Li Cao

Cross-correlation of multiplicative and additive noises in a single-mode laser white-gain-noise model and correlated noises induced transitions

Abstract We examine the mechanisms of cross-correlation of white multiplicative noise and white additive noise in a single-mode laser and establish a white-gain-noise model containing such a cross-correlation. We show that the cross-correlation between the white multiplicative noise and the white additive noise causes the phase of the laser field being locked at a fixed value, in contrast to that the phase diffuses freely when the cross-correlation is zero. Consequently, the laser intensity becomes decoupled from the phase and a closed form of Langevin equation is obtained for the intensity. Studying the steady intensity distribution, we find a new phase and re-entrant phase transition that were absent in the white-gain-noise model without cross-correlation.

Phase lock and stationary fluctuations induced by correlation between additive and multiplicative noise terms in a single-mode laser

Abstract According to a two-dimensional model stochastically equivalent to the single-mode cubic laser model with correlation between additive and multiplicative noise terms, it is found that a stable lock of laser phase will occur when the multiplicative noise has some forms of correlation with additive noise. A reduction of the fluctuation in phase is obtained consequently. The stationary fluctuation in the laser intensity increases when the two noises are positively correlated, and decreases when negatively correlated.

Noise-induced transport in a periodic system driven by Gaussian white noises with intensive cross-correlation

Abstract An analytical investigation of overdamped Brownian particle in a periodic system driven by intensive cross-correlated Gaussian white noises is presented. The center idea of this Letter is to construct an exact soluble model to exhibit the possible new effect of the cross-correlated Gaussian white noises on the noise-induced transport. The model clearly shows the following new aspects of this transport: (1) There is one and only extreme in the J – Q curve for the case of weakly cross-correlated noises here J and Q denote the current and multiplicative noise intensity, respectively. (2) When the two noises are intensive correlative, the J – Q curve behaves three extrema. (3) The J – Q curve exhibits a giant suppression plateau between the two maxima as the noise correlation coefficient is increased further. (4) The direction of the current is controlled by two parameters.

One-dimensional model of a single-mode laser with correlation between additive and multiplicative noises

Abstract Recently, Zhu [Phys. Rev. A 47 (1993) 2405] and Jia et al. [Phys. Rev. A 51 (1995) 3196] investigated the statistical properties of a single-mode laser with correlation between additive and multiplicative noises by using a one-dimensional model with a one-dimensional Langevin equation of the single-mode laser derived by Fox et al. [Phys. Rev. A 35 (1987) 1838]. We point out that this one-dimensional model, whose Langevin equation was obtained under the assumption that the noises are uncorrelated, is not always stochastically equivalent to the single-mode cubic laser model when additive and multiplicative noises are correlated. As a modification, a general model which is stochastically equivalent to the cubic model of a single-mode laser driven by correlated noises is derived. Based on this, a different one-dimensional model is given in the case where the former one used by Zhu and Jia et al. is not suitable.

Stochastic dynamics for systems driven by correlated colored noise

Abstract By means of substituting a linear combination of uncorrelated colored noise for correlated colored noise, we studied the stochastic dynamics of a system driven by correlated colored noise. As an example, we apply our approach to a bistable system driven by correlated colored noise.

Theory of nonlinear external noise

Abstract We investigate a stochastic differential equation (SDE) with general nonlinearity in the noise. We derive an integro-differential equation for the probability density (PD) and an approximate equation for the mean first-passage time (MFPT). The approximate Fokker-Planck equation (AFPE) and MFPT are obtained for some examples.

A new mechanism of phase locking in a single-mode laser

Abstract We study the motion of the laser phase in presence of the noise-correlation identified in a recent work [Phys. Lett. A 260 (1999) 126]. The laser phase is found to be locked around a fixed value and this phase locking is induced by the correlation between Γ t , the noise of the macroscopic atomic dipole moment, and Γ z t , the noise of atomic inversion. Furthermore, when the laser operates from an intensity level I0 1/A, the locked phase value φ0 exhibits a discontinuity, jumping up a finite value π, at I0=1/A.

Mean first-passage time of laser phase in a single-mode laser

Abstract We study the transient properties of the laser phase in presence of the noise-correlation identified in a recent work (Phys. Lett. A 260 (1999) 126). Numerical results of the mean first-passage time (MFPT) T of laser phase are obtained for a range of value of the noise intensity Q and for various values of the correlation strength λ . The main features of the MFPT of laser phase are the following. In the positive correlation region, 0 λ T – Q curves can be classified into four categories: They are curves that possess zero, one, two, and four extrema, respectively. In the negative correlation region, −1 λ T – Q dependence has two types. For λ =−0.1 to 0, T decreases monotonously with increasing Q . In the region λ =−0.2 to −1, the T – Q curve has a maximum.

Transient Properties of a Bistable System Driven by Cross-Correlated Noises: Correlation Times are Nonzero Case

The transient properties of a bistable system driven by cross-correlated noises are investigated, the correlation times of the correlations between the noises are nonzero. The explicit expression of the mean first-passage time (MFPT) is obtained. From numerical computations we find the following.(1) The MPPT of the system is affected by the correlation time tau and the correlation strength lambda, tau and lambda play opposing roles in the MFPT. (2) For the case of perfectly correlated noises (lambda = 1), the MFPT corresponding to alpha > D and alpha < D (alpha and D are the additive noise and multiplicative noise intensities, respectively) exhibit the same behaviors and the MFPT for alpha = D is continuous, which is very different from the case of tau = 0 [Phys. Rev. E 53 (1996) 5764].

Statistical Properties of the Output Light Intensity in a Single-Mode Laser Driven by Correlated Noises

By using linear approximation we derive expressions for the correlation function, power spectrum and correlation time of the output light intensity in a single-mode laser driven by additive white noise and multiplicative colored noise with an exponential correlation form. The effects of correlation strength and correlation time of the noises on the above quantities are discussed and compared with the case of a delta function correlation form for the noises.