Precision oscillator measurements to search for ultralight axions with twisted cavity resonators of anyon rotational symmetry with bulk modes of nonzero helicity*

Möbius-ring resonators stem from a well-studied and fascinating geometrical structure, which features a one-sided topology, the Möbius strip, and have been shown to exhibit fermion rotational symmetry with respect to a ring resonator with no twist (which exhibits boson rotational symmetry) [1]. Here, we present a new type of resonator through the formation of twisted hollow structures using equilateral triangular cross sections, which leads to the realization of a cavity with anyon rotational symmetry [2]. Unlike all previous cavity resonators, the anyon resonator permits the existence of bulk resonant modes that exhibit nonzero electromagnetic helicity in vacuo, with nonzero overlap of the electric and magnetic mode eigenvectors, integrated over the cavity volume. In the upconversion limit, we show that these nonzero helical modes couple naturally to ultralight dark matter axions within the bandwidth of the resonator by adding amplitude-modulated sidebands through the axion-photon chiral anomaly. Thus, we show a sensitive ultralight dark matter experiment may be realized by implementing such a resonator in an ultrastable oscillator configuration and searching for signals in the Fourier spectrum of amplitude fluctuations. This removes the typical requirement for an external magnetic field and therefore permits the use of superconducting materials to reduce surface losses and enhance sensitivity to axions.

[1] DJ Ballon, HU Voss, Classical Möbius-Ring Resonators Exhibit Fermion-Boson Rotational Symmetry, Phys. Rev. Lett. 101, 247701 (2008).

[2] JF Bourhill, ECI Paterson, M Goryachev, ME Tobar, Searching for ultralight axions with twisted cavity resonators of anyon rotational symmetry with bulk modes of nonzero helicity, Phys. Rev. D. 108, 052014, 2023.