Seminar by Mark Dykman, Michigan State University

Title: Parametric oscillators: from anomalous tunneling to a nonreciprocal Ising model

Abstract: Parametric resonance has been known for millennia, but mesoscopic systems -- such as microwave cavity modes, cold atoms, and nanomechanical resonators -- have breathed new life into this phenomenon. These systems enabled studying parametric resonance not only in the classical but also in the quantum domain. A notable application is qubits based on cat states, which are eigenstates of a parametric oscillator. Beyond applications, parametric oscillators offer a way to uncover some generic features of systems far from thermal equilibrium. In this talk, I will touch on quantum activation, a phenomenon with no counterpart in equilibrium systems. I will also talk about new experiments that demonstrated quantum tunneling accompanied by underbarrier interference. A broad area is the many-body effects that emerge when parametric oscillators are coupled. A weakly disordered system provides a long-sought physical implementation of the asymmetric, or nonreciprocal, Ising model. Here, unexpectedly, disorder leads to a stationary current in the system. Time permitting, I will touch on classical and quantum phase transitions to many-body states with broken discrete time translation symmetry, both in the coherent and dissipative regime.