Probing Nonlinear Effects in Unconventional Superconductors using a Nonlinear Superconducting Ring Resonator

Sensing of Time-Reversal Symmetry Breaking (TRSB) is fundamental in the quest to probe novel phenomena in quantum matter and create new states of matter. Here, we propose a new scheme to probe TRSB using a superconducting multimode ring resonator for unconventional superconductors. Using a driven-dissipative approach, we explore the nonlinear dynamics of a two-mode superconducting circuit with self- and cross-Kerr nonlinearities under conditions far beyond the bifurcation threshold. The critical behavior of the system serves as a highly sensitive detection method, and by mapping out the optimal parameter regions, we show that the photon occupation numbers exhibit bistability where the relative photon occupations significantly change according to the strength of the interaction and pump. Our findings highlight the utility of superconducting microwave resonators not only in quantum information processing but also as diagnostic tools for probing exotic states of matter. This work lays the foundation for future studies into the detection of TRSB, other symmetry-breaking and other nonreciprocal phenomena in quantum matter.