Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator

Transmon qubits are the predominant element in circuit-based quantum information processing, such as existing quantum computers, due to their controllability and ease of engineering implementation. But more than qubits, transmons are multilevel nonlinear oscillators that can be used to investigate fundamental physics questions. Here, they are explored as simulators of excited state quantum phase transitions (ESQPTs), which are generalizations of quantum phase transitions to excited states. We show that the spectral kissing (coalescence of pairs of energy levels) experimentally observed in the effective Hamiltonian of a driven SNAIL-transmon is an ESQPT precursor. We explore the dynamical consequences of the ESQPT, which include the exponential growth of out-of-time-ordered correlators, followed by periodic revivals, and the slow evolution of the survival probability due to localization. These signatures of ESQPT are within reach for current superconducting circuits platforms and are of interest to experiments with cold atoms and ion traps.

Automated summary

Transmon qubits are widely used in circuit-based quantum information processing due to their controllability and ease of engineering implementation. In addition to serving as qubits, transmons can also be used to investigate fundamental physics questions. This study explores their use as simulators of excited state quantum phase transitions (ESQPTs), and shows that experimentally observed spectral kissing in a driven SNAIL-transmon is a precursor to ESQPT. The study further explores the dynamical consequences of ESQPT, which have implications for superconducting circuits, cold atoms, and ion traps experiments.