Spin-Photon Interaction in a Cavity with Time-Reversal Symmetry Breaking

TL;DR

This paper investigates spin-photon interactions in a cavity with broken time-reversal symmetry, demonstrating gyrotropic effects and modifying the Tavis-Cummings model to account for conservation laws, with experimental validation using Fe$^{3+}$ ions.

Contribution

It introduces a modified Hamiltonian for high-Q cavities with broken symmetry and experimentally verifies the temperature-dependent behavior of impurity spin ensembles.

Findings

Degeneracy lifting of polarized cavity photons observed.

Modified Tavis-Cummings Hamiltonian successfully describes the system.

Temperature dependence of impurity populations matches theoretical predictions.

Abstract

Employing a sapphire whispering gallery mode resonator, we demonstrate features of the spin-photon interaction in cavities with broken time-reflection symmetry. The broken symmetry leads to a lifting of the degeneracy between left-handed and right-handed polarised cavity photons, which results in an observable gyrotropic effect. In the high-$Q$ cavity limit, such a situation requires a modification of the Tavis-Cummings Hamiltonian to take into account conservation of spin angular momentum and the corresponding selection rules. As a result, the system is represented by a system of two linearly coupled bosonic modes, with each one coupled to its own sub-ensemble of two-level systems with different energy splittings. In the experimental example, these sub-ensembles originate from Fe$^{3+}$ impurity ions effectively seen as a two level systems at the interaction frequency. The temperature dependence of the population of each sub-ensemble (in terms of effective susceptibility of the medium) is determined experimentally in accordance with the theoretical predictions revealing various paramagnetic impurity types in the solid. The regimes of backscatterer and spin ensemble domination are discussed and compared.