Quantum tunneling and level crossings in the squeeze-driven Kerr oscillator

The quasienergy spectrum of a squeeze-driven Kerr oscillator was recently measured with a SNAIL transmon superconducting circuit and showed good agreement with the low-level energy spectrum of the oscillator's corresponding static effective Hamiltonian. In this presentation, we provide a detailed analysis of the spectrum and the dynamics of the effective model up to high energies, which should soon be within experimental reach. The spectrum exhibits real (avoided) level crossings for specific values of the Hamiltonian parameters, which can then be chosen to suppress (enhance) quantum tunneling. The parameter values for the crossings can be obtained from a semiclassical approach and can also be identified directly from the dynamics. Our analysis of quantum tunneling is done with the effective flux of the Husimi volume of the evolved states between different regions of the phase space. Both initial coherent states and quench dynamics are considered. We argue that the level crossings and their consequences on the dynamics are typical to any quantum system with one degree of freedom, whose density of states presents a local logarithmic divergence and a local step discontinuity.