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Journal of Contemporary Physics (Armenian Academy of Sciences)

Negative Wigner functions of nonlinear dissipative oscillator in the pulsed regime

T. V. Gevorgyan, Gagik Yu. Kryuchkyan

Published Aug 29, 2013• 1 citation
Publisher

Abstract

Preparation of nonclassical states that are described by negative Wigner functions is studied for an anharmonic oscillator under parametric excitation (AOPE). The over-transient pulsed regime of AOPE driven by a train of Gaussian laser pulses is analyzed. The results are obtained by complete consideration of dissipative and decoherence effects.

DOI
10.3103/s1068337213050034

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Preparation of nonclassical states that are described by negative Wigner functions is studied for an anharmonic oscillator under parametric excitation (AOPE). The over-transient pulsed regime of AOPE driven by a train of Gaussian laser pulses is analyzed. The results are obtained by complete consideration of dissipative and decoherence effects.
We consider preparation of nonclassical oscillatory states in a degenerate parametric oscillator combined with phase modulation. In this scheme intracavity oscillatory mode is excited by train of Gaussian laser pulses through degenerate down-conversion process and phase modulation element inserted in a cavity leads to anharmonicity of oscillatory mode. We demonstrate production of nonclassical oscillatory states with two-fold symmetry in phase-space including the superposition of Fock states and quantum localized states on the level of few excitation numbers and in over-transient dissipative regime.
We discuss dissipative chaos showing symmetries in the phase space and nonclassical statistics for a parametrically driven nonlinear Kerr resonator (PDNR). In this system an oscillatory mode is created in the process of degenerate down-conversion of photons under interaction with a train of external Gaussian pulses. For chaotic regime we demonstrate, that the Poincaré section showing a strange attractor, as well as the resonator mode contour plots of the Wigner functions display two-fold symmetry in the phase space. We show that quantum-to-classical correspondence is strongly violated for some chaotic regimes of the PDNR. Considering the second-order correlation function we show that the high-level of photons correlation leading to squeezing in the regular regime strongly decreases if the system transits to the chaotic regime. Thus, observation of the photon-number correlation allows to extract information about the chaotic regime.
The output field from a continuously driven linear parametric oscillator may exhibit considerably more squeezing than the intracavity field.Inspired by this fact, we explore the nonclassical features of the steady-state output field of a driven nonlinear Kerr parametric oscillator using a temporal wave packet mode description.Utilizing a new numerical method, we have access to the density matrix of arbitrary wave packet modes.Remarkably, we find that even though the steady-state cavity field is always characterized by a positive Wigner function, the output may exhibit Wigner negativity, depending on the properties of the selected mode.
We consider quantum dynamics of a parametrically driven anharmonic oscillator (PDAO) at a few-photon level. In this scheme the oscillatory mode is excited through the degenerate down-conversion process. This scheme could be experimentally realized in superconducting solid-state devices based on the nonlinearity of the Josephson junction or in cooled nano-mechanical oscillators. We investigate PDAO in the strong quantum regime that means strong Kerr-nonlinearity of the mode with respect to the mode’s dissipation for two cases of excitations: by a monochromatic driving field or by a train of Gaussian pulses. We demonstrate production of the nonclassical oscillatory states with two-fold symmetry in phase-space which are approximately close to the lower pure Fock states. Production of the superposition of the Fock states for time-intervals exceeding the characteristic time of decoherence and dissipation is also shown.
We consider the quantum model of a driven anharmonic oscillator, in the presence of dissipation, and present an exact analytic solution for the corresponding Wigner function in the steady-state regime. This provides explicit phase-space images of the resulting state of the cavity mode, and allows us to understand how the quantum interference is built up into it. The photon number probability distribution is calculated and analysed as well. We monitor the transition from the semiclassical to extreme quantum regime of operation, and identify qualitative changes, where the conventional characteristics of the model, such as bistability or turning points, become meaningless.
We present an exact quantum treatment of the generalized model of a degenerate parametric oscillator, in which we allow for self-phase modulation of the signal mode. Using the steady-state solution of the Fokker-Planck equation in the complex P-representation we obtain an exact analytical result for the Wigner quasiprobability distribution function. The obtained Wigner function allows us to give an explicit phase-space description of the nonlinear system under consideration, including the critical transition behavior in the monostable and bistable (with respect to the signal mode intensity versus the pump field intensity) operation regimes and in the threshold region. The competitive effects influenced by the self-phase modulation and the phase-space tristability are analyzed. Nonclassical effects of quadrature squeezing and quantum superposition are discussed as well.