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M\"obius-ring resonators stem from a well-studied and fascinating geometricalstructure that features a one-sided topology; the M\"obius strip, and have beenshown to exhibit fermion rotational symmetry with respect to a ring resonatorwith no twist (which exhibits boson rotational symmetry) (seePhysRevLett.101.247701). Here, we present a new type of resonator through theformation of twisted hollow structures using equilateral triangularcross-sections, which leads to the realization of a cavity with anyonrotational symmetry. Unlike all previous cavity resonators, the anyon resonatorpermits the existence of bulk resonant modes that exhibit non-zeroelectromagnetic helicity in vacuo, with a non-zero overlap of the electric andmagnetic mode eigenvectors, $\int \mathbf{E}_p\cdot\mathbf{B}_p~d\tau$,integrated over the cavity volume. In the upconversion limit, we show thatthese non-zero helical modes couple naturally to ultra-light dark matter axionswithin the bandwidth of the resonator by adding amplitude-modulated sidebandsthrough the axion-photon chiral anomaly. Thus, we show a sensitive ultra-lightdark matter experiment may be realized by implementing such a resonator in anultra-stable oscillator configuration and searching for signals in the Fourierspectrum of amplitude fluctuations. This removes the typical requirement for anexternal magnetic field and therefore permits the use of superconductingmaterials to reduce surface losses and enhance sensitivity to axions.

Searching for Ultra-Light Axions with Twisted Cavity Resonators of Anyon Rotational Symmetry with Bulk Modes of Non-Zero Helicity