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Czech-Polish-Slovak Optical Conference on Wave and Quantum Aspects of Contemporary Optics

Kerr-type nonlinear quantum oscillator: quantum correlations, chaotic, and regular dynamics

W. Leoński, M.W. Jarosik, Radosław Szczȩśniak, Joanna K. Kalaga, A. Kowalewska-Kudłaszyk

Published Dec 18, 2018• 2 citations
Publisher

Abstract

We propose the second-order correlation function g(2) as an indicator of quantum chaotic evolution. We discuss a nonlinear Kerr-like oscillator's system excited by a series of ultra-short coherent pulses. For such model, we study the time-evolution of the function g(2) for various values of the strength of excitation which corresponds to the regular and chaotic behaviors of the classical counterpart of the Kerr-like quantum system.

DOI
10.1117/12.2516884

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We propose the second-order correlation function g(2) as an indicator of quantum chaotic evolution. We discuss a nonlinear Kerr-like oscillator's system excited by a series of ultra-short coherent pulses. For such model, we study the time-evolution of the function g(2) for various values of the strength of excitation which corresponds to the regular and chaotic behaviors of the classical counterpart of the Kerr-like quantum system.
We discuss a system of the Kerr-like quantum nonlinear oscillator excited by a series of ultrashort external pulses.These coherent excitations, along with the nonlinearity involved in the system, can lead to the quantum chaotic behaviour.For that model, we calculate the fidelities of the wave function which describe the system's dynamics.We show that such defined fidelity and its decay rate can be applied as an indicator of the quantum chaotic behaviour appearance.We also discuss the problem of how the initial distance between the two close wave functions can influence the fidelity changes.
We consider a system composed of two linearly mutually interacting, identical Kerr-like nonlinear oscillators.Assuming that the system initially is in a coherent state, we discuss the system's dynamics and concentrate on the field's mutual correlations.As a measure of such correlations, we apply the normalized first-and second-order coherence functions.We derive the analytical formulas for such functions showing that their time-evolution strongly depends on the linear coupling parameter.
A Kerr-nonlinear parametric oscillator (KPO) can generate a quantum superposition of two oscillating states, known as a Schr\"odinger 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.