Wigner function for a generalized model of a parametric oscillator: phase-space tristability, competition and nonclassical effects

Kheruntsyan, K. V.; Krähmer, D. S.; Kryuchkyan, G. Yu.; Petrossian, K.G.

doi:10.1016/s0030-4018(96)00753-5

Cited by 41 publications

(42 citation statements)

References 14 publications

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“…After integration the mean photon number and the probability distribution of photon-number states are repre- sented in the following form [39][40][41]:…”

Section: Kerr Nonlinear Resonator: Pulsed Regime and Cw Limitmentioning

confidence: 99%

Multiphoton blockades in pulsed regimes beyond stationary limits

2014

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We demonstrate multiphoton blockades (PB) in the pulsed regime by using Kerr nonlinear dissipative resonator driven by a sequence of Gaussian pulses. It is shown that the results obtained for single-photon, two-photon and three-photon blockades in the pulsed excitation regime differ considerably from analogous results obtained for the case of continuous-wave (cw) driving. We strongly demonstrate that for the case of cw pumping of the Kerr-nonlinear resonator there are fundamental limits on populations of lower photonic number-states (with n = 0, 1, 2, 3). Thus, such detailed comparison demonstrates that PB due to excitation with a suitable photon pulses is realized beyond the fundamental limits established for cw excitations. We analyze photon-number effects and investigate phase-space properties of PB on the base of photon number populations, the second-order correlation functions and the Wigner functions in phase space. Generation of Fock states due to PB in the pulsed regime is analysed in details.

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“…After integration the mean photon number and the probability distribution of photon-number states are repre- sented in the following form [39][40][41]:…”

Section: Kerr Nonlinear Resonator: Pulsed Regime and Cw Limitmentioning

confidence: 99%

Multiphoton blockades in pulsed regimes beyond stationary limits

2014

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“…The details of calculations involving contour integrations have been presented in [40][41][42]. The results for the mean photon number and the photon number probability distribution function read as…”

Section: Exact Quantum Treatment Of Knr: Short Descriptionmentioning

confidence: 99%

Selective excitations of a Kerr-nonlinear resonator: exactly solvable approach

2016

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Abstract. We study Kerr nonlinear resonators (KNR) driven by a continuous wave field in quantum regimes where strong Kerr interactions give rise to selective resonant excitations of oscillatory modes. We use an exact quantum theory of KNR in the framework of the Fokker-Planck equation without any quantum state truncation or perturbation procedure. This approach allows non-perturbative consideration of KNR for various quantum operational regimes including cascaded processes between oscillatory states. We focus on understanding of multi-photon non-resonant and selective resonant excitations of introcavity mode depending on the detuning, the amplitude of the driving field and the strength of nonlinearity. The analysis is provided on the base of photon number distributions, the photon-number correlation function and the Wigner function.

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“…Analogous solution has been obtained for a combined driven parametric oscillator with Kerr nonlinearity 34 . The Wigner functions for both these models have been obtained using these solutions 33,35 .…”

Section: Driven Nonlinear Oscillator As An Open Quantum Systemmentioning

confidence: 99%

Dissipative Chaos in Quantum Distributions

Gevorgyan¹,

Manvelyan²,

Shahinyan³

et al. 2010

Modern Optics and Photonics

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We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions. For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with time-dependent Kerr-nonlinearity and time-modulated driving field. This model showing both regular and chaotic dynamics in the classical limit is realized in several experimental schemes. Quantum dissipative chaos is analyzed on the base of numerical method of quantum trajectories. Three quantities are studied: the Wigner function of oscillatory mode from the point of view of quantum-assemble theory and both semiclassical Poincaré section and quantum Poincaré section calculated on a single quantum trajectory. The comparatively analysis of these distributions for various operational chaotic regimes of the models is performed, as well as scaling invariance in dissipative chaos and quantum interference effects assisted by chaos are discussed.

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Wigner function for a generalized model of a parametric oscillator: phase-space tristability, competition and nonclassical effects

Cited by 41 publications

References 14 publications

Multiphoton blockades in pulsed regimes beyond stationary limits

Multiphoton blockades in pulsed regimes beyond stationary limits

Selective excitations of a Kerr-nonlinear resonator: exactly solvable approach

Dissipative Chaos in Quantum Distributions

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