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Journal of Physics B Atomic Molecular and Optical Physics

The kinetics of the atomic relaxation induced by laser noise

Ouafae El Akramine, A. Makhoute

Published Oct 14, 1998• 2 citations
Publisher

Abstract

We present a theoretical study of strong laser-atom interactions, when the laser field parameters are subjected to random processes. The atom is modelled by a two- and a three-level system, while the statistical fluctuations of the laser field are described by a pre-Gaussian model. The interaction of the laser-target is treated nonperturbatively by using the calculation method based on the Hermitian Floquet theory. Our aim consists in studying the kinetics of atomic relaxation induced by laser noise. In the resonant case with electric field strengths small with respect to the atomic unit electric strength, the present nonperturbative results are in agreement with those obtained within the rotating wave approximation of Eberly et al and Wodkiewicz et al for an atom modelled by a two-level system. We discuss some examples which demonstrate the destruction of atomic coherence by the noise, the regime of relaxation to the equilibrium state and the optical analogue of motional narrowing. We also give new results for two- and three-level systems, and for a strong laser field at exact resonance, in the case of phase, amplitude noises. The case of fluctuation due to collisions is also discussed. Our numerical results indicate that ionization effects, in the presence of laser noise, can lead to important modifications of the populations for strong laser-atom interactions. The changes in the ionization rates generated by the noise are also investigated.

DOI
10.1088/0953-4075/31/19/019

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We present a theoretical study of strong laser-atom interactions, when the laser field parameters are subjected to random processes. The atom is modelled by a two- and a three-level system, while the statistical fluctuations of the laser field are described by a pre-Gaussian model. The interaction of the laser-target is treated nonperturbatively by using the calculation method based on the Hermitian Floquet theory. Our aim consists in studying the kinetics of atomic relaxation induced by laser noise. In the resonant case with electric field strengths small with respect to the atomic unit electric strength, the present nonperturbative results are in agreement with those obtained within the rotating wave approximation of Eberly et al and Wodkiewicz et al for an atom modelled by a two-level system. We discuss some examples which demonstrate the destruction of atomic coherence by the noise, the regime of relaxation to the equilibrium state and the optical analogue of motional narrowing. We also give new results for two- and three-level systems, and for a strong laser field at exact resonance, in the case of phase, amplitude noises. The case of fluctuation due to collisions is also discussed. Our numerical results indicate that ionization effects, in the presence of laser noise, can lead to important modifications of the populations for strong laser-atom interactions. The changes in the ionization rates generated by the noise are also investigated.
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 nonlinear dynamics of dissipative quantum systems in incoherent laser fields is studied in the framework of a master equation with the random telegraph model describing the laser noise and the Markovian approximation dealing with the system-bath couplings. Floquet theory and time-dependent perturbation methods are used to facilitate both analytical and numerical solutions. We develop a theoretical formalism that provides a powerful tool for the detailed analysis of the dissipative quantum dynamics of multilevel systems driven by intense stochastic laser fields. It is found that the system relaxes to a steady state from the effect of the laser phase and frequency noise and the kinetics of this relaxation increases with the addition of dissipative terms, introduced by the coupling to the reservoir. Amplitude fluctuations show a different behavior. Other results concerning the destruction of quantum coherence and the dynamical localization will be established and further relaxation mechanisms such as spontaneous emission and the ionization process will also be considered.
A quantum statistical theory of resonant optical phenomena is developed for the case when the fluctuations of the laser, used for exciting transitions, are important. The general equations describing the dynamics of a relaxing two-level atom (TLA) are solved exactly for different types of mean values and the two-time amplitude and intensity correlations. The phase-diffusion model is adopted for laser fluctuations. The exact results are used to analyze the effect of laser fluctuations on a number of optical effects-optical free-induction decay, adiabatic following, the spectrum of the scattered light from a relaxing TLA, the energy-absorption spectrum from a weak field, Hanle resonances, etc. In each case, the laser fluctuations are found to affect in an important way the characteristics of the above optical-resonance phenomena. For example, the spectrum of scattered radiation from a TLA has the usual three-peak structure for fields at resonance and with strengths $\ensuremath{\alpha}$ above the threshold and for $\ensuremath{\alpha}\ensuremath{\gg}{\ensuremath{\gamma}}_{c}$; however, now the peak heights (widths) are in the ratio 3x3x3x (23x\frac{2}{3x}3x2​), $x=\frac{[{\ensuremath{\gamma}}_{c}+\frac{({T}_{1}^{\ensuremath{-}1}+{T}_{2}^{\ensuremath{-}1})}{3}]}{[2{\ensuremath{\gamma}}_{c}+{T}_{2}^{\ensuremath{-}1}]}$, where ${\ensuremath{\gamma}}_{c}^{\ensuremath{-}1}$ is the correlation time for laser phase fluctuations. For ${\ensuremath{\gamma}}_{c}\ensuremath{\gg}\ensuremath{\alpha}$, one gets a single-peak spectrum. The laser field is treated as a second-quantized field with excitation in either a coherent state or a Fock state. The results, obtained by straightforward perturbation theory, but valid for arbitrary values of the relaxation parameters, detuning, and the laser correlation time, are also presented.
Significant fluctuations, above the shot-noise limit, have been observed in the intensity of fluorescent light scattered from atoms excited by an intense noisy laser, where a central role is played by the nonlinearity of the atom-field interaction. By considering the variance of the atomic populations, we show that ``noise spectroscopy'' is sensitive to the field statistics of the laser. We specifically consider the cases of resonance fluorescence (analogous in the weak-field limit to analysis by a Fabry-P\'erot interferometer), two-photon excitation, and double optical resonance for variable laser intensity and bandwidth. We show that large differences in the ``noise'' spectra can occur between lasers characterized by a phase-diffusion or a phase-jump model, although these models would give the same values for the mean atomic populations. We believe that observation of population fluctuations can become a useful method for characterizing laser noise.