Research Article
Journal of the Optical Society of America B
1
Comparison of collimated blue light generation in 85Rb
atoms via the D1 and D2 lines
arXiv:1802.07305v1 [physics.atom-ph] 20 Feb 2018
N IKUNJ P RAJAPATI1,* , A LEXANDER M. A KULSHIN2,3 ,
AND I RINA
N OVIKOVA1
1 Department
of Physics, College of William & Mary, Williamsburg, Virginia 23187, USA
for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Australia
3 Johannes Gutenburg University, Helmholtz Institute, D-55128, Mainz, Germany
* Corresponding author: nprajapati@email.wm.edu
2 Centre
Compiled November 14, 2021
We experimentally studied the characteristics of the collimated blue light (CBL) produced in 85 Rb vapor
by two resonant laser fields exciting atoms into the 5D3/2 state, using either the 5P1/2 or the 5P3/2 intermediate state. We compared the CBL output at different values of frequency detunings, powers, and
polarizations of the pump lasers in these two cases, and confirmed the observed trends using a simple theoretical model. We also demonstrated that the addition of the repump laser, preventing the accumulation
of atomic population in the uncoupled hyperfine ground state, resulted in nearly an order of magnitude
increase in CBL power output. Overall, we found that the 5S1/2 − 5P1/2 − 5D3/2 excitation pathway results
in stronger CBL generation, as we detected up to 4.25 µW using two pumps of the same linear polarization.
The optimum CBL output for the 5S1/2 − 5P3/2 − 5D3/2 excitation pathway required the two pump lasers
to have the same circular polarization, but resulted only in a maximum CBL power of 450 nW. © 2021 Optical
Society of America
OCIS codes:
(020.4180) Multiphoton processes; (270.1670) Coherent optical effects.
http://dx.doi.org/10.1364/ao.XX.XXXXXX
1. INTRODUCTION
Multi-photon processes have become an important tool in nonlinear and quantum optics for non-classical light and entanglement generation in a wide spectral range. While traditionally
nonlinear crystals are used for frequency conversion and wave
mixing, a strong nonlinearity can be also achieved in the proximity of optical transitions in atoms, reducing required laser power
and removing the requirement of an optical cavity [1]. A broad
variety of interaction configurations have been considered and
realized for numerous applications. Among them, the scheme involving two-photon excitation reaching higher energy levels has
been investigated for efficient frequency up-conversion [2–4],
single-photon frequency conversion [5], quantum memory [6],
selective non-linearity suppression [7], quantum noise dynamics [8], etc.
An excitation to the nD states of alkali metal atoms opens
interesting possibilities for nonlinear optics, as the population
inversion, guaranteed between certain excited levels with appropriate lifetimes and branching ratios, results in amplified
spontaneous emission (ASE) and spontaneously-seeded fourwave mixing for the involved optical transitions. A lot of attention was recently given to the generation of the collimated
blue light (CBL) at 420.3 nm via the 5S1/2 → 5P3/2 → 5D5/2
transition in Rb vapor [9–16]. Such interacting systems have
been successfully used to study the interplay of co-existing nonlinear processes [17, 18], the effects of externally-seeded optical
fields [19], and of optical resonators [20]. It also served as a
tool for studies on orbital angular momentum conservation and
manipulations in nonlinear processes [21–23].
We report on the investigation of CBL generation in the twophoton transition reaching the 5D3/2 state, providing an opportunity to investigate the interference between competing excitation channels, spontaneous decays, and nonlinear processes.
It allows for an alternative, more symmetric, four-wave mixing
diamond scheme involving only near-IR optical fields [24–27].
Since it is important to understand the interplay between the
multiple excitation and relaxation channels to maximize the
efficiency of a particular nonlinear process, here we experimentally compared the two excitation pathways to the 5D3/2 level
through either 5P1/2 or 5P3/2 intermediate levels, and identified
the optimal conditions for the collimated blue light generation
in each case.
2. EXPERIMENTAL ARRANGEMENTS
The schematic of the experimental apparatus is shown in Fig. 1.
We employed three individual lasers. Two external cavity diode
Research Article
lasers – ECDL-D1 and ECDL-D2 – tunable in the vicinity of the
Rb D1 line (wavelength 795 nm) and Rb D2 line (wavelength
780 nm). Each ECDL, depending on the stage of the experiment,
can serve as either lower pump or re-pump laser while the upper
pump optical field is generated using the continuous wave (cw)
Titanium Sapphire (Ti:Sapph) laser. The first stage utilizes the
D1 laser as the lower pump, the D2 as the re-pump, and the
Ti:Sapph tuned to 762 nm (for 5P1/2 → 5D3/2 transition) while
the second stage involves the D1 and D2 lasers swapping roles
and the Ti:Sapph being tuned to 776 nm (for the 5P3/2 → 5D3/2
transition).
The two fields generated by the ECDLs were combined first
so they could be adjusted together before combining with the
Ti:Sapph laser. In order to further increase the laser intensities,
the laser beams were weakly focused inside the Rb cell using
a 1000 mm (L1) lens and then collimated using a 500 mm (L2)
lens. All beams had gaussian intensity profiles with diameters
230 µm, 250 µm, and 840 µm at the center of the Rb cell, for the
D1, D2, and Ti:Sapph laser beams, respectively.
Journal of the Optical Society of America B
2
at a relatively low temperature of 88o C, corresponding to the
density of ≈ 1.7x1012 cm−3 . The cell was housed in three
layer magnetic shielding, with the innermost layer wrapped in a
heating wire. Thermal insulation was placed between each layer
of the magnetic shield to help with temperature stability.
Under these conditions we observed the emergence of collimated blue light. To maximize its power, we adjusted the relative angles between the two co-propagating pump laser fields
and the repump laser as shown in the inset of the Fig. 1: all
three beams were arranged in the same plane, with the angles
between the Ti:Sapph laser and D1 and D2 laser beams being
θ1 = 2.1 mrad and θ2 = 7.5 mrad correspondingly. The output CBL beam then emerged at the angle of θ3 = 3.3 mrad
from the Ti:Sapph beam. We found that for both intermediate
5P states, the generated blue light was produced at a wavelength of 421.7 nm (measured using an Ocean Optics spectrometer with spectral resolution ±0.2 nm) corresponding to the
6P1/2 → 5S1/2 optical transition. We were not able to detect any
directional radiation at the 5D3/2 → 6P1/2 and 5D3/2 → 6P3/2
transitions, since the glass cell is not transparent in the mid-IR
spectral range. We also did not observe optical fields corresponding to the alternative relaxation pathways through the
6S1/2 state [14, 15, 22] or 5P states [26, 27].
To separate the CBL beam from the pump fields after the
Rb cell, the output beams passed through a diffraction grating
(DG) which directed ≈ 46 % of the total power of each field
into the first diffraction order. We then used irises to isolate
individual laser fields before the photodetectors (PD). To avoid
contamination of the CBL measurements by any scattered IR
laser light, we placed a blue spectral filter (transmission ≈ 40%
at 421.7 nm) before the corresponding photo-detector.
85 Rb
3. CBL GENERATION VIA THE D1 LINE
Fig. 1. The optical layout of the experimental setup. ECDLD1, ECDL-D2, and Ti:Sapph denote three independent lasers
used in the experiment. The optical paths of the D1, D2, and
Ti:sapph pump lasers and the generated blue light are show in,
red, black, green, and blue, respectively. Inset shows relative
orientation of the optical beams. See text for the abbreviations.
For maximum flexibility in setting the pump field polarizations, all optical fields were combined using edge mirrors. We
found that the polarization of the re-pump field relative to the
lower pump field had very little effect on CBL generation, and
thus we always matched the repump laser polarization to that of
the lower pump field. The polarizations of the lower and upper
pump fields, before entering the cell, were controlled independently using half- and quarter -wave plates. The polarizations of
the indavidual beams were cleaned using beam splitters before
they were combined. However, polarization imperfections could
have risen from the use of zero-order waveplates designed for
795 nm light.
In the experiment we used a 75 mm - long cylindrical Pirex
cell (diameter 22 mm), containing isotopically enriched 85 Rb
vapor. The cell was tilted by approximately 6◦ to avoid the
retroreflection effects from the cell’s windows on the generated
CBL [19]. For all the measurements the cell was maintained
In this section we present the measurements in which the D1
transition (5S1/2 → 5P1/2 , λ D1 = 795 nm) served as the first
step of the excitation scheme; the second pump laser with the
wavelength 762 nm was used to further excite atoms into the
5D3/2 excited state, as shown in Fig.2. In this configuration
the D2 laser, acting as a repump, was tuned to the transition
between the excited 5P3/2 level and the ground-state hyperfine
sublevel, not coupled by the D1 pump laser (F = 2 in this case).
Unless otherwise noted, all the reported data are recorded with
the repump laser on, as it produced a uniform increase in the
recorded CBL power, regardless of polarizations and powers of
the pump lasers.
Fig. 2. Interaction configuration through the 5P1/2 intermediate level: lower pump (794.97 nm) and the upper pump
(762.103 nm) excite Rb atoms to the 5D3/2 level, followed
by the emission of 5.032 µm (not detectable) and collimated
blue light at 421.7 nm. The repump field is tuned to the
5S1/2 , F = 2 → 5P3/2 transition.
Research Article
Fig. 3. Power of the generated blue light as the lower pump
was swept across: (a) 5S1/2 , F = 3 → 5P1/2 transition, (b)
5S1/2 , F = 2 → 5P1/2 , and (c) 1.2 GHz above 5S1/2 , F = 2 →
5P1/2 transitions. The upper pump was tuned to 762.1036 nm
for (a,b), and 762.1054 nm for (c). Four different polarization
configurations of the two pump lasers are shown: linear parallel (red, solid line), linear orthogonal (magenta, solid line),
circular parallel (blue, dashed line), and circular orthogonal
(green, dashed line). The powers of both lower pump (D1
laser) and the repump (D2 laser) were kept at 16 mW, and the
power of the upper pump (Ti:Sapph laser) at 200 mW . The
zero detuning of the D1 pump corresponds to the cross-over
transition of the 5S1/2 , F = 3 → 5P1/2 state.
CBL generation was analyzed for four pump polarization
configurations, in which the two pump fields had either parallel or orthogonal linear or circular polarization. The resulting
observations are shown in Fig.3, in which we plotted the CBL
power for each polarization configuration as the function of
the lower pump frequency (the upper pump frequency was
fixed). We have considered three cases in which the lower pump
laser was scanned across each hyperfine transition of the D1 line
[Fig.3(a,b)], as well as when it was detuned by ≈ +1.2 GHz from
the 5S1/2 , F = 2 → 5P1/2 [Fig.3(c)]. For the resonance cases we
found that the maximum blue light power corresponds to the
frequency of the maximum D1 laser absorption.
We found that the polarization configuration leading to the
maximum blue light generation was different, depending on the
laser frequency. We detected the strongest CBL generation at
the lower frequency transition (5S1/2 , F = 2, 3 → 5P1/2 ) when
the two pump field were linearly polarized, with parallel arrangement results in slightly higher CBL power. However, the
circularly polarized pump fields produced a similar amount of
blue light for both the lower and higher-frequency transitions
(5S1/2 , F = 3 → 5P1/2 ), but since the blue output for the linearly
polarized pumps dropped significantly in the latter case, the circular parallel pumps maximized the CBL generation. Finally, the
circular orthogonal configuration led to the smallest generation
of CBL.
We also analyzed the CBL polarization for linearly polarized
pump lasers. We found that for all investigated laser detunings
the polarization of the generated blue light matched the polarization of the lower pump field, even for orthogonally polarized
laser fields. Unfortunately, we were not able to carry out the
CBL polarization analysis for the circularly polarized pumps
since a quarter-wave plate for blue light unavailable.
On-resonant D1 -line excitation
To investigate the power dependence of the generated blue light
on all three involved laser fields, we considered on- and off-
Journal of the Optical Society of America B
3
resonant tuning of the pump fields. In the first case, both pump
fields were tuned near the centers of the corresponding optical
resonant absorption peaks (5S1/2 → 5P1/2 and 5P1/2 → 5D3/2 ).
As CBL is the product of parametric wave mixing of two pump
laser fields and the internally generated mid-IR field [10, 18],
the maximum of the blue spectral profile did not always occur exactly at the two-photon resonance (in which the sum of
the two laser frequencies exactly matched the frequency difference between the ground state and the excited D state), but
was shifted toward the frequency corresponding to the maximum lower pump absorption and often resembled two poorlyresolved peaks. For the power dependence studies we chose the
lower pump detuning near the 5S1/2 , F = 3 → 5P1/2 transition
and parallel linearly polarized pump fields which produced the
highest CBL output.
Fig. 4. Generated CBL power as a function of normalized
power of each pump and repump fields. For each individual dependence the power of one laser was varied between
zero and its maximum value, while the other two lasers were
kept at their maximum powers: 65 mW for the lower pump
(795 nm), 200 mW for the upper pump (762 nm), and 17 mW
for the repump laser (780 nm). The laser detuning corresponded to the conditions for the maximum CBL power as
shown in Fig. 3(a).
At maximum power for all three fields, we measured 4.25 µW
of the generated blue light. As we decreased the power of the
upper pump field, the CBL power dropped more or less linearly,
as expected for the optically-driven population of the 5D3/2 excited state [28]. The reduction of the repump power resulted
in a similar nearly linear drop in CBL until leveling off at 30%
of the repump power. It is likely that the effect of the repumping became negligible for lower repump laser powers due to
its strong absoprtion, since the measured CBL power output
(500 − 700 nW) matched the blue light generated in the complete
absence of the repump field.
However, the lower pump power dependence is more complicated: as the D1 laser power increases, the CBL power grew
steadily until it reached its plateau at 4.25 µW at ≈ 50% of the
maximum available laser power (≈ 30 mW), and then began
slowly decrease. The origin of such behavior is related to the
optimization of excitation and relaxation rates from and to the
ground state via stimulated processes, as will be discussed later
in Sec. 5. We have verified that the resonant absorption of the
D1 laser field displayed no similar trends, steadily decreasing
from 70% to 40% with the growing laser power. It also should be
noted that the reduction in the generated CBL power at higher
pump power occurred only when the repump field was present.
Research Article
Journal of the Optical Society of America B
4
Without the repump, the CBL reached saturation at the D1 field
power of ≈ 35 mW, and then stayed roughly at the same level
with further laser power increase.
Off-resonant D1 -line excitation
CBL power dependences were also analyzed for the pump fields
detuned by approximately +1.2 GHz from the 5S1/2 , F = 2 →
5P1/2 transition [Fig. 3(c)]. At this detuning the lower pump
field experienced almost no resonant absorption making the contribution of the step-wise excitation process significantly smaller
compared with the direct two-photon excitation. Thus, we observed the maximum blue light generation at the two-photon
resonance conditions for the 5S1/2 → 5D3/2 transition. We chose
to use the linear parallel polarizations arrangement for direct
comparison with the resonant case. As one can see in Fig. 5, in
this case the blue light power displays fairly linear dependence
on each pump laser field, without reaching saturation or maximum. The repumping power dependence is also qualitatively
similar to the resonant case, although it is important to note
significantly higher enhancement for the same repump power
(×10 CBL power increase) compare to the resonant case (×4 CBL
power increase).
Fig. 5. Generated CBL power as a function of normalized
power of each pump and repump field. As in Fig. 4, for each
individual measurement the power of one laser was varied
between zero and its maximum amount, while the other two
lasers were kept at their maximum powers: 65 mW for the
lower pump (795 nm), 200 mW for the upper pump (762 nm),
and 17 mW for the repump laser (780nm). The laser detuning corresponded to the conditions for the maximum CBL
generation in Fig. 3(c), approximately +1.2 GHz blue of the
5S1/2 , F = 2 → 5P1/2 transition.
4. CBL GENERATION VIA THE D2 LINE
The alternative excitation pathway to the 5D3/2 level is through
the 5P3/2 intermediate level. In this case, the two-photon transition was executed using the D2 (780 nm) laser and the Ti:sapph
laser, tuned to the 776 nm, while the D1 (795 nm) laser served
as the repump, as shown in Fig. 6. This pump configuration is
traditionally used for the excitation of Rb atoms into the 5D5/2
state [9–11, 13–15]. Under the identical experimental conditions, we have obtained up to 120 µW of blue light using the
5S1/2 → 5P3/2 → 5D5/2 excitation scheme, while in the case of
the 5S1/2 → 5P3/2 → 5D3/2 pathway the maximum obtained
CBL power was just ≤ 450 nW.
Fig. 6. Interaction configuration for CBL generation via the
5P3/2 intermediate state, that uses the lower pump (780 nm)
and the upper pump (776.15 nm) to excite Rb atoms into the
5D3/2 state, resulting in emission of 5.032 µm (not experimentally observed) and collimated blue light (421.7 nm). The repump (795 nm) field is tuned to the hyperfine ground state
opposite of the lower pump.
Fig. 7. Measured CBL power for varying polarizatins of lower
pump (780 nm) and upper pump (776.1568 nm) as the lower
pump is swept across the hyper-fine split ground states. The
considered polarization arrangements for the two pumps are:
linear parallel (red, solid line), linear orthogonal (magenta,
solid line), circular parallel (blue, dashed line), and circular
orthogonal (green, dashed line).
Fig.7 demonstrates the measured CBL output power as a
function of the lower pump (D2 ) laser detuning for the previously tested four polarization combinations, shown in Fig. 3.
We observed an even more pronounced dependence of the blue
light power on the pump polarizations than in the D1 excitation
scheme. For the two-photon 5S1/2 , F = 2 → 5D3/2 transition,
the orthogonally circularly-polarized pump fields yielded CBL
output that was stronger than the other three configurations by
at least an order of magnitude. Remarkably, the same pump polarization arrangement produced no CBL when the lower pump
was tuned to the other hyperfine ground state 5S1/2 F = 3. At
that frequency the blue light was detected only for the circular orthogonal and linear orthogonal polarizations. Overall, we
found significantly weaker (approximately by a factor of 10) blue
light generation, compare to the D1 excitation scheme. Also, the
blue light power dropped very rapidly with the laser detuning
away from the resonance, so that no detectable CBL output was
found at +1.2 GHz detuning used for the off-resonant case in
previous section.
Research Article
Journal of the Optical Society of America B
5
transient relaxation.
Fig. 8. Generated CBL as a function of normalized power of
the pump and repump fields. As in Fig. 4, for each individual dependence, the power of one laser was varied between
zero and its maximum value, while the other two lasers were
kept at their maximum powers: 17 mW for the lower pump
(780 nm), 200 mW for the upper pump (776 nm), and 65 mW
for the remupmer (795 nm). The laser detuning corresponded
to the conditions for the maximum CBL generation in Fig. 7(b),
near S1/2 F = 2 → 5P3/2 F ′ transition. The upper pump wavelength was fixed at 776.1568 nm.
Fig. 8 shows the dependences of the CBL power on the power
of the pump and the repump lasers, measured for parallel circular polarization of the pumps, the configuration yielding the
highest CBL powers. When either pump power was varied, we
observed a roughly linear dependence for the blue light output.
Unlike the resonant excitation using the D1 optical transition
shown in Fig. 4, no signs of saturation or peaking was observed
at the available range of the lower pump (D2 laser) power. It is
important to note, however, that we operated with less available
laser power. In the case of the D1 excitation channel, the CBL
power started to saturate at around 12 mW of the lower pump
power, reaching the maximum value at 35 mW. Since the maximum available D2 laser power was only 17 mW, it is possible
that nonlinear power dependence can be observed at higher
pump powers.
The repump power dependence shows clear saturation for
the D1 laser powers above ≈ 20 mW, the power level necessary
to provide efficient depopulation of the 5S1/2 F = 3 ground state.
Unsurprisingly, further repump power increase did not provide
any additional advantages. We confirmed this by the additional
measurements of the D2 laser resonant absorption, observing
an increase in absorption from 30% without the repump to a
plateau of ≈ 50% with repump power above 20 mW.
Despite many simplifications, the calculations qualitatively
match the experimental observations and provide explination
for the observed behaviors. Fig. 9(a) demonstrates the dependences of the CBL gain on the powers of the pump lasers in
the range of Rabi frequencies comparable with those used in
the experiment. The simulated trends are similar to the experimental dependencies, shown in Fig. 4, in which the CBL power
grows with the upper pump, but reaches a maximum and then
declines when the lower pump power is increased. However, if
we allow either pump power to vary at a larger range, as shown
in Fig. 9(b), we see that the maximum CBL output occurs when
the upper to lower pump Rabi frequencies ratio is roughly 2.3.
Increase of either pump power leads to reduction of populations of the atomic levels, involved in blue light generation and
consequently to the reduction of CBL output.
This understanding also help to explain the difference in the
CBL output dependence on the lower pump power at D1 and
D2 lines, shown in Figs. 4 and 8. Since the D1 laser output is
higher, we were able to realize the optimal power ratio for the
lower and upper pumps and observed the CBL maximization.
However, if the maximum value of the D1 pump was used, we
were not able to reach the optimal CBL conditions due to power
limitation of the Ti:Sapph laser. However, when we tested the
alternative configuration through the 5P3/2 state, the mismatch
between the available powers of the two pumps restricted the
CBL generation to the lower part of the theoretical curve.
5. SIMPLIFIED THEORETICAL SIMULATIONS
To gain some qualitative understanding of the observed experimental behavior, we built a simplified theoretical model of
the blue light generation using the methodology described in
Ref. [29] adopted for in a four-level diamond scheme. To reduce
the complexity, we have neglected the nuclear spin, eliminating
the hyperfine structure. To account for alternative spontaneous
decay paths and the optical pumping of atoms in the second
ground hyperfine state, we introduced an additional fictional
non-degenerate ground state. Lifetime and branching ratios of
which, match those of the corresponding Rb states. We also
do not account for the Doppler broadening of the optical transition due to the thermal motion of the atom, but incorporate
the ground-state decoherence rate of 1 MHz, mimicking the
Fig. 9. Calculated CBL gain as a function of either pump Rabi
frequency. While the Rabi frequency of one of the pump fields
is varied, the other is maintained at its maximum value of 5 ×
1010 Hz. In (a) the Rabi frequencies change in the range similar
to those used for experimental data in Fig. 4. In (b) the range
of variation is increased by a factor of 10 to display the more
complete power dependence. For these simulations we used
parallel circular polarizations for all optical fields; however,
the same general behavior is observed for other polarization
configurations.
Research Article
Journal of the Optical Society of America B
6
6. CONCLUSION
Fig. 10. Calculated CBL gain as a function of repump Rabi
frequency. For these simulations we used parallel circular
polarizations for all optical fields, and the Rabi frequencies
of the lower and upper pump fields of 2 × 1010 Hz and 5 ×
1010 Hz, corresponding to the calculated maximum CBL gain.
We also calculated the dependence of CBL yield on the repump laser strength. As expected, efficient repumping of atomic
population from uncoupled ground state magnifies the CBL gain
significantly, reaching saturation. This is qualitatively the same
behavior as observed experimentally in Fig. 8, when a more
powerful D1 laser served as a repumper. Because of the lower
maximum available output of the D2 laser and its stronger resonant absorption, we did not achieve such saturation when it
was used for repumping, and the corresponding line at Fig. 4
resembles the lower end of the simulated curve.
Finally, we can check the effect of the polarizations of the
pump fields. Fig. 11 presents the results of the simulations of
CBL gain for the four polarization configurations tested in the
experiment. While inclusion of accurate Zeeman and hyperfine
atomic structure is necessary to match the experimentally measured dependences, the simplified simulations still display some
general features, characteristic to the observations. For example, in the simulations for both linearly and circularly polarized
pump fields, larger CBL gain is observed when the two pumps
have parallel, rather than orthogonal. We also verified that the
observed changes in CBL strength for different polarizations is
general, and not specific for particular values of pump powers.
For that we replicated the CBL gain dependence on the lower
pump Rabi frequency, shown in Fig. 11(b).
In conclusion, we report on characterization of the collimated
blue light generation via two-photon excitation from the 85 Rb
5S1/2 ground state to the 5D3/2 excited state through either
5P1/2 or 5P3/2 intermediate levels. We have studied the characteristics of the generated blue light for various pump laser
frequencies, and found that the polarization arrangement leading to the maximum CBL power output strongly depends on
the optical transitions used. This indicates the importance of
selection rules and individual Zeeman transition probabilities.
The experimental results shared various qualitative characteristics with the theoretical simulation. We found that under the
optimized experimental conditions the blue light output was
noticeably stronger when the D1 optical transition was used
as the first excitation step. In the case of the D1 resonant excitation we demonstrated the existence of the optimal pump
powers that led to maximum blue output. For other situations
(off-resonant D1 excitation or resonant D2 excitation) a linear
dependence of output CBL power on the lower pump power
was detected. Theoretical simulations allow us to explain this
behavior: for each set of experimental parameters there seems
to be an optimal ratio between the lower and upper pumps that
lead to maximum CBL yield. Any deviations from this value
result in sub-optimal population redistribution between the involved atomic transitions, and in the reduction of blue light
generation. In case of the D1 resonant excitation we were able
to realize such optimal conditions for the lower pump power.
For the other configurations, however, we were limited to the
initial rising power dependence, before the CBL maximum was
reached. Our measurements and simulation also demonstrated
the importance of the repumping of atomic population from the
uncoupled ground state sublevels, that led to an order of magnitude increase in blue light generation in all tested configurations.
A more detail simulation and further study may shed light on
the specific temperatures, powers, and polarizations for a better
optimized and efficient CBL generation.
7. AKNOWLEDGENETS
This research was supported by the National Science Foundation
grant PHY-308281. We would like to thank S. Rochester for making the Mathematica package AtomicDensityMatrix available
on-line that enabled us to carry out the numerical simulations.
REFERENCES
Fig. 11. (a) Calculated CBL gain as a function of lower pump
frequency for the four polarization arrangements tested in the
experiment. For these simulations the Rabi frequencies of the
lower and upper pump fields of 2 × 1010 Hz and 5 × 1010 Hz,
and the upper pump was resonant with the corresponding optical transition. (b) Modification of the CBL gain lower power
dependence for different polarization arrangements. The simulation parameters are identical to those using in Fig. 9.
1. H.-A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum
Optics (Wiley-VCH, USA, 2004), 2nd ed.
2. R. W. Boyd, M. S. Malcuit, D. J. Gauthier, and K. Rza¸ewski, “Competition
between amplified spontaneous emission and the four-wave-mixing
process,” Phys. Rev. A 35, 1648–1658 (1987).
3. W. R. Garrett, “Forward gain suppression of optically pumped stimulated
emissions due to self-induced wave-mixing interference during a pump
pulse,” Phys. Rev. Lett. 70, 4059–4062 (1993).
4. A. I. Lvovsky, S. R. Hartmann, and F. Moshary, “Omnidirectional superfluorescence,” Phys. Rev. Lett. 82, 4420–4423 (1999).
5. A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins,
A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecomwavelength conversion,” Nature Photon. 6, 894–899 (2010).
6. K. T. Kaczmarek, P. M. Ledingham, B. Brecht, S. E. Thomas, G. S.
Thekkadath, O. Lazo-Arjona, J. H. D. Munns, E. Poem, A. Feizpour, D. J.
Saunders, J. Nunn, and I. A. Walmsley, “A room-temperature noise-free
quantum memory for broadband light,” (2017).
7. N. Prajapati, G. Romanov, and I. Novikova, “Suppression of four-wave
Research Article
mixing in hot rubidium vapor using ladder scheme raman absorption,” J.
Opt. Soc. Am. B 34, 1994–1999 (2017).
8. G. O. Ariunbold, V. A. Sautenkov, and M. O. Scully, “Quantum fluctuations
of superfluorescence delay observed with ultrashort optical excitations,”
Physics Letters A 376, 335 – 338 (2012).
9. A.S.Zibrov, M.D.Lukin, L.Hollberg, and M.O.Scully, “Efficient frequency
up-conversion in resonant coherent media,” Phys. Rev. A 65, 051801
(2002).
10. A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Coherent
and collimated blue light generated by four-wave mixing in rb vapour,”
Opt. Express 17, 22861–22870 (2009).
11. A. Vernier, S. Franke-Arnold, E. Riis, and A. S. Arnold, “Enhanced
frequency up-conversion in rb vapor,” Opt. Express 18, 17020–17026
(2010).
12. E. Brekke and L. Alderson, “Parametric four-wave mixing using a single
cw laser,” Opt. Lett. 38, 2147–2149 (2013).
13. M. B. Kienlen, N. T. Holte, H. A. Dassonville, A. M. C. Dawes, K. D.
Iversen, R. M. McLaughlin, and S. K. Mayer, “Collimated blue light
generation in rubidium vapor,” American Journal of Physics 81, 442–449
(2013).
14. J. F. Sell, M. A. Gearba, B. D. DePaola, and R. J. Knize, “Collimated
blue and infrared beams generated by two-photon excitation in rb vapor,”
Opt. Lett. 39, 528–531 (2014).
15. A. Akulshin, D. Budker, and R. McLean, “Directional infrared emission
resulting from cascade population inversion and four-wave mixing in rb
vapor,” Opt. Lett. 39, 845–848 (2014).
16. E. Brekke and E. Herman, “Frequency characteristics of far-detuned
parametric four-wave mixing in rb,” Opt. Lett. 40, 5674–5677 (2015).
17. T. Meijer, J. D. White, B. Smeets, M. Jeppesen, and R. E. Scholten,
“Blue five-level frequency-upconversion system in rubidium,” Opt. Lett.
31, 1002–1004 (2006).
18. Y.-S. Lee and H. S. Moon, “Atomic coherence effects in four-wave
mixing process of a ladder-type atomic system,” Opt. Express 24, 10723–
10732 (2016).
19. A. M. Akulshin, D. Budker, and R. J. McLean, “Parametric wave mixing
enhanced by velocity-insensitive two-photon excitation in rb vapor,” J.
Opt. Soc. Am. B 34, 1016–1022 (2017).
20. E. Brekke and S. Potier, “Optical cavity for enhanced parametric fourwave mixing in rubidium,” Appl. Opt. 56, 46–49 (2017).
21. G. Walker, A. S. Arnold, and S. Franke-Arnold, “Trans-spectral orbital
angular momentum transfer via four-wave mixing in rb vapor,” Phys. Rev.
Lett. 108, 243601 (2012).
22. A. M. Akulshin, R. J. McLean, E. E. Mikhailov, and I. Novikova, “Distinguishing nonlinear processes in atomic media via orbital angular
momentum transfer,” Opt. Lett. 40, 1109–1112 (2015).
23. A. M. Akulshin, I. Novikova, E. E. Mikhailov, S. A. Suslov, and R. J.
McLean, “Arithmetic with optical topological charges in stepwise-excited
rb vapor,” Opt. Lett. 41, 1146–1149 (2016).
24. B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich,
and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs
via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111,
123602 (2013).
25. B. Srivathsan, G. K. Gulati, A. Cerè, B. Chng, and C. Kurtsiefer, “Reversing the temporal envelope of a heralded single photon using a cavity,”
Phys. Rev. Lett. 113, 163601 (2014).
26. M. Parniak and W. Wasilewski, “Interference and nonlinear properties
of four-wave-mixing resonances in thermal vapor: Analytical results and
experimental verification,” Phys. Rev. A 91, 023418 (2015).
27. A. Leszczyński, M. Parniak, and W. Wasilewski, “Phase matching alters
spatial multiphoton processes in dense atomic ensembles,” Opt. Express
25, 284–295 (2017).
28. T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L.
Gould, “Two-photon two-color diode laser spectroscopy of the rb 5 d 5/2
state,” Physica Scripta 52, 271 (1995).
29. N. B. Phillips, I. Novikova, E. E. Mikhailov, D. Budker, and S. Rochester,
“Controllable steep dispersion with gain in a four-level n-scheme with
four-wave mixing,” Journal of Modern Optics 60, 64–72 (2013).
Journal of the Optical Society of America B
7