Quantum simulation of the nonlinear bosonic Kitaev chain in a parametric cavity

Multimode superconducting parametric cavities have been demonstrated as a versatile platform for analog quantum simulation. Cavity modes represent lattice sites in synthetic dimensions, and tunable interactions between these modes are created in-situ by parametrically driving a superconducting quantum interference device (SQUID), which terminates the cavity, with external flux pumps. Here we numerically study the nonlinear bosonic Kitaev chain model realized in a multimode cavity. The sites in the chain are coupled by external hopping and pairing drives, and further subjected to single-photon losses and Kerr nonlinearity. Above the threshold for the pairing strength, we show that apart from the usual bistable behavior in Kerr parametric oscillators, the system allows a dissipation-induced time crystal phase, in which the delayed temporal correlation functions exhibit sustained oscillations in the steady state.