Dielectric Haloscopes as Gravitational Wave Detectors

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Preprint
Report number	CERN-TH-2024-151 ; arXiv:2409.06462
Title	Dielectric Haloscopes as Gravitational Wave Detectors
Author(s)	Domcke, Valerie (CERN) ; Ellis, Sebastian A.R. (Geneva U., Dept. Theor. Phys.) ; Kopp, Joachim (CERN ; Mainz U.)
Imprint	2024-09-10
Number of pages	8
Note	12 + 8 pages, 6 + 3 figures
Subject category	hep-ex ; Particle Physics - Experiment ; gr-qc ; General Relativity and Cosmology ; astro-ph.IM ; Astrophysics and Astronomy ; hep-ph ; Particle Physics - Phenomenology
Abstract	We argue that dielectric haloscopes like MADMAX, originally designed for detecting axion dark matter, are also very promising gravitational wave detectors. Operated in resonant mode at frequencies around $\mathcal{O}(10\,\text{GHz})$, these detectors benefit from enhanced gravitational wave to photon conversion at the surfaces of a stack of thin dielectric disks. Since the gravitational wave is relativistic, there is an additional enhancement of the signal compared to the axion case due to increased conversion probability of gravitational waves to photons in the vacuum between the disks. A gravitational wave search using a dielectric haloscope imposes stringent requirements on the disk thickness and placement, but relaxed requirements on the disk smoothness. An advantage is the possibility of a broadband or hybrid resonant/broadband operation mode, which extends the frequency range down to $\mathcal{O}(100\,\text{MHz})$. We show that strain sensitivities down to $10^{-21} \text{Hz}^{-1/2} \times (10\,\text{GHz}/f)$ will be possible in the coming years for the broadband setup, while a resonant setup optimized for gravitational waves could even reach $3\times 10^{-23} \text{Hz}^{-1/2} \times (10\,\text{GHz}/f)$ with current technology.
Other source	Inspire
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0)

$Schematic setup of a dielectric gravitational wave detector of length $\ell$ with only two disks (light blue). The thickness of the disks is inflated here to show more clearly the trajectories inside. In reality, $d \ll \ell, \, R$. The incoming GW is depicted as dotted green line, the sourced electromagnetic waves are shown in solid purple. At each disk surface, boundary conditions enforce the presence of both left-moving ($L_i$) and right-moving ($R_i$) EM plane waves. The full field at the receiver $E_{\rm rec}(\ell)$ is the sum of all the right-moving waves plus the particular solution of Maxwell's equations in the presence of the GW source. We use the transfer matrix formalism described in \cref{sec:TransferMatrix} to compute the relevant quantities. The receiver is depicted as a dipole antenna at the right end of the setup.$ $The reflection coefficient $|\mathsf{r}_R|$ (blue solid) and effective source terms $|(M_{\rm tot})_R|/25$ (red dotted) and $|(M_{\rm tot})_L|/25$ (green dashed) as a function of $D$ in units of $\w/\pi$ for $N_d = 5$ and $\epsilon = 25$. We see that the analytical result \cref{eq:lmax}, which corresponds to the dotted vertical line, also corresponds to the largest value of $(M_{\rm tot})_R$ that coincides with a zero of $|\mathsf{r}_R|$ (horizontal grid line). From \cref{eq:ErecDet}, we see that this value of $D$ maximises the received electric field.$ $Performance of a dielectric haloscope operated in resonant mode with \emph{variable} detector length $\ell = (N_d+1) D_{\rm max} + N_d \, d_{\rm max}$. \textbf{\textit{Upper panel:}} Poynting vector ratio $|\vec{S}|/|\vec{S}_{\rm vac}|$ as a function of the number of disks for perfect disk placement ($D_\text{max}$) and thickness ($d_\text{max}$). Different colored curves correspond to different values of the dielectric constant $\epsilon$. The curves demonstrate the $\vec{S} \propto N_d^2$ growth until a plateau is reached for $N_d \gtrsim 10\sqrt{\epsilon}$. \textbf{\textit{Lower panel:}} Fixing $\epsilon = 25$, we study the impact of imperfect disk placement (red curve) and imperfect disk thickness (yellow curve) compared to case of the perfect $D_\text{max}$ and $d_\text{max}$ (blue). Also shown is a polynomial fit $\vec{S}\propto N_d^2$ in dashed blue.$ Show more plots

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Record created 2024-09-12, last modified 2024-11-11

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