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Physical Review A

Mean first-passage times for non-Markovian continuous noise

Jaume Masoliver A

Published Feb 1, 1992• 6 citations
Publisher

Abstract

A method for the calculation of first-passage times for non-Markovian processes driven by continuous noise is presented. The input noise is identical to that of phase fluctuations in laser fields in the jump models. Both linear and nonlinear random processes are studied. In addition to the general formalism, some examples are worked out in detail.

DOI
10.1103/physreva.45.2256

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A method for the calculation of first-passage times for non-Markovian processes driven by continuous noise is presented. The input noise is identical to that of phase fluctuations in laser fields in the jump models. Both linear and nonlinear random processes are studied. In addition to the general formalism, some examples are worked out in detail.
A new non Markovian, correlated jump model for phase fluctuations of an electromagnetic field is introduced'. The phase diffusion, generalized telegraph, Burshtein and Brownian-motion-like models are all obtained from this model in the proper limits. The spectrum and correlation functions of the stochastic field are predicted, and detailed lineshapes of the Mollow triplet of resonance fluorescence are given and shown to depend on the field intensity, a purely non Markovian effect. Two different experimental procedures are proposed for the determination of the stochastic parameters of a laser field.
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A new non-Markovian, correlated-jump model for phase fluctuations of an electromagnetic field is introduced. The phase-diffusion, generalized telegraph, Burshtein, and Brownian-motion-like models are all obtained from this model in the proper limits. The spectrum and correlation functions of the stochastic field are predicted, and detailed line shapes of the Mollow triplet of resonance fluorescence are given and shown to depend on the field intensity, a purely non-Markovian effect. Two different experimental procedures are proposed for the determination of the stochastic parameters of a laser field.
A new model describing laser noise in terms of non-Markovian stochastic phase jumps has been introduced by A.G. Kofman et al. (1988, 1990). An exact expression for the correlation function for the electric field is obtained. This expression, valid for all possible values of the parameters of the stochastic process, reduces to approximations reported by B.R. Mollow (1969). A procedure is described for the inverse problem of determining the stochastic parameters from measured data for real lasers.>
We present a continuation of a general theoretical approach to noisy laser-atom interactions based on a special Markov-chain description of external fluctuations. This chain, composed of n independent two-state jump processes, forms a non-Gaussian stochastic process from which a detailed discussion of the atomic response can be given. We show that the n-component Markov chain also has the property of pre-Gaussian noise, because in the limit of n → ∞ it converges to a Gaussian stochastic process. We exhibit solutions for the field spectrum and the atomic-fluorescence spectrum for phase, frequency, and amplitude pre-Gaussian fluctuations of the driving-laser light.