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Chinese Physics B

The mean first passage time of a three-level atomic optical bistable system subjected to noise

Yonggang Wei, Chunhua Zeng, Hua Wang, Kongzhai Li, Jianhang Hu

Published Jun 1, 2013• 4 citations
Publisher

Abstract

The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time (MFPT) of the transition from the high intracavity intensity state to the low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise D M and the additive noise D A , the intensity of correlation between two noises λ, and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show: (i) for the case of no correlation between two noises (λ = 0.0), the increase in D M and D A can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and (ii) for the case of correlation between two noises (λ = 0.0), the increase in λ can cause an increase in the probability of the transition, and the increase in D A can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.

DOI
10.1088/1674-1056/22/6/060503

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The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time (MFPT) of the transition from the high intracavity intensity state to the low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise D M and the additive noise D A , the intensity of correlation between two noises λ, and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show: (i) for the case of no correlation between two noises (λ = 0.0), the increase in D M and D A can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and (ii) for the case of correlation between two noises (λ = 0.0), the increase in λ can cause an increase in the probability of the transition, and the increase in D A can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.
The relaxation time T of an optical bistable system with cross-correlated color noises and small time delay is investigated. Using the Novikov theorem and Fox approach, the steady probability distribution is obtained. The expression of T is derived using the Stratonovich decoupling ansatz formalism. It is found that the relaxation time T increases with the increasing cross-correlation time τ 0 between the two noises or the self-correlation time τ 1 of the multiplicative noise, but decreases with the increasing self-correlation time τ 2 of the additive noise. T decreases with the increasing correlation intensity λ or the multiplicative noise intensity Q , but increases with the increasing additive noise intensity D . There exists a peak in the curve of T versus delay time τ.
Investigated are the effects of the cross-correlation time τ or the self-correlation times τ1 and τ2 on the relaxation time T of an optical bistable system using the Mei's method(Mei D C, Xie C W, Zhang L 2003 Phys. Rev. E 68 051102). It is found that the relaxation time T increases with the increase of the cross-correlation time τ between the two noises or the self-correlation time τ1 of the multiplicative noise, and that a one-peak structure appears on the T-τ2 plot. T increases with the increase of correlation intensity λ but decreases with the increase of multiplicative noise intensity Q.
Fluctuational transitions between stable states of an all-optical lumped-parameter bistable system have been observed. The dependences of the transition probabilities, and of the statistical distribution of the transmitted-light intensity, on the intensities of incident light and noise have been investigated. Two types of stochastic modulation, that of the incident-light intensity and that of the device itself, have been used. They correspond to multiplicative and additive noise for the intracavity-phase gain and give rise to qualitatively different pictures of the fluctuations. In particular, for the latter type of noise the logarithm of the statistical distribution of the transmitted-light intensity is described by a multibranch function, and the peaks of the distribution are strongly asymmetric. The onset of a zero-frequency peak in the power spectrum of the transmitted light in the range of the kinetic phase transition has been observed. The experimental data are in good qualitative and quantitative agreement with the theory.
Effects of multiplicative noise on optical bistability in a three-level atomic medium in a ring cavity are investigated experimentally and theoretically. Steady-state intensity distributions as well as switching and dwell times have been measured as functions of noise strength. System response to an external periodic signal is also explored. It is found that the probability for the system to stay in the upper state increases with increasing noise strength. When a small periodic signal is added to the input field, the probability for the upper state has a maximum as a function of multiplicative noise strength. A simple theoretical model based on nonlinear atomic susceptibility is presented to interpret the experimental observations.
With the unified colored noise approximation theory,the steepest descent method and the two-state approach theory,the effects of noise on the stochastic resonance and the mean first passage time of the dispersive optical bistability system are investigated.It is found that when there is a weak periodic signal included in the system,with both multiplicative colored noise and multiplicative white noise,the signal-to-noise ratio and the mean first passage time of the system are affected not only by the noise correlation time,but also by the intensity of both multiplicative colored noise and multiplicative white noise.It is shown that the stochastic resonance phenomenon depends on the initial conditions of the system.