Quantum chaos in an ultra-strongly coupled bosonic junction

TL;DR

This paper investigates quantum and classical chaos in ultra-strongly coupled bosonic resonators, revealing non-integrability, chaos windows, and unpredictable tunneling times, with implications for experimental superconducting systems.

Contribution

It introduces a model beyond the Rotating Wave Approximation to analyze chaos in ultra-strongly coupled resonators, highlighting the transition to chaos and tunneling unpredictability.

Findings

Classical model becomes chaotic in certain parameter regimes.

Quantum dimer exhibits regions of stability and chaos.

Tunneling times are unpredictable in chaotic regimes.

Abstract

The classical and quantum dynamics of two ultra-strongly coupled and weakly nonlinear resonators cannot be explained using the Discrete Nonlinear Schr\"odinger Equation or the Bose-Hubbard model, respectively. Instead, a model beyond the Rotating Wave Approximation must be studied. In the classical limit this model is not integrable and becomes chaotic for a finite window of parameters. For the quantum dimer we find corresponding regions of stability and chaos. The more striking consequence for both classical and quantum chaos is that the tunneling time between the sites becomes unpredictable. These results, including the transition to chaos, can be tested in experiments with superconducting microwave resonators.