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Journal of the Optical Society of America B

Modeling noise by jump processes in strong laser-atom interactions

Bruce W. Shore

Published Apr 1, 1984• 41 citations
Publisher

Abstract

In this paper, a practical scheme for computing time-dependent properties, such as excitation probabilities and dipole correlation functions of a multilevel atom strongly excited by a laser in the presence of noise, is described in detail. The method, which is based on the notion of randomly interrupted, multivalued jump processes, can be used to treat laser phase, amplitude, and/or frequency noise, and fluctuating microfields. The method provides analytic expressions, which are based on eigenvalues and eigenvectors of a finite-dimensional matrix, for time dependence and spectral dependence, and it permits computation of time-dependent fluorescence emitted from atoms excited by a noisy laser. The method is illustrated by application to time-dependent spectra.

DOI
10.1364/josab.1.000176

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•Feb 23, 1983•1 citation
In this paper, a practical scheme for computing time-dependent properties, such as excitation probabilities and dipole correlation functions of a multilevel atom strongly excited by a laser in the presence of noise, is described in detail. The method, which is based on the notion of randomly interrupted, multivalued jump processes, can be used to treat laser phase, amplitude, and/or frequency noise, and fluctuating microfields. The method provides analytic expressions, which are based on eigenvalues and eigenvectors of a finite-dimensional matrix, for time dependence and spectral dependence, and it permits computation of time-dependent fluorescence emitted from atoms excited by a noisy laser. The method is illustrated by application to time-dependent spectra.
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.
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.
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.
The authors apply the recently developed theory of multiplicative stochastic correlation functions with Markovian random jumps to the problem of resonance fluorescence from a two-level atom in a strong laser field. The finite bandwidth of a single-mode laser or the appearance of distinct lines in a multimode laser is considered to be brought about by a random mode-switching process. The two-time dipole correlation functions, which determine the spectral distribution of the fluorescence and the temporal correlations between the emitted photons are averaged exactly over the stochastics of the driving field. The authors' explicit expressions only involve single-time averages, which can be easily evaluated for a given probability distribution. These results generalise and modify earlier results. The authors obtain closed expressions, rather than implicit differential equations, which can handle the continuous case as well, and take into account the initial correlations, which always arise when the laser coherence time is finite. They illustrate the dependence on the stochastics of the laser model by comparing the multimode description with the phase-diffusion process and the Lorentz wave, which all give rise to the same laser profile, but to a different fluorescence spectrum.
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.
The definition of a time-dependent spectrum registered by an idealized spectrometer responding to a time-varying electromagnetic field as proposed by Eberly and Wodkiewicz and subsequently applied to the spectrum of laser-induced fluorescence by Eberly, Kunasz, and Wodkiewicz is here extended to allow a stochastically fluctuating (interruption model) environment: we provide an algorithm for numerical determination of the time-dependent fluorescence spectrum of an atom subject to excitation by an intense noisy laser and interruptive relaxation.