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

Abstract

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.

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

“…We gain insight into the system described by Eq. (1) by examining the classical limit [33,34] of the Hamiltonian in the canonical variables q and p, which reads…”

“…The ESQPT critical energy value marks the boundary between two regions with different dominating symmetries. Pairs of eigenvalues, one with negative parity and the other with positive parity, are degenerate for energies below the ESQPT energy and they split once they get above the ESQPT energy [33].…”

“…Some of the dynamical properties of this system, which includes the exponential growth of the out-of-timeordered correlator due to instability [32], were investigated in Ref. [33]. Tunneling in the squeeze-driven Kerr oscillator was recently observed experimentally for the few lowest excited states in Refs.…”

Symmetries of the squeeze-driven Kerr oscillator

“…The value of N = 800 is chosen here in order that the eigenvalues in the range 0 ⩽ ξ ⩽ 25 of the figure are well converged. While the convergence of the eigenvalues of the pairing term P2 is very slow due to its non-compacteness, the convergence of the Hamiltonian (32) is faster due to the presence of the Kerr term n(n − 1) which increases as n 2 for large n. The spectrum exhibits an ESQPT [37] similar to that encountered in the one-dimensional vibron model and the Lipkin-Meshkov-Glick model [49,54,55]. It is divided into two parts (phases) with separatrix E s .…”

“…Specifically, the spectrum presents real crossings when η is even and avoided crossings when η is odd [10], which implies that by tuning the parameters of the system, one can suppress or enhance quantum tunneling [10,36]. The spectrum also exhibits an excited state quantum phase transition (ESQPT) as a function of the squeezing amplitude ε 2 [36,37]. This ESQPT is similar to the QPTs observed in other systems, such as driven Rabi and Dicke models [38,39] and the Jaynes-Cummings model [38].…”