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arXiv:2009.01603 · Physical Review A

Echoes in a single quantum Kerr-nonlinear oscillator

Ilia Tutunnikov, K. V. Rajitha, Ilya Sh. Averbukh

Published Jan 13, 2021• 6 citations
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Abstract

A quantum Kerr-nonlinear oscillator is a paradigmatic model in cavity and circuit quantum electrodynamics, and quantum optomechanics. We theoretically study the echo phenomenon in a single impulsively excited (``kicked'') Kerr-nonlinear oscillator. We reveal two types of echoes, ``quantum'' and ``classical'' ones, emerging on the long and short time scales, respectively. The mechanisms of the echoes are discussed, and their sensitivity to dissipation is considered. These echoes may be useful for studying decoherence processes in a number of systems related to quantum information processing.

DOI
10.1103/physreva.103.013717

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A quantum Kerr-nonlinear oscillator is a paradigmatic model in cavity and circuit quantum electrodynamics, and quantum optomechanics. We theoretically study the echo phenomenon in a single impulsively excited (kicked'') Kerr-nonlinear oscillator. We reveal two types of echoes, quantum'' and ``classical'' ones, emerging on the long and short time scales, respectively. The mechanisms of the echoes are discussed, and their sensitivity to dissipation is considered. These echoes may be useful for studying decoherence processes in a number of systems related to quantum information processing.
Parametrically driven Kerr nonlinear quantum oscillator plays a central role in quantum optics, superconducting circuits, and in engineered light-matter interactions. For the development of future quantum technologies, it is crucial to understand the behavior of this quantum system under realistic dissipative conditions. The objective of this thesis is to investigate the phase-space dynamics of a dissipative Kerr nonlinear oscillator under different driving regimes and corresponding dissipation channels, with a particular focus on the emergence of nonclassical features in phase space. The aim is also to understand how nonlinearity and different driving mechanisms influence quantum properties such as coherence, nonclassicality, and phase-space structure. The analysis was carried out using the Wigner phase-space formalism and numerical simulations of the Lindblad master equation. The results show that in the case of finite nonlinearity the coherence time is prolonged compared to the harmonic case. In the single photon regime, the interplay between the photon drive and nonlinearity can lead to coherence revivals after which the system relaxes into a squeezed steady state. In the two photon and dissipation regime, the system exhibits parity-protected dynamics, leading to very long coherence times.
We consider a parametric amplifier driven by a periodically pulsed pump field inside a cavity containing a Kerr nonlinearity. The dynamics of the device is modeled as a kicked nonlinear system. The pulsed parametric amplifier constitutes the kick. In between kicks the dynamics is determined by the Kerr nonlinearity and damping. In the absence of damping, a classical description of the device exhibits a rich phase-space structure including fixed points of multiple period and chaos. We contrast the classical behavior of the mean intensity with that predicted by quantum dynamics. The mean photon number inside the cavity is shown to undergo regular collapse and revival in the regular region of the phase space and irregular revivals in the chaotic region. When damping is included, the quantum recurrences are rapidly suppressed, and the classical behavior is restored. In this case a stable steady state is possible. The damping represents the effect of photon-number measurements on the system. We also discuss the photon statistics in the steady state.
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 study nonlinear phenomena of bistability and chaos at a level of few quanta. For this purpose, we consider a single-mode dissipative oscillator with strong Kerr nonlinearity with respect to the dissipation rate driven by a monochromatic force as well as by a train of Gaussian pulses. The quantum effects and decoherence in the oscillatory mode are investigated in the framework of the purity of states and the Wigner functions calculated from the master equation. We demonstrate the quantum chaotic regime by means of a comparison between the contour plots of the Wigner functions and the strange attractors on the classical Poincaré section. Considering bistability at a low limit of quanta, we analyze the minimal level of excitation numbers at which the bistable regime of the system is displayed. We also discuss the formation of an oscillatory chaotic regime by varying oscillatory excitation numbers at ranges of a few quanta. We demonstrate quantum-interference phenomena that are assisted hysteresis-cycle behavior and quantum chaos for the oscillator driven by a train of Gaussian pulses. We establish the border of quantum-classical correspondence for chaotic regimes in the case of strong nonlinearities.