Chaos in coupled Kerr-nonlinear parametric oscillators

Abstract

A Kerr-nonlinear parametric oscillator (KPO) can generate a quantum superposition of two oscillating states, known as a Schrödinger 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 Poincaré 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.

Detecting few-body quantum chaos: out-of-time ordered correlators at saturation

“…Various indicators of chaos relevant also for small systems, and their relation to OTOC and scrambling were studied by [21][22][23][24][25][26][27][28] among others. In particular, in [27] some important insights can be found: even in small systems devoid of the locality notion, OTOC can be interpreted as a measure of delocalization of a state in phase space, and the oscillatory component of the OTOC dynamics has to do with the power spectrum of the system.…”