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

Abstract

The quasi-energy spectrum recently measured in experiments with a squeeze-driven superconducting Kerr oscillator showed good agreement with the energy spectrum of its corresponding static effective Hamiltonian. The experiments also demonstrated that the dynamics of low-energy states can be explained with the same emergent static effective model. The spectrum exhibits real (avoided) level crossings for specific values of the Hamiltonian parameters, which can then be chosen to suppress (enhance) quantum tunneling. Here, we analyze the spectrum and the dynamics of the effective model up to high energies, which should soon be within experimental reach. We show that the parameters values for the crossings, which can be obtained from a semiclassical approach, 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 to 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.

13 pages, 8 figures

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• Quantum squeezing amplification with a weak Kerr nonlinear oscillator
• Symmetries of Liouvillians of squeeze-driven parametric oscillators
• Impact of chaos on the excited-state quantum phase transition of the Kerr parametric oscillator
• Excited-state quantum phase transitions in constrained systems
• Phase transitions, symmetries, and tunneling in Kerr parametric oscillators
• A numerical study of the Bose-Einstein condensates in a double-well trap using finite differences
• Dynamical system analysis of quantum tunneling in an asymmetric double-well potential
• Degeneracy beyond the parity-symmetry protection in one-dimensional spinless models: The parity-violating Kerr parametric oscillator
• Quantum signatures and semiclassical limitations in the transmission of Fock states