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Physical Review A

Shot noise and general jump processes in strong laser-atom interactions

K. Wódkiewicz, Joseph H. Eberly

Published Apr 1, 1985• 23 citations
Publisher

Abstract

We discuss relations between different jump processes used by us and other workers for the description of external electromagnetic field fluctuations. We show that the shot noise, the random telegraph signal, and the Poisson process are examples of a general class of fluctuations described by the relevant Burshtein-Chapman-Kolmogorov-Smoluchowski equation. We establish general conditions for which all these processes lead to the same atomic response in strong field-atom interactions.

DOI
10.1103/physreva.31.2314

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We discuss relations between different jump processes used by us and other workers for the description of external electromagnetic field fluctuations. We show that the shot noise, the random telegraph signal, and the Poisson process are examples of a general class of fluctuations described by the relevant Burshtein-Chapman-Kolmogorov-Smoluchowski equation. We establish general conditions for which all these processes lead to the same atomic response in strong field-atom interactions.
We discuss strong laser-atom interactions that are subjected to jump-type (random telegraph) random-phase noise. Physically, the jumps may arise from laser fluctuations, from collisions of various kinds, or from other external forces. Our discussion is carried out in two stages. First, direct and partially heuristic calculations determine the laser spectrum and also give a third-order differential equation for the average inversion of a two-level atom on resonance. At this stage a number of general features of the interaction are able to be studied easily. The optical analog of motional narrowing, for example, is clearly predicted. Second, we show that the theory of generalized Poisson processes allows laser-atom interactions in the presence of random telegraph noise of all kinds (not only phase noise) to be treated systematically, by means of a master equation first used in the context of quantum optics by Burshtein. We use the Burshtein equation to obtain an exact expression for the two-level atom's steady-state resonance fluorescence spectrum, when the exciting laser exhibits phase telegraph noise. Some comparisons are made with results obtained from other noise models. Detailed treatments of the effects of other than phase noise are given in other papers.
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.
We extend our study of the effects of jump-type noise on laser-atom interactions to frequency-telegraph noise. Such noise can be used as a model of collisional effects, in which the atomic transition frequency randomly jumps, or as a model of finite laser bandwidth effects, in which the laser frequency exhibits random jumps. We show that these two types of frequency noise can be distinguished in light-scattering spectra. We also discuss examples which demonstrate both temporal and spectral motional narrowing, nonexponential correlations, and non-Lorentzian spectra. Its exact solubility in finite terms makes the frequency-telegraph noise model an attractive alternative to the white-noise Ornstein-Uhlenbeck frequency noise model which has been previously applied to laser-atom interactions.
Atomic excitation by strong noisy lasers with Kubo-Anderson--type fluctuations (randomly-interrupted-jump-process noise) is examined. A unified exact approach (based on the Bourret theorem) to phase and amplitude fluctuations is presented. Comparison with the Burshtien method, which was extensively used in recent works, is given. An exact analytical formula for the resolvent of the master Bloch equation in the general case, not necessarily only in resonant excitation, with simultaneous amplitude and phase fluctuations is derived. Some examples are analyzed.
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.
The Jaynes-Cummings model of a two-level atom interacting with a single quantized mode of radiation field is generalized to include the effects of stochastic fluctuations in the atom-field coupling. The coupling coefficient is assumed to fluctuate either in phase or in frequency. The fluctuations are modeled by binary random telegraph processes. Invoking the Markovian property of the telegraph noise, we derive in these two cases an equation for the density operator averaged over the distribution of fluctuations. The solution of this equation is used to study the resulting decoherence effects in the dynamical behavior of the atom and the statistical properties of the field.