Historical research guide · 0873 · 2022

Novel Search for High-Frequency Gravitational Waves with Low-Mass Axion Haloscopes

Valerie Domcke · Camilo Garcia-Cely · Nicholas L. Rodd

In one minute

A gravitational wave is a ripple in the shape of space. Valerie Domcke, Camilo Garcia-Cely and Nicholas Rodd point out that when one crosses a strong laboratory magnet, it stirs up a faint electrical signal — and that the machines built to hunt axion dark matter are already exactly the machines that could catch it. The trick is an analogy: a passing wave modifies electromagnetism in almost the same way a passing axion does, so the same magnet and pickup loop respond to both. The authors work out the size of the signal for a doughnut-shaped magnet, recast published data from two existing experiments as the first limits of their kind on megahertz gravitational waves, and project the reach of the DMRadio programme now being built. Then they find something practical: the ordinary circular pickup loop cancels the leading part of the wave signal, and a loop shaped like a figure eight brings it back. Bigger magnets help the wave search faster than they help the axion search.

Connection

Chapter 4 is about engineering the metric with electromagnetic fields, and this is the same coupling run the other way — the graviton-two-photon vertex used as an instrument, so that a change in the shape of space becomes a current in a coil. Chapter 10 gets a precise account of how the geometry of a magnet and its pickup loop decides which part of a passing wave is visible at all. Chapter 1 gets a live measurement floor from 100 kilohertz to 100 megahertz with named experiments attached, and a named improvement that costs almost nothing to build. The same team’s fuller treatment, deriving the symmetry selection rules behind all of this, is on the site at /library/stm-259fcab99d.

From the source

A gravitational wave modifies electromagnetism in a way that can be written as an effective current, with effective polarisation and magnetisation vectors built from the metric perturbation and the background fields. This is the same form the axion takes, with the axion’s polarisation and magnetisation given by its coupling times the field — so near large static electric or magnetic fields a passing wave sources oscillating fields at the wave frequency.Gravitational Wave Electrodynamics, Eqs. (1) and (2)
Matching the strain sensitivity of these instruments to the axion-photon coupling they are designed to reach for the QCD axion sets the scale of what is potentially detectable at a strain of about ten to the minus twenty-two. Cosmological wave sources are held below that by limits on the total radiation content of the Universe, so the promising targets are rare exotic astrophysical sources such as binaries of light primordial black holes.Gravitational Wave Electrodynamics, paragraph beginning ‘We can extend this analogy’
Working in the proper detector frame, the effective current and the fields it induces are rapidly suppressed for frequencies below the inverse length scale of the instrument, and suppressed further if the experiment is highly symmetric. For a circular pickup loop inside a toroidal magnet the plus polarisation decouples entirely and the expected second-order-in-frequency flux cancels, because the second-order Bessel function begins at the square of its argument, leaving a leading flux that goes as the cube of the frequency.Application to a Toroidal Magnetic Field, Eqs. (4), (8) and (9)
Replacing the circular pickup loop with a figure-eight made of two oppositely oriented semicircles restores the second-order term and makes the instrument sensitive to both polarisations. The gravitational-wave flux then carries an extra power of the loop radius relative to the axion flux, so that once the minimal inductance of the loop is accounted for it scales as the seven-sixths power of the volume where the axion flux scales as the five-sixths power.The figure-8 configuration, Eqs. (12) and (13)
Published measurements from ABRACADABRA-10 cm and SHAFT can already be recast as limits on gravitational waves in the 100 kilohertz to 100 megahertz band, and the DMRadio instruments now being built extend the reach substantially: with no modification at all, DMRadio-m³ reaches a strain sensitivity of about ten to the minus twenty at 200 megahertz.Abstract; Gravitational Wave Sensitivity; Fig. 3
The open questions the authors name are concrete. Lumped-element instruments have so far only measured where the frequency is far below the inverse radius, so results at higher frequency would be particularly welcome; the regime where the frequency approaches the inverse radius, in which the Biot-Savart law alone is insufficient, has not been quantified even for axions; and extending the treatment to the solenoidal geometry used by ADMX SLIC and planned for DMRadio-m³ matters for the programme.Conclusions, second paragraph

The way in

https://doi.org/10.1103/PhysRevLett.129.041101

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

LICENCE. Two records establish the Creative Commons grant. The arXiv posting of this paper, arXiv:2202.00695v2, submitted 3 May 2022, carries CC BY 4.0 on its abstract page, and the Crossref licence record for the version of record in Physical Review Letters names creativecommons.org/licenses/by/4.0 as well, with Unpaywall and OpenAlex both reporting the article as open access under CC BY. TEXT. The publisher’s server declines automated retrieval, so the text below is taken from the arXiv copy, which is the one carrying the explicit grant; it is version 2, the version that matches the published Letter, and it carries the report numbers DESY-22-017 and CERN-TH-2022-010. The complete Letter is reproduced — abstract, main text, conclusions, the note added and the acknowledgements. The two figures (the ultra-high-frequency landscape and the strain-sensitivity curves) and the detector schematic are plots that cannot be reproduced as text, the sixty-five-item reference list is omitted and is at the source, and reference-number markers are removed from the prose. The Supplementary Material — three sections deriving the gravitational wave in the proper detector frame, the effective current induced by a passing wave, and a review of possible sources in this band — is almost entirely displayed equations and is omitted for length; it is at the source. The equations in the main text reached the library with Greek letters, indices and vector arrows lost in extraction, so they are given as named results in plain words with their original numbers, and inequalities are written in words. Published as Valerie Domcke, Camilo Garcia-Cely and Nicholas L. Rodd, Physical Review Letters 129, 041101 (2022), from the Theoretical Physics Department at CERN, the Institute of Physics at EPFL Lausanne, and DESY Hamburg. The arXiv title begins ‘A novel search’; the journal title drops the article.

How to cite it

Valerie Domcke, Camilo Garcia-Cely, Nicholas L. Rodd (2022) Novel Search for High-Frequency Gravitational Waves with Low-Mass Axion Haloscopes doi:10.1103/PhysRevLett.129.041101

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