Spin-photon interaction in a cavity with time-reversal symmetry breaking

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 polarized 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 subensemble of two-level systems with different energy splittings. In the experimental example, these subensembles originate from Fe3+ impurity ions effectively seen as a two-level system at the interaction frequency. The temperature dependence of the population of each subensemble (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.