Historical research guide · 0410 · 2022
Detecting high-frequency gravitational waves with microwave cavities
Asher Berlin · Diego Blas · Raffaele Tito D’Agnolo · Sebastian A. R. Ellis · Roni Harnik · Yonatan Kahn · Jan Schütte-Engel
In one minute
A gravitational wave is a ripple in the geometry of space itself. Berlin, Blas, D’Agnolo, Ellis, Harnik, Kahn and Schütte-Engel show that when such a ripple crosses a strong static magnetic field inside a metal cavity, it drives a tiny electric current and rings the cavity like a bell — so a microwave cavity is a metric detector. Their central contribution is bookkeeping done right: earlier calculations, working in a mathematically convenient coordinate frame, concluded that certain field geometries give no signal at all. Working instead in the laboratory’s own frame, and summing the effect to all orders rather than truncating it, the team shows that conclusion was an artefact of the coordinates. The practical payoff is immediate. Cavities already built and running to hunt axion dark matter — ADMX, HAYSTAC, ORGAN, CAPP — are already sensitive to gigahertz gravitational waves at strains near ten to the minus twenty-two, and need only reanalyse data they have already taken. Reading several cavity modes at once could even give the wave’s direction.
Connection
Chapter 4 argues that the metric is a thing you can act on and measure; this paper supplies the laboratory instrument that reads a metric perturbation directly, turning a ripple in spacetime into an electric current you can amplify. Chapter 11 cares because the conversion is exactly the electromagnetism-to-gravity coupling the site follows, and because the next factor of sensitivity comes from superconducting cavity technology already being built at Fermilab.
From the source
A gravitational wave crossing a static external magnetic field sources an oscillating electromagnetic field at the wave’s own frequency. In the language of classical fields the wave acts as an effective current of size given by the wave frequency times the strain times the background field, producing a signal field of amplitude equal to the strain times the background field. At the level of single quanta this is graviton-photon mixing in a background magnetic field, the inverse Gertsenshtein effect.Sec. II, opening; Eqs. (1)–(2)
Because gravitational-wave signals are usually computed in the transverse-traceless gauge, where the background field and the cavity modes no longer coincide with their flat-space forms, several earlier studies concluded that no electromagnetic signal is generated when the background magnetic field is aligned with the wave’s direction of propagation. That statement is at odds with gauge invariance. Computing in the proper detector frame — the laboratory’s own frame — and resumming the metric perturbation to all orders in detector size over wavelength gives analytic results that are exact for waves of arbitrary wavelength.Abstract; Sec. I; Sec. II
Cavity experiments already built and operating to search for axion dark matter therefore have sensitivity to gigahertz gravitational waves, and need only reanalyse existing data with a different signal template. With parameters similar to ADMX — 8 T field, 0.1 cubic metre cavity, quality factor 100000, one-kelvin system temperature, one minute of integration — the reach is a strain of about 3 times 10⁻²², and a phase-sensitive matched-filter readout improves it to about 1 times 10⁻²³.Abstract; Sec. V A, Eqs. (29) and (30); Fig. 4
The geometry of the graviton-induced current differs from the axion case, so the two obey different cavity selection rules. For a wave travelling along the axis of a cylindrical cavity with the magnetic field also along that axis, only modes with azimuthal index 2 couple — a direct fingerprint of the spin-2 nature of the gravitational field. Tilting the magnetic field away from the cavity axis introduces a spin-1 component that couples to azimuthal-index-1 modes. Across a large fraction of solid angle the coupling coefficient is of order 0.1, including for the TM010 and TM020 modes already used by ADMX and ORGAN.Sec. III B; Sec. V; Sec. V B
Because the signal structure depends strongly on the incoming direction and polarisation of the wave, reading multiple cavity modes, or several cavities, would in principle allow the source to be localised on the sky and its polarisation determined — directional gravitational-wave detection from a tabletop instrument.Abstract; Sec. V; Sec. VI
The gigahertz band has no known astrophysical sources, which is what makes it interesting: the candidates surveyed are mergers of sub-solar-mass compact objects such as primordial black holes, and annihilating boson clouds grown by black-hole superradiance. A merger sweeps its own frequency upward, so unlike an axion search the cavity need not be tuned; the source finds the resonance. Best-case strains estimated here are around 10⁻²³ for superradiant clouds and far smaller for inspirals, so the sources are the open question, and the sensitivity gap is what advances in superconducting cavities — quality factor 10⁷ at 6 T, under development at the SQMS Center at Fermilab — are aimed at closing.Sec. IV; Sec. V A; Sec. VI
The way in
https://doi.org/10.1103/PhysRevD.105.116011How to cite it
Asher Berlin, Diego Blas, Raffaele Tito D’Agnolo, Sebastian A. R. Ellis, Roni Harnik, Yonatan Kahn, Jan Schütte-Engel (2022) Detecting high-frequency gravitational waves with microwave cavities doi:10.1103/PhysRevD.105.116011