Chaos in coupled Kerr-nonlinear parametric oscillators

TL;DR

This paper explores chaotic dynamics in two coupled Kerr-nonlinear parametric oscillators at a quantum level, revealing classical and quantum signatures of chaos, and suggesting their potential for quantum computing and studying quantum chaos.

Contribution

It introduces a detailed analysis of chaos in coupled KPOs, providing quantum analogs of classical chaos indicators and highlighting their relevance for quantum computing and chaos research.

Findings

Classical model of coupled KPOs exhibits nonintegrable, chaotic behavior.

Quantum signatures of chaos identified through Wigner and Husimi functions, and energy-level statistics.

Coupled KPOs serve as a platform for quantum computing and studying quantum chaos.

Abstract

A Kerr-nonlinear parametric oscillator (KPO) can generate a quantum superposition of two oscillating states, known as a Schr\"{o}dinger cat state, via quantum adiabatic evolution, and can be used as a qubit for gate-based quantum computing and quantum annealing. In this work, we investigate complex dynamics, i.e., chaos, in two coupled nondissipative KPOs at a few-photon level. After showing that a classical model for this system is nonintegrable and consequently exhibits chaotic behavior, we provide quantum counterparts for the classical results, which are quantum versions of the Poincar\'{e} surface of section and its lower-dimensional version defined with time integrals of the Wigner and Husimi functions, and also the initial and long-term behavior of out-of-time-ordered correlators. We conclude that some of them can be regarded as quantum signatures of chaos, together with energy-level spacing statistics (conventional signature). Thus, the system of coupled KPOs is expected to offer not only an alternative approach to quantum computing, but also a promising platform for the study on quantum chaos.