Probing time-reversal-symmetry breaking using a nonlinear superconducting ring resonator

Time-reversal-symmetry breaking (TRSB) has been central to detecting exotic phases of matter. Here, we leverage the circuit electrodynamics capabilities of superconducting devices to propose a scheme based on a multimode superconducting ring resonator for the sensitive probing of TRSB in quantum materials. A ring resonator enables nonlinear cross-interactions between the modes which act as built-in amplifiers to be harnessed for enhanced sensing. Using a driven-dissipative model, we explore the nonlinear dynamics of a two-mode superconducting circuit with self- and cross-Kerr nonlinearities under conditions near the bifurcation threshold. By mapping the optimal parameter regimes, we show that even when the photon occupation numbers are subjected to different initial conditions, they can be driven into a symmetric configuration which is broken even with weak TRSB. Through a full quantum analysis we demonstrate that the Kerr-nonlinear interactions up-convert the magnetic effects of the material-resonator hybrid system, enhancing the probing of TRSB. Our findings highlight the utility of superconducting microwave resonators outside of quantum information processing, as a tool for probing exotic states of matter.