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Physical Review Letters

Atomic Relaxation in the Presence of Intense Partially Coherent Radiation Fields

Joseph H. Eberly

Published Nov 22, 1976• 203 citations
Publisher

Abstract

I develop a nonperturbative relaxation theory appropriate for an atom subjected to strong finite-bandwidth radiation fields. The partial coherence implied by the finite bandwidth is modeled by simple phase and amplitude correlation functions. Modifications of the Mollow theory of resonance fluorescence are calculated as an example. The finite bandwidth of the applied field does not have a simply additive effect on the predicted fluorescence spectrum.

DOI
10.1103/physrevlett.37.1387

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I develop a nonperturbative relaxation theory appropriate for an atom subjected to strong finite-bandwidth radiation fields. The partial coherence implied by the finite bandwidth is modeled by simple phase and amplitude correlation functions. Modifications of the Mollow theory of resonance fluorescence are calculated as an example. The finite bandwidth of the applied field does not have a simply additive effect on the predicted fluorescence spectrum.
We generalize our earlier formalism to treat the effects of both the finite-bandwidth excitations and finite arbitrary detunings, on the fluorescent spectra and second-order intensity correlation functions in optical double resonance. It is assumed that the bandwidth arises from the phase and/or amplitude fluctuations in the fields driving a three-level atom in cascade configuration. Under the conditions that one or both of these fields are intense, secular approximation and the theory of multiplicative stochastic processes are invoked to derive a Markovian master equation for the atomic-density operator averaged over both phase and amplitude. The quantum regression theorem is used to derive analytical expressions for the fluorescent spectra and the second-order intensity correlation functions which explicitly display the effects due to detunings and fluctuations.
A formalism is presented to treat the effects of finite-bandwidth excitations on the fluorescent spectra and second-order intensity-correlation functions in optical double resonance. It is assumed that the bandwidth arises from the phase and/or amplitude fluctuations in the fields driving a three-level atom. Under the conditions that one or both these fields are intense, secular approximation and the theory of multiplicative stochastic processes are invoked to derive a Markovian master equation for the atomic-density operator averaged over both phase and amplitude ensembles. The quantum regression theorem is used to derive analytical expressions for the fluorescent spectra and the second-order intensity-correlation functions.
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 authors incorporate in the theory of collisional redistribution of resonance radiation the effect of a finite bandwidth of the intense incident radiation. The phase of the radiation is treated as a process with independent increments, which contains the phase-diffusion model as a special case. These phase fluctuations give rise to effective decay operators affecting the evolution of the density matrix and the regression of the correlation function. For a two-level atom suffering binary collisions the combined effect of collisions and phase fluctuations on the fluorescence spectrum is evaluated in several limiting cases of practical interest.
The authors give a theoretical description of the spectrally resolved intensity correlations of an electromagnetic field, in analogy with the definition of the physical time-dependent spectrum. The results are applied to evaluate the time correlations between the three lines in the spectrum of resonance fluorescence of a two-level atom. The authors include the possibility of a finite bandwidth of the incident radiation, and they allow for collisions with perturber atoms. Photons in the central Rayleigh line are emitted in a fully random fashion, without any correlation with previous or subsequent emissions. Two photons from the same sideband display antibunching in time, whereas two photons from opposite sidebands tend to bunch with a strong asymmetry in time. The effect of collisions and of a finite bandwidth is to diminish this asymmetry.