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Chinese Physics Letters

Relaxation Time for an Optical Bistable System Subjected to Color Noises

Bing Wang, Wu Xiu-Qing, Dongchao Cheng

Published Jan 1, 2011• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0256-307x/28/1/014202

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Relaxation Time for an Optical Bistable System Subjected to Color Noises

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有跨 correlated 颜色噪音和小时间延期的一个光双稳态的系统的松驰时间 T 被调查。用 Novikov 定理和福克斯途径，稳定的概率分发被获得。T 的表示用 Stratonovich 去耦 ansatz 形式主义被导出。松驰时间 T 与增加增加 0 在二噪音或自我关联之间预定 1 趋于增加的噪音的跨关联的时间，这被发现，但是有增加的自我关联的减少预定 2 添加剂噪音。T 与增加的关联紧张或趋于增加的噪音紧张 Q 减少，但是与增加的添加剂噪音紧张 D 增加。在那里存在在 T 对延期时间的曲线的一座山峰。

Chinese Physics Letters•Jan 1, 2011•0 citations
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.
Considering an optical bistable system with cross-correlated additive white noise and multiplicative colored noise, we study the effects of correlation between the noises on the correlation function C(s) using the unified colored noise approximation and the Stratonovich decoupling ansatz formalism.The effects of the self-correlation time τ of the multiplicative colored noise and the correlation intensity λ between the two noises are studied with numerical calculation.It is found that C(s) increases with the increase of the self-correlation time τ, but decreases with the increase of the correlation intensity λ.At large value of τ, there is almost no change for C(s) when τ changes.
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.
The stochastic resonance (SR) of an optical bistable system with cross-correlated additive white and multiplicative colored noises and periodic signal is studied using the unified colored noise approximation and the theory of signal-to-noise ratio (SNR).Results show that cross-correlation intensity λ enforces the SR of the system.The position of the peak on the SNR-τ curves moves to the right direction along with the increase of λ (τ is the self-correlation time of the multiplicative colored noise).We find the SR phenomenon in the SNR-D and SNR-Q curves (D and Q are the intensities of the additive and multiplicative noises, respectively), but not in the SNR-λ curves.
By adopting the linear approximation method,the signal-to-noise ratio of optical bistability system driven by colored pump noise and colored quantum noise was calculated. The influence on the signal-to-noise ratio of the pump noise intensity(P),quantum noise intensity(Q),pump noise self-correlation time (τ1) and quantum noise self-correlation time (τ2) was studied. The stochastic resonance was found in the curve of signal-to-noise ratio R versus the pump noise self-correlation time (τ1) was discussed,while the great influence on the stochastic resonance is posed by quantum noise self-correlation time,when (τ2) increases,the curve of signal-to-noise ratio R versus the pump noise self-correlation time (τ1) upgrates integratedly,and resonance-peak increases.It could prolong the quantum noise self-correlation time (τ2) to increase the signal-to-noise ratio R.There is a maximum in the curve of signal-to-noise ratio R versus the parameter of the optical bistability system c,while pump noise self-correlation time (τ1) greatly influences the curve of signal-to-noise ratio R versus the parameter of the optical bistability system c. With the increase of pump noise self-correlation time (τ1),the maximum declines and the curve becomes flat.It is indicated that the signal-to-noise ratio increases through reducing the pump noise self-correlation time (τ1).Besides,signal-to-noise ratio R monotonously increases with the increase of pump noise intensity P,and motonously decreases with the increase of quantum noise intensity Q.
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.
有跨 correlated 颜色噪音和小时间延期的一个光双稳态的系统的松驰时间 T 被调查。用 Novikov 定理和福克斯途径，稳定的概率分发被获得。T 的表示用 Stratonovich 去耦 ansatz 形式主义被导出。松驰时间 T 与增加增加 0 在二噪音或自我关联之间预定 1 趋于增加的噪音的跨关联的时间，这被发现，但是有增加的自我关联的减少预定 2 添加剂噪音。T 与增加的关联紧张或趋于增加的噪音紧张 Q 减少，但是与增加的添加剂噪音紧张 D 增加。在那里存在在 T 对延期时间的曲线的一座山峰。