Signatures of High-Frequency Gravitational Waves in Electromagnetic Cavities

TL;DR

The paper tackles high-frequency gravitational waves by exploiting the inverse Gertsenshtein effect in electromagnetic cavities, deriving a TT-gauge framework to connect GW strain to resonant cavity excitations. It introduces a dimensionless coupling coefficient $\eta_n^{+,\times}$ and analyzes both cylindrical and spherical geometries, showing how the deposited energy and resulting antenna power depend on mode structure, degeneracy, and the incidence angle relative to an external magnetic field. For monochromatic signals near resonance, the energy deposition is captured by the overlap between the GW-induced current and cavity modes; for non-monochromatic signals, especially PBH-merger–driven transients, the signal is constrained by decoherence from the time-varying frequency and by the cavity quality factor, limiting the practical sensitivity. The study finds that, even under favorable conditions, high $Q$ does not always improve sensitivity to transient GHz GWs, and observable signals from PBH mergers require very nearby sources (within the solar system); nonetheless, the framework suggests that arrays of cavities or multi-mode excitations could enhance reach and sky coverage in future experiments.

Abstract

Similar to axions, gravitational waves (GW) can induce oscillating electromagnetic fields inside electromagnetic cavities. We explore their experimental sensitivity to monochromatic and non-monochromatic GW signals, using the total deposited energy as a primary measure. Focusing on cylindrical and spherical cavities, we present the coupling coefficients of GWs to the dominant electromagnetic resonances in transverse-traceless gauge, which is most appropriate in this regime. By considering the superposition of degenerate modes, we further examine their angular sensitivity. In addition, we calculate the response of a spherical cavity to non-monochromatic GWs emitted by primordial black hole mergers. We find that, for transient signals, a high quality factor with $Q \gtrsim 10^5$ does not necessarily enhance experimental sensitivity. In fact, even in the most optimistic scenario, only mergers within the solar system yield an observable energy deposit in the cavity.

Figures (10)

• Figure 1: Coupling coefficients $\eta^{+,\times}_{npq}$ of the TE (top) and TM modes (bottom) of a cylindrical cavity as a function of the incidence angle $\alpha$ of the incoming GW, parametrized in TT gauge. The different colors illustrate the longitudinal quantum numbers $q=0$ (solid blue), $q=1$ (dashed green), and $q=2$ (dotted orange), while the principal quantum number is fixed, $p=1$. In both rows, the azimuthal quantum number $n$ is increased to the right, with $n=0$ (left), $n=1$ (center), and $n=2$ (right). Note that the cylinder dimensions are chosen such that $R=L$, and that different polarizations are shown for the top and bottom panels.
• Figure 2: Coupling coefficients $\eta^{+,\times}_{np}$ of the TE (top) and TM modes (bottom) of a spherical cavity as a function of the incidence angle $\alpha$ of the incoming GW, parametrized in the TT frame. The different colors illustrate the azimuthal quantum numbers $n=1$ (solid blue), $n=2$ (dashed green), and $n=3$ (dotted orange), while the principal quantum number is fixed, $p=1$. The modes are $(2n+1)$-fold degenerate with respect to the azimuthal quantum number, which is hence marginalized in this example (see main text).
• Figure 3: Similar to \ref{['fig:etasCylindrical']}, but with dimensions $L / R = 6$.
• Figure 4: Integrated coupling coefficient, $\int \mathrm{d} t \, \eta$, of a monochromatic GW source corresponding to a low-lying TM mode of a cylindrical (left) and a spherical (right) cavity, as a function of galactic longitude $l$ and latitude $b$. Both experiments are assumed to be set up in Mainz, Germany, with an external magnetic field normal to the Earth's surface and a measurement integration period of 24 hours. For the geometry of the cylindrical cavity we assume $L/R = 6$. Note that the colored contours are shown in arbitrary units.
• Figure 5: Rescaled mode functions $\epsilon_n$ as a function of dimensionless time $\tau$, for different quality factors, $Q_n=10$ (top), $Q_n=100$ (center), and $Q_n=1000$ (bottom). The scanning rate is chosen as $\chi / \omega_n^2 = 10^{-3}$ and the cavity's resonant frequency is reached at $\tau_n = 200$.