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Annalen der Physik

Intensity Correlation of the Resonance Fluorescence Light in Quasi‐monochromatic Chaotic Fields

K.‐E. Süsse, W. Vogel, D.‐G. Welsch

Published Jan 1, 1982• 1 citation
Publisher

Abstract

Abstract The behaviour of the intensity correlation function of the resonance fluorescence light from a single atom is studied in the case of a quasi‐monochromatic chaotic pump field of arbitrary mean intensity. In particular, it is found that the factorization of the intensity correlation function, which is impossible in the case of a narrow band chaotic pump field of low intensity, becomes a better approximation when the mean intensity of the pump field is enhanced.

DOI
10.1002/andp.19824940503

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Abstract The behaviour of the intensity correlation function of the resonance fluorescence light from a single atom is studied in the case of a quasi‐monochromatic chaotic pump field of arbitrary mean intensity. In particular, it is found that the factorization of the intensity correlation function, which is impossible in the case of a narrow band chaotic pump field of low intensity, becomes a better approximation when the mean intensity of the pump field is enhanced.
The problem of resonance fluorescence from a two-level atom that is driven near resonance by a laser beam of finite bandwidth is tackled via the Heisenberg equations of motion, by a simple generalization of our previous treatment. It is found that the two-time intensity correlation function is again factorizable into a product of the mean light intensities at the two times, each of which is slightly modified under broad-band excitation from its value under monochromatic excitation. The spectrum of the fluorescence is affected rather more drastically, and, in general, becomes asymmetric under broad-band excitation.
The dynamical behavior of an atom interacting with a coherent field and a chaotic field is studied. Monte Carlo methods are used to integrate the equations describing the dipole moment, population inversion, and two-time correlation functions. The chaotic field can have a finite correlation time. Numerical results for a wide range of the parameters are given. The results depend sensitively on the ratio of the Rabi frequency and the bandwidth of the chaotic field. It is shown how an intense coherent field can suppress the effects of incoherence. The intensity of fluorescence as a function of detuning exhibits narrowing as the strength of the coherent field increases.
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 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.
We use a recently developed model for the interaction of a two-level atom with a coherent and a chaotic field of arbitrary bandwidth to study population fluctuations induced by the chaotic pump. We report numerical results for the fluctuations in the intensity of the fluorescence and their power spectra. We also give results for the effect of field fluctuations on the macroscopic polarization produced by the atoms. We show how detuning of the laser from the resonance frequency of the atoms affects the fluctuations in the fluorescence. The fluctuation behavior is quite sensitive to the correlation time of the chaotic field.