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Journal de physique

Collective resonance fluorescence in an intense laser field with phase and amplitude fluctuations

A.S. Shumovsky, R. Tanaś, Tran Quang

Published Jan 1, 1988• 3 citations
Publisher

Abstract

The collective resonance fluorescence from a system of two-level atoms resonantly driven by a strong laser field with the phase and amplitude fluctuations is considered. The effect of the laser field fluctuations on the spectrum as well as the degrees of the second-order coherence of the fluorescent field is discussed in detail for the off-resonance case.

DOI
10.1051/jphys:01988004905078700

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The collective resonance fluorescence from a system of two-level atoms resonantly driven by a strong laser field with the phase and amplitude fluctuations is considered. The effect of the laser field fluctuations on the spectrum as well as the degrees of the second-order coherence of the fluorescent field is discussed in detail for the off-resonance case.
A method of calculation of multiple-time correlation functions of the resonance fluorescence light from a two-level atom driven by a realistic laser field with phase and amplitude fluctuations is developed. Both kinds of fluctuations are assumed to be Gaussian. The phase fluctuations are treated in the phase-diffusion model. The averaging over the amplitude fluctuations can be performed in a closed way when the relative mean-square amplitude fluctuation is small compared with the ratio of the amplitude correlation decay rate to the characteristic atomic relaxation rate. There is no restriction to Markovian amplitude fluctuations. Arbitrary values for the mean Rabi frequency are allowed. Results are presented for the intensity, the intensity correlation function, and the spectrum of the fluorescent light. It is shown that even in the case when the relative strength of the amplitude fluctuations is small, significant effects can occur due to the finite correlation length of the fluctuations. The results for fast amplitude correlation decay correspond to the situation without amplitude fluctuations. When the correlation time of the amplitude fluctuations becomes comparable with the atomic relaxation times, the Rabi oscillations of the intensity and the intensity correlation function are nearly washed out, and non-Lorentzian line shapes for the side peaks in the spectrum are observed. It is found that the ratio of the heights of the central peak to the side peak increases with increasing correlation time.
The relaxation process and resonance fluorescence of a two-level atom strongly driven by stochastically fluctuating laser light is studied. A laser with small intensity fluctuations about a constant mean value and a diffusing phase is assumed. Depending on the relative time scales of the intensity fluctuations and the atomic response to these fluctuations, the time decay of the atomic population is found to be non-exponential. The broadening of the sidebands in the triplet spectrum of resonance fluorescence is shown to be non-Lorentzian.
We discuss analytically the resonance fluorescence of a three-level ladder system whose two transitions are simultaneously saturated by the fields from two lasers. The laser fields have fluctuating phases, which may be correlated to some extent. We generalize the dressed-atom approach of Cohen-Tannoudji and Reynaud [J. Phys. B 10, 345 (1977)] to deal with phase fluctuations under conditions of overall two-photon resonance, but not single-photon resonance on the individual transitions. In this respect we also generalize the master-equation approach of Lawande, Puri, and D'Souza [Phys. Rev. A 33, 2504 (1986)]. The effect of spontaneous emission and laser fluctuations on the resonance fluorescence quintet is discussed in detail, and shown to marked effects. We also investigate the effect of these quantities on the steady-state dressed-atom occupation probabilities, and point out that the double-resonance experiment can be used to prepare the atom in a given dressed state with high probability.
Resonance-fluorescence power spectrum of two-level atoms driven by a strong monochromatic laser field is discussed, taking into account effects due to the dipole-dipole interaction between the atoms. For two atoms confined to a region smaller than the wavelength of the driving field, we predict significant deviations of the power spectrum from the single-atom case. The two-atom spectrum is nonsymmetric, the wing peaks are shifted from their Rabi-frequency positions, and additional maxima may appear.
The effects of amplitude and phase fluctuations of the pump laser on the resonance fluorescence under two-photon resonant excitation are studied. The averaging of the stochastic Bloch equations is carried out within the approximation scheme that has recently been applied to the case of one-photon resonant excitation. In the case of two-photon resonant excitation the stochastic pump field gives rise to multiplicative nonlinear Gaussian fluctuation effects. The phase fluctuations are treated in the phase-diffusion model, and the averaging over the amplitude fluctuations is performed by means of generating-function methods. Both the intensity and the intensity correlation of the fluorescent light are studied. When the amplitude fluctuations are weak, the cases of one- and two-photon resonant excitations are similar. The difference between both cases consists of a modification of the Rabi frequency and a faster damping of the Rabi oscillations in the two-photon case. For sufficiently fast correlation decay of the amplitude fluctuations their effect can simply be described by a rate. In the general case of n-photon resonant excitation this rate is larger by a factor of n2{n}^{2}n2 than that in the case of one-photon resonant excitation. When the amplitude fluctuations are sufficiently strong, the Rabi oscillations are ``washed out.'' In the case of one-photon resonant excitation both the intensity and the intensity correlation function of the scattered light develop into step functions over time. In the two-photon case the dynamics of both quantities is determined by a new time constant which acts as both the oscillation time and the damping time. Consequently an overshoot peak occurs in both the intensity and the intensity correlation instead of the tendency to become step functions.