Cavity Multimodes as an Array for High-Frequency Gravitational Waves

TL;DR

High-frequency gravitational waves are difficult to detect with conventional networks. This work proposes a single multi-cell cavity as an internal detector array, exploiting the inverse Gertsenshtein effect to read out 18 mode responses. The authors show that the mode amplitudes carry directional and polarization information, with the signal-to-noise ratio scaling as $\mathrm{SNR}^2 \propto \sum_a Q_a^L (\omega_a^2 \eta_{\rm eff}^a)^2$, so the sensitivity improves as if you had $N$ detectors, i.e., $h_0 \propto N^{-1/2}$. A PBH-binary-inspired chirp waveform demonstrates recovery of eight GW parameters (direction, polarization ratio, phase, drift, etc.) from seven loud modes via MCMC, breaking degeneracies with the chirp parameters. The results point to a scalable path for HFGW astronomy and motivate extending the approach to networks and advanced readout schemes.

Abstract

Microwave cavities operated in the presence of a background magnetic field provide a promising avenue for detecting high-frequency gravitational waves (HFGWs). We demonstrate for the first time that the distinct antenna patterns of multiple electromagnetic modes within a single cavity enable localization and reconstruction of key properties of an incoming HFGW signal, including its polarization ratio and frequency drift rate. Using a 9-cell cavity commonly employed in particle accelerators as a representative example, we analyze the time-domain response of 18 nearly degenerate modes, which can be sequentially excited by a frequency-drifting signal. The sensitivity is further enhanced by the number of available modes, in close analogy to the scaling achieved by a network of independent detectors, enabling sensitivity to astrophysically plausible binary sources.

Figures (5)

• Figure 1: Electric-field configurations of the first three modes ($a = 1, 2, 3$) of the $\mathrm{TE}_{111+}$ family in a 9-cell elliptical TESLA cavity. The cavity symmetry axis is aligned with the $z$ axis. The left three panels show the electric fields on the $y=0$ plane and do not have perpendicular components. The right three panels show the fields on the $z=0$ plane in the center of the $5$-th cell, without perpendicular components. In each panel, arrow lengths are proportional to the normalized electric-field amplitude, normalized by maximum of each mode $|\vec{E}_a^{\rm max}|$. The corresponding $\mathrm{TE}_{111-}$ modes are obtained by a $\pi/2$ rotation about the cavity axis.
• Figure 2: Overlap functions $\eta_{+,\times}^a$ for GWs incident from direction $\hat{k} \equiv (\phi, \theta)$, shown for the $\mathrm{TE}_{111+}$ modes of the 9-cell cavity. For each mode, the GW frequency is taken to match the corresponding cavity resonance $\omega_a$. The plots are shown for $\phi, \theta \in (0, \pi/2)$; overlap functions in other regions of the sky, as well as those for the $\mathrm{TE}_{111-}$ modes, can be obtained via the symmetry relations discussed in Supplemental Material.
• Figure 3: Time evolution of the loudest cavity mode, $a=3$ ($\mathrm{TE}_{111+}$), characterized by the mode amplitude $e_3(t)$, for the benchmark GW waveform. The time axis is shifted by $t - t_3$, where $t_3$ denotes the moment when the GW frequency $\omega_g = |\vec{k}|$ (indicated on the upper axis) crosses the cavity resonance $\omega_3$.
• Figure 4: Posterior distributions for the GW waveform parameters $\vec{\Theta} = (\phi, \theta, h_0, \kappa, \xi, \delta_0, t_0, \alpha)$, where $(\phi,\theta)$ denote the GW propagation direction, $h_0$ is the GW strain amplitude, $\kappa$ and $\xi$ are the two polarizations’ ratio and relative phase, $t_0$ is the time at which the GW frequency reaches the first cavity resonance with phase $\delta_0$, and $\alpha$ is the frequency drift rate. The red solid lines indicate the true parameter values. On the diagonal panels, black solid lines mark the posterior modes, while dashed lines indicate the $1\sigma$ ($68\%$) credible intervals; the inferred values and corresponding uncertainties are listed at the top of each panel. In the off-diagonal panels, the $4$ shaded regions represent confidence levels of $38\%$, $68\%$, $86\%$, and $95\%$, respectively. Uniform priors are assumed within the figure range for each parameter.
• Figure S1: Side view of the 9-cell cavity along the $y$ direction. Two straight antenna couplers are employed: the left coupler predominantly reads out the $\mathrm{TE}_{111+}$ modes, while the right coupler reads out the $\mathrm{TE}_{111-}$ modes.