Historical research guide · 0598 · 2024
Symmetries and selection rules: optimising axion haloscopes for Gravitational Wave searches
Valerie Domcke · Camilo Garcia-Cely · Sung Mook Lee · Nicholas L. Rodd
In one minute
Valerie Domcke and her co-authors at CERN show that a machine built to hunt axions is already a gravitational-wave telescope. An axion and a passing gravitational wave both do the same thing when they cross a strong static magnetic field: they stir up a faint oscillating magnetic field that a pickup loop can catch. The team computes how large that signal is for the solenoid magnets used by ADMX SLIC, BASE and WISPLC, and then finds something more useful than any single number. The answer is fixed mostly by the shape of the instrument. Three selection rules, derived from symmetry alone, tell you the leading sensitivity of any cylindrical detector without doing the calculation — and they reveal that the very symmetry which maximises the axion signal cancels the leading wave signal. Break it slightly, by reshaping or repositioning the pickup loop, and the leading term comes back for an order-one price in axion reach.
Connection
This is chapter 4’s subject read backwards: instead of shaping an electromagnetic field to move the metric, it shapes an electromagnetic field to hear the metric move — the graviton-two-photon vertex turned into an instrument that already exists in half a dozen laboratories. It also gives chapter 10 a precise statement of how the geometry of a magnet and its pickup loop decides which part of a passing wave you can see at all, and chapter 1 a live measurement floor from 100 kHz to 100 MHz with named experiments attached to it.
From the source
A gravitational wave crossing a static laboratory magnetic field induces an oscillating magnetic field, in close analogy to the signal an axion produces through its coupling to two photons — so the instruments already built to search for wave-like dark matter can be used as gravitational-wave telescopes in the megahertz band.Section 1; Section 2.2, Equations 2.5 to 2.8
Working in the proper detector frame, where coordinate distance to the origin equals proper distance, the metric perturbation has no first-order term: it begins at second order in the product of wave frequency and instrument size, so the best electromagnetic observable available in a rigid instrument also scales at that second order.Section 2.1, Equation 2.1 and the discussion following it
Three selection rules follow from symmetry alone: an azimuthally symmetric instrument sees only the plus polarisation at leading order; it responds to one polarisation and one only, at every order; and with full cylindrical symmetry its flux is either an even or an odd function of frequency. Together these fix the leading power of any cylindrical detector without an explicit calculation.Section 4.1, Selection rules 1, 2 and 3; Table 3
Because the axion transforms under parity like the cross polarisation, an instrument shaped to maximise the axion signal is forced into precisely the geometry where the leading gravitational-wave flux cancels; breaking the pickup loop’s azimuthal symmetry — a partial opening angle, an offset, or a figure-eight winding — restores the leading term at a cost of only an order-one factor in axion sensitivity.Section 4, opening summary; Section 4.2, Equation 4.8
The analysis adds a contribution earlier work had overlooked: an effective surface current at the boundary of the magnetic volume, set by the component of the effective magnetisation parallel to that surface. It is generically the same order as the bulk effect and corrects the toroidal horizontal-pickup-loop result by a factor of one third.Section 1, closing paragraphs; Section 5, first technical improvement
Recasting published axion limits gives strain sensitivity across roughly 100 kHz to 100 MHz for ABRACADABRA, BASE, ADMX SLIC, SHAFT, WISPLC and the DMRadio programme — ADMX SLIC’s best estimate is a strain of about 1.7 times 10 to the minus 16 for a persistent plane wave — which is competitive with other concepts in this band and still above expected astrophysical and cosmological signals.Section 3.2; Fig. 3 and Table 2
The way in
https://doi.org/10.1007/JHEP03(2024)128How to cite it
Valerie Domcke, Camilo Garcia-Cely, Sung Mook Lee, Nicholas L. Rodd (2024) Symmetries and selection rules: optimising axion haloscopes for Gravitational Wave searches doi:10.1007/JHEP03(2024)128