr kIC kISC kreaction kQc Q kFRETr
The quantum yield is a dimensionless quantity, and, most importantly, the only absolute
measure of fluorescence of a molecule. Measuring the quantum yield is a difficult process
and requires comparison with a fluorophore of known quantum yield. In biochemical
applications, this measurement is rarely done. Most commonly, the fluorescence emissions of
two or more related samples are compared and their relative differences analysed.
12.3.2 Instrumentation
Fluorescence spectroscopy works most accurately at very low concentrations of emitting
fluorophores. UV/Vis spectroscopy, in contrast, is least accurate at such
Slit 45˚
Half Sample
mirror cuvette
Xenon
lamp
90˚
Grating
Grating
Slit
Photomultiplier
Reference detector Sample detector
Computer
Fig. 12.9 Schematics of a spectrofluorimeter with ‘T’ geometry (90). Optical paths are shown
as green lines. Inset: Geometry of front-face illumination.
low concentrations. One major factor adding to the high sensitivity of fluorescence
applications is the spectral selectivity. Due to the Stokes shift, the wavelength of the emitted
light is different from that of the exciting light. Another feature makes use of the fact that
fluorescence is emitted in all directions. By placing the detector perpendicular to the
excitation pathway, the background of the incident beam is reduced.
The schematics of a typical spectrofluorimeter are shown in Fig. 12.9. Two monochromators
are used, one for tuning the wavelength of the exciting beam and a second one for analysis of
the fluorescence emission. Due to the emitted light always having a lower energy than the
exciting light, the wavelength of the excitation monochromator is set at a lower wavelength
than the emission monochromator. The better fluorescence spectrometers in laboratories have
a photon-counting detector yielding very high sensitivity. Temperature control is required for
accurate work as the emission intensity of a fluorophore is dependent on the temperature of
the solution.
Two geometries are possible for the measurement, with the 90 arrangement most commonly
used. Pre- and post-filter effects can arise owing to absorption of light prior to reaching the
fluorophore and the reduction of emitted radiation. These phenomena are also called inner
filter effects and are more evident in solutions with high concentrations. As a rough guide,
the absorption of a solution to be used for fluorescence experiments should be less than 0.05.
The use of microcuvettes containing less material can also be useful. Alternatively, the front-
face illumination geometry (Fig. 12.9 inset) can be used which obviates the inner filter effect.
Also, while the 90 geometry requires cuvettes with two neighbouring faces being clear
(usually, fluorescence cuvettes have four clear faces), the front-face illumination technique
requires only one clear face, as excitation and emission occur at the same face. However,
front-face illumination is less sensitive than the 90 illumination.
12.3.3 Applications
There are many and highly varied applications for fluorescence despite the fact that relatively
few compounds exhibit the phenomenon. The effects of pH, solvent composition and the
polarisation of fluorescence may all contribute to structural elucidation. Measurement of
fluorescence lifetimes can be used to assess rotation correlation coefficients and thus particle
sizes. Non-fluorescent compounds are often labelled with fluorescent probes to enable
monitoring of molecular events. This is termed extrinsic fluorescence as distinct from
intrinsic fluorescence where the native compound exhibits the property. Some fluorescent
dyes are sensitive to the presence of metal ions and can thus be used to track changes of these
ions in in vitro samples, as well as whole cells.
Since fluorescence spectrometers have two monochromators, one for tuning the excitation
wavelength and one for analysing the emission wavelength of the fluorophore, one can
measure two types of spectra: excitation and emission spectra. For fluorescence excitation
spectrum measurement, one sets the emission monochromator at a fixed wavelength (lem)
and scans a range of excitation wavelengths which are then recorded as ordinate (x-
coordinate) of the excitation spectrum; the fluorescence emission at lem is plotted as abscissa.
Measurement of emission spectra is achieved by setting a fixed excitation wavelength (lexc)
and scanning a wavelength range with the emission monochromator. To yield a spectrum, the
emission wavelength lem is recorded as ordinate and the emission intensity at lem is plotted
as abscissa.
Intrinsic protein fluorescence
Proteins possess three intrinsic fluorophores: tryptophan, tyrosine and phenylalanine,
although the latter has a very low quantum yield and its contribution to protein fluorescence
emission is thus negligible. Of the remaining two residues, tyrosine has the lower quantum
yield and its fluorescence emission is almost entirely quenched when it becomes ionised, or is
located near an amino or carboxyl group, or a tryptophan residue. Intrinsic protein
fluorescence is thus usually determined by tryptophan fluorescence which can be selectively
excited at 295–305nm. Excitation at 280nm excites tyrosine and tryptophan fluorescence and
the resulting spectra might therefore contain contributions from both types of residues.
The main application for intrinsic protein fluorescence aims at conformational monitoring.
We have already mentioned that the fluorescence properties of a fluorophore depend
significantly on environmental factors, including solvent, pH, possible quenchers,
neighbouring groups, etc.
A number of empirical rules can be applied to interpret protein fluorescence spectra:
• As a fluorophore moves into an environment with less polarity, its emission spectrum
exhibits a hypsochromic shift (lmax moves to shorter wavelengths) and the intensity at lmax
increases.
• Fluorophores in a polar environment show a decrease in quantum yield with
increasing temperature. In a non-polar environment, there is little change.
• Tryptophan fluorescence is quenched by neighbouring protonated acidic groups.
Fluorescence emission in a.u. Fluorescence emission in a.u.
(a) (b)
350 250
300
200
250
200 150
150 100
100
50
50
0 0
200 250 300 350 400 450 500 200 250 300 350 400 450 500
l (nm) l (nm)
Fig. 12.10 Comparison of fluorescence excitation and emission spectra can yield insights into
internal quenching. Excitation spectra with emission wavelength 340 nm are shown in dark
green. Emission spectra with excitation wavelength 295 nm are shown in light green;
emission spectra with excitation wavelength 280 nm are grey. (a) PDase homologue
(Escherichia coli). (b) CPDase (Arabidopsis thaliana); in this protein, the fluorophores are
located in close proximity to each other which leads to the effect of intrinsic quenching, as
obvious from the lower intensity of the emission spectrum as compared to the excitation
spectrum.
When interpreting effects observed in fluorescence experiments, one has to consider carefully
all possible molecular events. For example, a compound added to a protein solution can cause
quenching of tryptophan fluorescence. This could come about by binding of the compound at
a site close to the tryptophan (i.e. the residue is
surfaceexposedtoacertaindegree),orduetoaconformationalchangeinducedbythecompound.
The comparison of protein fluorescence excitation and emission spectra can yield insights
into the location of fluorophores. The close spatial arrangement of fluorophores within a
protein can lead to quenching of fluorescence emission; this might be seen by the lower
intensity of the emission spectrum when compared to the excitation spectrum (Fig. 12.10).
Extrinsic fluorescence
Frequently, molecules of interest for biochemical studies are non-fluorescent. In many of
these cases, an external fluorophore can be introduced into the system by chemical coupling
or non-covalent binding. Some examples of commonly used external fluorophores are shown
in Fig. 12.11. Three criteria must be met by fluorophores in this context. Firstly, it must not
affect the mechanistic properties of the system under investigation. Secondly, its fluorescence
emission needs to be sensitive to environmental conditions in order to enable monitoring of
the molecular events. And lastly, the fluorophore must be tightly bound at a unique location.
A common non-conjugating extrinsic chromophore for proteins is 1-anilino-8naphthalene
sulphonate (ANS) which emits only weak fluorescence in polar environment, i.e. in aqueous
solution. However, in non-polar environment, e.g. when bound to hydrophobic patches on
proteins, its fluorescence emission is significantly increased and the spectrum shows a
hypsochromic shift; lmax shifts from 475nm to 450nm. ANS
Fig. 12.11 Structures of some extrinsic fluorophores. Fura-2 is a fluorescent chelator for
divalent and higher valent metal ions (Ca2þ, Ba2þ, Sr2þ, Pb2þ, La3þ, Mn2þ, Ni2þ, Cd2þ).
is thus a valuable tool for assessment of the degree of non-polarity. It can also be used in
competition assays to monitor binding of ligands and prosthetic groups.
Reagents such as fluorescamine, o-phthalaldehyde or 6-aminoquinolyl-N-
hydroxysuccinimidyl carbamate have been very popular conjugating agents used to derivatise
amino acids for analysis (see Section 8.4.2). o-Phthalaldehyde, for example, is a non-
fluorescent compound that reacts with primary amines and b-mercaptoethanol to yield a
highly sensitive fluorophore.
Metal-chelating compounds with fluorescent properties are useful tools for a variety of
assays, including monitoring of metal homeostasis in cells. Widely used probes for calcium
are the chelators Fura-2, Indo-1 and Quin-1. Since the chemistry of such compounds is based
on metal chelation, cross-reactivity of the probes with other metal ions is possible.
The intrinsic fluorescence of nucleic acids is very weak and the required excitation
wavelengthsaretoo farintheUVregion tobe usefulfor practical applications. Numerous
extrinsic fluorescent probes spontaneously bind to DNA and display enhanced emission.
While in earlier days ethidium bromide was one of the most widely used dyes for this
application,ithasnowadaysbeenreplacedbySYBRGreen,asthelatterprobeposesfewer hazards
for health and environment and has no teratogenic properties like ethidium bromide. These
probes bind DNA by intercalation of the planar aromatic ring systems between the base pairs
of double-helical DNA. Their fluorescence emission in water is very weak and increases
about 30-fold upon binding to DNA.
Quenching
In Section 12.3.1, we have seen that the quantum yield of a fluorophore is dependent on
several internal and external factors. One of the external factors with practical implications is
the presence of a quencher. A quencher molecule decreases the quantum yield of a
fluorophore by non-radiating processes. The absorption (excitation) process of the
fluorophore is not altered by the presence of a quencher. However, the energy of the excited
state is transferred onto the quenching molecules. Two kinds of quenching processes can be
distinguished:
• dynamic quenching which occurs by collision between the fluorophore in its excited
state and the quencher; and
• static quenching whereby the quencher forms a complex with the fluorophore. The
complex has a different electronic structure compared to the fluorophore alone and returns
from the excited state to the ground state by non-radiating processes.
It follows intuitively that the efficacy of both processes is dependent on the concentration of
quencher molecules. The mathematical treatment for each process is different, because of two
different chemical mechanisms. Interestingly, in both cases the degree of quenching,
expressed as I0 I1, is directly proportional to the quencher concentration. For collisional
(dynamic) quenching, the resulting equation has been named the Stern– Volmer equation
(equation 12.4).
I0
I 1 ¼ kQcQ0 ð12:4Þ
I0
I 1 ¼ KacQ ð12:5Þ
The Stern–Volmer equation relates the degree of quenching (expressed as I0 I1) to the molar
concentration of the quencher cQ, the lifetime of the fluorophore 0, and the rate constant of
the quenching process kQ. In case of static quenching (equation 12.5), I0 I1 is related to the
equilibrium constant Ka that describes the formation of the complex between the excited
fluorophore and the quencher, and the concentration of the quencher. Importantly, a plot of I0
I1 versus cQ yields for both quenching processes a linear graph with a y-intercept of 1.
Thus, fluorescence data obtained by intensity measurements alone cannot distinguish
between static or collisional quenching. The measurement of fluorescence lifetimes or the
temperature/viscosity dependence of quenching can be used to determine the kind of
quenching process. It should be added, that both processes can also occur simultaneously in
the same system. The fact that static quenching is due to complex formation between the
fluorophore and the quencher makes this phenomenon an attractive assay for binding of a
ligand to a protein. In the simplest case, the fluorescence emission being monitored is the
intrinsic fluorescence of the protein. While this is a very convenient titration assay when
validated for an individual protein–ligand system, one has to be careful when testing
unknown pairs, because the same decrease in intensity can occur by collisional quenching.
Highly effective quenchers for fluorescence emission are oxygen, as well as the iodide ion.
Usage of these quenchers allows surface mapping of biological macromolecules. For
instance, iodide can be used to determine whether tryptophan residues are exposed to solvent.
Fluorescence resonance energy transfer (FRET)
Fluorescence resonance energy transfer (FRET) was first described by Fo¨rster in 1948. The
process can be explained in terms of quantum mechanics by a non-radiative energy transfer
from a donor to an acceptor chromophore. The requirements for this process are a reasonable
overlap of emission and excitation spectra of donor and acceptor chromophores, close spatial
vicinity of both chromophores (10–100 A˚ ), and an almost parallel arrangement of their
transition dipoles. Of great practical importance is the correlation
1
FRET / R 60 ð12:6Þ
showing that the FRET effect is inversely proportional to the distance between donor and
acceptor chromophores, R0.
The FRET effect is particularly suitable for biological applications, since distances of 10–100
A˚ are in the order of the dimensions of biological macromolecules. Furthermore,
therelationbetweenFRETandthedistanceallowsformeasurementofmoleculardistances and
makes this application a kind of ‘spectroscopic ruler’. If a process exhibits changes in
molecular distances, FRET can also be used to monitor the molecular mechanisms.
The high specificity of the FRET signal allows for monitoring of molecular interactions and
conformational changes with high spatial (1–10nm) and temporal resolution (<1ns).
Especially the possibility of localising and monitoring cellular structures and proteins in
physiological environments makes this method very attractive. The effects can be observed
even at low concentrations (as low as single molecules), in different environments (different
solvents, including living cells), and observations may be done in real time.
In most cases, different chromophores are used as donor and acceptor, presenting two
possibilities to record FRET: either as donor-stimulated fluorescence emission of the acceptor
or as fluorescence quenching of the donor by the acceptor. However, the same chromophore
may be used as donor and acceptor simultaneously; in this case, the depolarisation of
fluorescence is the observed parameter. Since non-FRET stimulated fluorescence emission by
the acceptor can result in undesirable background fluorescence, a common approach is usage
of non-fluorescent acceptor chromophores.
FRET-based assays may be used to elucidate the effects of new substrates for different
enzymes or putative agonists in a quick and quantitative manner. Furthermore, FRET
detection might be used in high-throughput screenings (see Section 17.3.2 and 18.2.3), which
makes it very attractive for drug development.
Bioluminescence Resonance Energy Transfer (BRET)
Bioluminescence resonance energy transfer (BRET) uses the FRET effect with native
fluorescent or luminescent proteins as chromophores. The phenomenon is observed naturally
for example with the sea pansy Renilla reniformis. It contains the enzyme luciferase, which
oxidises luciferin (coelenterazin) by simultaneously emitting light at lexc= 480 nm. This light
directly excites green fluorescent protein (GFP), which, in turn, emits fluorescence at lem=
509 nm.
Fluorescence labelling of proteins by other proteins presents a useful approach to study
various processes in vivo. Labelling can be done at the genetic level by generating fusion
proteins. Monitoring of protein expression by GFP is an established technique and further
development of ‘living colours’ will lead to promising new tools.
While nucleic acids have been the main players in the genomic era, the postgenomic/
proteomic era focusses on gene products, the proteins. New proteins are being discovered and
characterised, others are already used within biotechnological processes. In particular for
classification and evaluation of enzymes and receptors, reaction systems can be designed
such that the reaction of interest is detectable quantitatively using FRET donor and acceptor
pairs.
For instance, detection methods for protease activity can be developed based on BRET
applications. A protease substrate is fused to a GFP variant on the N-terminal side and
dsRED on the C-terminal side. The latter protein is a red fluorescing FRET acceptor and the
GFP variant acts as a FRET donor. Once the substrate is cleaved by a protease, the FRET
effect is abolished. This is used to directly monitor protease activity. With a combination of
FRET analysis and two-photon excitation spectroscopy it is also possible to carry out a
kinetic analysis.
A similar idea is used to label human insulin receptor (see Section 17.4.4) in order to
quantitatively assess its activity. Insulin receptor is a glycoprotein with two a and two b
subunits, which are linked by dithioether bridges. The binding of insulin induces a
conformational change and causes a close spatial arrangement of both b subunits. This, in
turn, activates tyrosine kinase activity of the receptor.
In pathological conditions such as diabetes, the tyrosine kinase activity is different than in
healthy conditions. Evidently, it is of great interest to find compounds that stimulate the same
activity as insulin. By fusing the b subunit of human insulin receptor to Renilla reniformis
luciferase and yellow fluorescent protein (YFP) a FRET donor– acceptor pair is obtained,
which reports the ligand-induced conformational change and precedes the signal transduction
step. This reporter system is able to detect the effects of insulin and insulin-mimicking
ligands in order to assess dose-dependent behaviour.
Fluorescence recovery after photo bleaching (FRAP)
If a fluorophore is exposed to high intensity radiation it may be irreversibly damaged and lose
its ability to emit fluorescence. Intentional bleaching of a fraction of fluorescently labelled
molecules in a membrane can be used to monitor the motion of labeled molecules in certain
(two-dimensional) compartments. Moreover, the time-dependent monitoring allows
determination of the diffusion coefficient. A well-established application is the usage of
phospholipids labelled with NBD (e.g. NBD-phosphatidylethanolamine, Fig. 12.13b) which
are incorporated into a biological or artificial membrane. The specimen is subjected to a pulse
of high-intensity light (photo bleaching), which causes a sharp drop of fluorescence in the
observation area (Fig. 12.13). Re-emergence of fluorescence emission in this area is
monitored as unbleached molecules diffused into the observation area. From the time-
dependent increase of fluorescence emission, the rate of diffusion of the
Fig. 12.13 (a) Schematic of a FRAP experiment. Time-based monitoring of fluorescence
emission intensity enables determination of diffusion coefficients in membranes. (b) A
commonly used fluorescence label in membrane FRAP experiments: chemical structure of
phosphatidylethanolamine conjugated to the fluorophore NBD.
phospholipid molecules can becalculated. Similarly, membrane proteins such as receptors or
even proteins in a cell can be conjugated to fluorescence labels and their diffusion
coefficients can be determined.
Fluorescence polarisation
A light source usually consists of a collection of randomly oriented emitters, and the emitted
light is a collection of waves with all possible orientations of the E vectors (non-polarised
light). Linearly polarised light is obtained by passing light through a polariser that transmits
light with only a single plane of polarisation; i.e. it passes only those components of the E
vector that are parallel to the axis of the polariser (Fig. 12.14). The intensity of transmitted
light depends on the orientation of the polariser. Maximum transmission is achieved when the
plane of polarisation is parallel to the axis of the polariser; the transmission is zero when the
orientation is perpendicular. The polarisation P is defined as P ¼ Il I$ ð12:7Þ Il þ I$ I
and I$ are the intensities observed parallel and perpendicular to an arbitrary axis. l
The polarisation can vary between 1 and þ1; it is zero when the light is unpolarised.
Light with 0 < |P| < 0.5 is called partially polarised.
E vectors
Direction of propagation
Polariser
Fig. 12.15 Absorption dipole moment mA (describing the probability of photon absorption)
and transition dipole moment mE (describing the probability for photon emission) for any
chromophore are usually not parallel. Absorption of linearly polarised light varies with cos2y
and is at its maximum parallel to mA. Emission of linearly polarised light varies with sin2f
and is highest at a perpendicular orientation to mE.
Experimentally, this can be achieved in a fluorescence spectrometer by placing a polariser in
the excitation path in order to excite the sample with polarised light. A second polariser is
placed between the sample and the detector with its axis either parallel or perpendicular to the
axis of the excitation polariser. The emitted light is either partially polarised or entirely
unpolarised. This loss of polarisation is called fluorescence depolarisation.
Absorption of polarised light by a chromophore is highest when the plane of polarisation is
parallel to the absorption dipole moment mA (Fig. 12.15). More generally, the probability of
absorption of exciting polarised light by a chromophore is proportional to cos2 y, with y
being the angle between the direction of polarisation and the absorption dipole moment.
Fluorescence emission, in contrast, does not depend on the absorption dipole moment, but on
the transition dipole moment mE. Usually, mA and mE are tilted against each other by about
10 to 40. The probability of emission of polarised light at an angle f with respect to the
transition dipole moment is proportional to sin2 f, and thus at its maximum in a perpendicular
orientation.
As a result if the chromophores are randomly oriented in solution, the polarisation P is less
than 0.5. It is thus evident that any process that leads to a deviation from random orientation
will give rise to a change of polarisation. This is certainly the case when a chromophore
becomes more static. Furthermore, one needs to consider Brownian motion. If the
chromophore is a small molecule in solution, it will be rotating very rapidly. Any change in
this motion due to temperature changes, changes in viscosity of the solvent, or binding to a
larger molecule, will therefore result in a change of polarisation.
Fluorescence cross-correlation spectroscopy
With fluorescence cross-correlation spectroscopy the temporal fluorescence fluctuations
between two differently labelled molecules can be measured as they diffuse through a small
sample volume. Cross-correlation analysis of the fluorescence signals from separate detection
channels extracts information of the dynamics of the duallabelled molecules. Fluorescence
cross-correlation spectroscopy has thus become an essential tool for the characterisation of
diffusion coefficients, binding constants, kinetic rates of binding and determining molecular
interactions in solutions and cells (see also Section 17.3.2).
Fluorescence microscopy, high-throughput assays
Fluorescence emission as a means of monitoring is a valuable tool for many biological and
biochemical applications. We have already seen the usage of fluorescence monitoring in
DNA sequencing; the technique is inseparably tied in with the success of projects such as
genome deciphering.
Fluorescence techniques are also indispensable methods for cell biological applications with
fluorescence microscopy (see Sections 4.6 and 17.3.2). Proteins (or biological
macromolecules) of interest can be tagged with a fluorescent label such as e.g. the green
fluorescent protein (GFP) from the jelly fish Aequorea victoria or the red fluorescent protein
from Discosoma striata, if spatial and temporal tracking of the tagged protein is desired.
Alternatively, the use of GFP spectral variants such as cyan fluorescent protein (CFP) as a
fluorescence donor and yellow fluorescent protein (YFP) as an acceptor allows investigation
of mechanistic questions by using the FRET phenomenon. Specimens with cells expressing
the labelled proteins are illuminated with light of the excitation wavelength, and then
observed through a filter that excludes the exciting light and only transmits the fluorescence
emission. The recorded fluorescence emission can be overlaid with a visual image
computationally, and the composite image then allows for localisation of the labelled species.
If different fluorescence labels with distinct emission wavelengths are used simultaneously,
even co-localisation studies can be performed.
Time-resolved fluorescence spectroscopy
The emission of a single photon from a fluorophore follows a probability distribution. With
time-correlated single photon counting, the number of emitted photons can be recorded in a
time-dependent manner following a pulsed excitation of the sample.
12.4 Luminometry
By sampling the photon emission for a large number of excitations, the probability
distribution can be constructed. The time-dependent decay of an individual fluorophore
species follows an exponential distribution, and the time constant is thus termed the lifetime
of this fluorophore. Curve fitting of fluorescence decays enables the identification of the
number of species of fluorophores (within certain limits), and the calculation of the lifetimes
for these species. In this context, different species can be different fluorophores or distinct
conformations of the same fluorophore.
12.4 LUMINOMETRY
Polarimetry essentially measures the angle through which the plane of polarisation is changed after
linearly polarised light is passed through a solution containing a chiral substance. Optical rotation
dispersion (ORD) spectroscopy is a technique that measures this ability of a chiral substance to
change the plane-polarisation as a function of the wavelength. The angle al between the plane of the
resulting linearly polarised light against that of the incident light is dependent on the refractive index
for left (nleft) and right (nright) circularly polarised light. The refractive index can be calculated as
the ratio of the speed of light in vacuo and the speed of light in matter. After normalisation against
the amount of substance present in the sample (thickness of sample/cuvette length d, and mass
concentration r*), a substance-specific constant [a]l is obtained that can be used to characterise
chiral compounds.
(a) (b)
Q
Fig. 12.17 (a) Linearly polarised light can be thought of consisting of two circularly polarised
components with opposite ‘handedness’. The vector sum of the left- and right-handed circularly
polarised light yields linearly polarised light. (b) If the amplitudes of left- and right-handed polarised
components differ, the resulting light is elliptically polarised. The composite vector will trace the
ellipse shown in grey. The ellipse is characterised by a major and a minor axis. The ratio of minor and
major axis yields tan Y. Y is the ellipticity.
Circular dichroism
In addition to changing the plane of polarisation, an optically active sample also shows unusual
absorption behaviour. Left- and right-handed polarised components of the incident light are
absorbed differently by the sample, which yields a difference in the absorption coefficients De = eleft
eright. This latter difference is called circular dichroism (CD). The difference in absorption coefficients
De (i.e. CD) is measured in units of cm2 g1, and is the observed quantity in CD experiments.
Historically, results from CD experiments are reported as ellipticity Yl. Normalisation of Yl similar to
the ORD yields the molar ellipticity:
It is common practice to display graphs of CD spectra with the molar ellipticity in units of 1 cm2
dmol1 = 10 cm2 mol1 on the ordinate axis (Fig. 12.18).
• if an optically active molecule has a positive CD, then its enantiomer will have a negative CD
of exactly the same magnitude; and
• the phenomenon of CD can only be observed at wavelengths where the optically active
molecule has an absorption band.
100x10 3
40 x 103
20 x 103
–20x10 3
–40x10 3
–60x10 3
190 200 210 220 230 240 250
(nm)
Fig. 12.18 Circular dichroism spectra for three standard secondary structures according to Fasman.
An a-helical peptide is shown in dark green, a peptide adopting b-strand structure ingrey, anda
random coil peptide in light green.
In Section 12.2, we saw that the peptide bond in proteins possesses UV absorption bands in the area
of 220–190 nm. The carbon atom vicinal to the peptide bond (the Ca atom) is asymmetric and a
chiral centre in all amino acids except glycine. This chirality induces asymmetry into the peptide
bond chromophore. Because of the serial arrangement of the peptide bonds making up the
backbone of a protein, the individual chromophores couple with each other. The (secondary)
structure of a polypeptide thus induces an ‘overall chirality’ which gives rise to the CD phenomenon
of a protein in the wavelength interval 260–190 nm.
With protein circular dichroism, the molar ellipticity y also appears as mean residue ellipticity yres,
owing to the fact that the chromophores responsible for the chiral absorption phenomenon are the
peptide bonds. Therefore, the number of chromophores of a polypeptide in this context is equal to
the number of residues. Because of the law of Beer–Lambert (Equation 12.2), the number of
chromophores is proportional to the magnitude of absorption, i.e. in order to normalise the
spectrum of an individual polypeptide for reasons of comparison, the CD has to be scaled by the
number of peptide bonds.
12.5.2 Instrumentation
Generally, left and right circularly polarised light passes through the sample in an alternating fashion.
This is achieved by an electro-optic modulator which is a crystal that transmits either the left- or
right-handed polarised component of linearly polarised light, depending on the polarity of the
electric field that is applied by alternating currents. The photomultiplier detector produces a voltage
proportional to the ellipticity of the resultant beam emerging from the sample. The light source of
the spectrometer is continuously flushed with nitrogen to avoid the formation of ozone and help to
maintain the lamp.
CD spectrometry involves measuring a very small difference between two absorption values which
are large signals. The technique is thus very susceptible to noise and measurements must be carried
out carefully. Some practical considerations involve having a clean quartz cuvette, and using buffers
with low concentrations of additives. While this is sometimes tricky with protein samples, reducing
the salt concentrations to values as low as 5 mM helps to obtain good spectra. Also, filtered
solutions should be used to avoid any turbidity of the sample that could produce scatter. Saturation
of the detector must be avoided, this becoming more critical with lower wavelengths. Therefore,
good spectra are obtained in a certain range of protein concentrations only where enough sample is
present to produce a good signal and does not saturate the detector. Typical protein concentrations
are 0.03–0.3mgcm3.
In order to calculate specific ellipticities (mean residue ellipticities) and be able to compare the CD
spectra of different samples with each other, the concentration of the sample must be known.
Provided the protein possesses sufficient amounts of UV/Vis-absorbing chromophores, it is thus
advisable to subject the CD sample to a protein concentration determination by UV/Vis as described
in Section 12.2.3.
12.5.3 Applications
The main application for protein CD spectroscopy is the verification of the adopted secondary
structure. The application of CD to determine the tertiary structure is limited, owing to the
inadequate theoretical understanding of the effects of different parts of the molecules at this level
of structure.
Rather than analysing the secondary structure of a ‘static sample’, different conditions can be tested.
For instance, some peptides adopt different secondary structures when in solution or membrane-
bound. The comparison of CD spectra of such peptides in the absence and presence of small
unilamellar phospholipid vesicles shows a clear difference in the type of secondary structure.
Measurements with lipid vesicles are tricky, because due to their physical extensions they give rise
to scatter. Other options in this context include CD experiments at lipid monolayers which can be
realised at synchrotron beam lines, or by usage of optically clear vesicles (reverse micelles).
CD spectroscopy can also be used to monitor changes of secondary structure within a sample over
time. Frequently, CD instruments are equipped with temperature control units and the sample can
be heated in a controlled fashion. As the protein undergoes its transition from the folded to the
unfolded state, the CD at a certain wavelength (usually 222 nm) is monitored and plotted against the
temperature, thus yielding a thermal denaturation curve which can be used for stability analysis.
Further applications include the use of circular dichroism for an observable for kinetic
measurements using the stopped flow technique (see Section 15.3).
The scattering of light can yield a number of valuable insights into the properties of macromolecules,
including the molecular mass, dimensions and diffusion coefficients, as well as
association/dissociation properties and internal dynamics. The incident light hitting a macromolecule
is scattered into all directions with the intensity of the scatter being only about 105 of the original
intensity. The scattered light is measured at angles higher than 0 and less than 180. Most of the
scattered light possesses the same wavelength as the incident light; this phenomenon is called
elastic light scattering. When the scattered light has a wavelength higher or lower than the incident
light, the phenomenon is called inelastic light scattering. The special properties of lasers (see Section
12.1.3) with high monochromaticity, narrow focus and strong intensity, make them ideally suited for
light scattering applications.
Elastic light scattering is also known as Rayleigh scattering and involves measuring the intensity of
light scattered by a solution at an angle relative to the incident laser beam. The scattering intensity
of macromolecules is proportional to the squared
molecular mass, and thus ideal for determination of M, since the contribution of small solvent
molecules can be neglected. In an ideal solution, the macromolecules are entirely independent from
each other, and the light scattering can be described as:
I0 R ¼ P K c M ð12:9Þ
where Iy is the intensity of the scattered light at angle y, I0 is the intensity of the incident light, K is a
constant proportional to the squared refractive index increment, c is the concentration and Ry the
Rayleigh ratio. Py describes the angular dependence of the scattered light.
For non-ideal solutions, interactions between molecules need to be considered. The scattering
intensity of real solutions has been calculated by Debye and takes into account concentration
fluctuations. This results in an additional correction term comprising the second virial coefficient B
which is a measure for the strength of interactions between molecules:
Kc 1 1
2Bc 12:10
R ¼ PM þ ð Þ
In solution, there are only three methods for absolute determination of molecular mass: membrane
osmometry, sedimentation equilibrium centrifugation and light scattering. These methods are
absolute, because they do not require any reference to molecular mass standards. In order to
determine the molecular mass from light scattering, three parameters must be measured: the
intensity of scattered light at different angles, the concentration of the macromolecule and the
specific refractive index increment of the solvent. As minimum instrumentation, this requires a light
source, a multi-angle light scattering (MALS) detector, as well as a refractive index detector. These
instruments can be used in batch mode, but can also be connected to an HPLC to enable online
determination of the molecular mass of eluting macromolecules. The chromatography of choice is
size-exclusion chromatography (SEC), also called gel filtration (see Section 11.7), and the
combination of these methods is known as SEC–MALS. Unlike conventional sizeexclusion
chromatography, the molecular mass determination from MALS is independent of the elution
volume of the macromolecule. This is a valuable advantage, since the retention time of a
macromolecule on the size-exclusion column can depend on its shape and conformation.
12.6.2 Quasi-elastic (dynamic) light scattering – photon correlation spectroscopy
While intensity and angular distribution of scattered light yields information about molecular mass
and dimension of macromolecules, the wavelength analysis of scattered light allows
The diffusion coefficient is related to the particle size by an equation known as the
Stokes–Einstein relation. The parameter derived is the hydrodynamic radius, or Stokes radius, which
is the size of a spherical particle that would have the same diffusion coefficient in a solution with the
same viscosity. Most commonly, data from dynamic light scattering are presented as a distribution
of hydrodynamic radius rather than wavelength of scattered light.
Notably, the hydrodynamic radius describes an idealised particle and can differ significantly from the
true physical size of a macromolecule. This is certainly true for most proteins which are not strictly
spherical and their hydrodynamic radius thus depends on their shape and conformation.
In contrast to size exclusion chromatography, dynamic light scattering measures the hydrodynamic
radius directly and accurately, as the former method relies on comparison with standard molecules
and several assumptions.
When the incident light beam hits a molecule in its ground state, there is a low probability that the
molecule is excited and occupies the next higher vibrational state (Figs. 12.3, 12.8). The energy
needed for the excitation is a defined increment which will be missing from the energy of the
scattered light. The wavelength of the scattered light is thus increased by an amount associated with
the difference between two vibrational states of the molecule (Stokes shift). Similarly, if the
molecule is hit by the incident light in its excited state and transitions to the next lower vibrational
state, the scattered light has higher energy than the incident light which results in a shift to lower
wavelengths (anti-Stokes shift). These lines constitute the Raman spectrum. If the wavelength of the
incident light is chosen such that it coincides with an absorption band of an electronic transition in
the molecule, there is a significant increase in the intensity of bands in the Raman spectrum. This
technique is called resonance Raman spectroscopy (see Section 13.2).
So far, all methods have dealt with probing molecular properties. In Section 12.1.2, we discussed the
general theory of electronic transitions and said that molecules give rise
12.7 Atomic spectroscopy
to band spectra, but atoms yield clearly defined line spectra. In atomic emission spectroscopy (AES),
these lines can be observed as light of a particular wavelength (colour). Conversely, black lines can
be observed against a bright background in atomic absorption spectroscopy (AAS). The wavelengths
emitted from excited atoms may be identified using a spectroscope with the human eye as the
‘detector’ or a spectrophotometer.
12.7.1 Principles
In a spectrum of an element, the absorption or emission wavelengths are associated with transitions
that require a minimum of energy change. In order for energy changes to be minimal, transitions
tend to occur between orbitals close together in energy terms. For example, excitation of a sodium
atom and its subsequent relaxation gives rise to emission of orange light (‘D-line’) due to the
transition of an electron from the 3s to the 3p orbital and return (Fig. 12.19).
Filling orbitals with electrons is subject to two major rules: • one orbital can be occupied with a
maximum of two electrons; and
• the spins of electrons in one orbital need to be paired in an antiparallel fashion (Pauli principle).
Together, these limitations mean that emission and absorption lines are characteristic for an
individual element.
12.7.2 Instrumentation
In general, atomic spectroscopy is not carried out in solution. In order for atoms to emit or absorb
monochromatic radiation, they need to be volatilised by exposing them to high thermal energy.
Usually, nebulisers are used to spray the sample solution into a flame or an oven. Alternatively, the
gaseous form can be generated by using inductively coupled plasma (ICP). The variations in
temperature and composition of a flame make standard conditions difficult to achieve. Most modern
instruments thus use an ICP.
Atomic emission spectroscopy (AES) and atomic absorption spectroscopy (AAS) are generally used to
identify specific elements present in the sample and to determine their concentrations. The energy
absorbed or emitted is proportional to the number of atoms in the optical path. Strictly speaking, in
the case of emission, it is the number of excited atoms that is proportional to the emitted energy.
Concentration determination with AES or AAS is carried out by comparison with calibration
standards.
Sodium gives high backgrounds and is usually measured first. Then, a similar amount of sodium is
added to all other standards. Excess hydrochloric acid is commonly added, because chloride
compounds are often the most volatile salts. Calcium and magnesium emission can be enhanced by
the addition of alkali metals and suppressed by addition of phosphate, silicate and aluminate, as
these form nondissociable salts. The suppression effect can be relieved by the addition of lanthanum
and strontium salts. Lithium is frequently used as an internal standard. For storage of
Energy
4d
4p
4s
3p
D-line transition
3s
2p
2s
1s
Fig. 12.19 Energy levels of atomic orbitals in the sodium atom. Each atomic orbital can be occupied
by electrons following the rules of quantum chemistry until the total number of electrons for that
element is reached (in case of sodium: 11 electrons). The energy gap between the 3s and the 3p
orbitals in the sodium atom is such that it can be overcome by absorption of orange light.
samples and standards, polyethylene bottles are used, since glass can absorb and release metal ions,
and thus impact the accuracy of this sensitive technique.
Cyclic analysis may be performed that involves the estimation of each interfering substance in a
mixture. Subsequently, the standards for each component in the mixture are doped with each
interfering substance. This process is repeated two or three times with refined estimates of
interfering substance, until self-consistent values are obtained for each component.
Biological samples are usually converted to ash prior to determination of metals. Wet ashing in
solution is often used, employing an oxidative digestion similar to the Kjeldahl method (see Section
8.3.2).
12.7.3 Applications
Sodium and potassium are assayed at concentrations of a few p.p.m. using simple filter
photometers. The modern emission spectrophotometers allow determination of about
20 elements in biological samples, the most common being calcium, magnesium and manganese.
Absorption spectrophotometers are usually more sensitive than emission instruments and can
detect less than 1 p.p.m. of each of the common elements with the exception of alkali metals. The
relative precision is about 1% in a working range of 20–200 times the detection limit of an element.
AES and AAS have been widely used in analytical chemistry, such as environmental and clinical
laboratories. Nowadays, the technique has been superseded largely by the use of ion-selective
electrodes (see Section 16.2.2).
Despite being limited to only a few metals, the main importance of atomic fluorescence
spectrophotometry (AFS) lies in the extreme sensitivity. For example, zinc and cadmium can be
detected at levels as low as 1–2 parts per 1010.
AFS uses the same basic setup as AES and AAS. The atoms are required to be vaporised by one of
three methods (flame, electric, ICP). The atoms are excited using electromagnetic radiation by
directing a light beam into the vaporised sample. This beam must be intense, but not spectrally pure,
since only the resonant wavelengths will be absorbed, leading to fluorescence (see Section 12.3.1).
Applications in healthcare:
3. Applications of Quantum Computing for Healthcare
Recent research shows that quantum computing has a clear advantage over
classical computing systems. Quantum computing provides an incremental speedup of
disease diagnosis and treatment and, in some use cases, can drastically reduce the
computation times from years to minutes [33,49]. It provokes innovative ways of
realizing a higher level of skills for certain tasks, new architectures, and strategies.
Therefore, quantum computing has an immense potential to be employed for a wide
variety of use cases in the health sector in general and for healthcare service providers
in particular, especially in the areas of accelerated diagnoses, personalized medicine,
and price optimization. A literature survey shows that there is a visible increase in the
use of classical modeling and quantum-based approaches, primarily due to the
improvement in access to worldwide health-relevant data sources and availability. This
section brings forward some potential use cases for the applications of quantum
computing in healthcare; an illustration of these use cases is presented in Figure 4.