Nonlinear superconducting ring resonator for sensitive measurement of time reversal symmetry broken order

Time-reversal symmetry breaking (TRSB) has been central to detecting exotic phases of matter, often linked to complex superconducting order parameters or unique magnetic phenomena. Here, we leverage circuit electrodynamics capabilities of superconducting devices to propose a novel scheme based on a multimode superconducting ring resonator for sensitive probing of TRSB in quantum materials. Our device enables strong nonlinear interactions between the modes and we show that these interactions can lead to highly symmetric configurations which are sensitive to TRSB. 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. When TRSB coupling is introduced, the critical behavior of the system serves as a highly sensitive detection method. Specifically, by mapping out 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 can be broken even with weak TRSB. Our findings highlight the utility of superconducting microwave resonators other than quantum information processing as a tool for probing exotic states of matter.