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Physical Review A

Monte Carlo calculations of radiation from a randomly modulated atom in a strong field

Gautam Vemuri, G. S. Agarwal

Published Sep 1, 1993• 12 citations
Publisher

Abstract

The nature of light scattered from a two-level atom, where the transition frequency between the two levels is a stochastic quantity, pumped by a strong monochromatic field is investigated. The optical Bloch equations, modified to include the stochastic nature of the atomic frequency, are solved using Monte Carlo techniques to include arbitrary strengths and bandwidths of the frequency noise. We find in the spectrum of scattered light a shift of the Rabi sidebands due to the stochastic nature of the transition frequency. We also find the height of the Rabi sideband first decreases and then increases with increasing strength of the noise. The intensity-intensity correlation function for the emitted fluorescence is observed to be sensitive to the time scale of the noise. The calculated line shapes for weak driving fields can be fitted to a superposition of Gaussian and Lorentzian lines.

DOI
10.1103/physreva.48.2386

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 1, 1991•0 citations
The nature of light scattered from a two-level atom, where the transition frequency between the two levels is a stochastic quantity, pumped by a strong monochromatic field is investigated. The optical Bloch equations, modified to include the stochastic nature of the atomic frequency, are solved using Monte Carlo techniques to include arbitrary strengths and bandwidths of the frequency noise. We find in the spectrum of scattered light a shift of the Rabi sidebands due to the stochastic nature of the transition frequency. We also find the height of the Rabi sideband first decreases and then increases with increasing strength of the noise. The intensity-intensity correlation function for the emitted fluorescence is observed to be sensitive to the time scale of the noise. The calculated line shapes for weak driving fields can be fitted to a superposition of Gaussian and Lorentzian lines.
The steady-state populations, the fluorescent intensity-intensity correlation function, and the resonance fluorescence and absorption spectra of a two-level atom bichromatically driven by a strong, coherent field and a weak, stochastic field with tunable carrier frequency and wide bandwidth are investigated analytically. Surprisingly, the population is inverted if the stochastic field is appropriately detuned from the coherent field, which is assumed resonant with the atomic transition. The resonance fluorescence spectrum still displays a three-peaked structure, but with linewidths and heights that depend upon the frequency and bandwidth of the stochastic field as well as the intensities of both fields. Asymmetric fluorescence spectra are found when the coherent field is detuned from the atomic resonance frequency. The intensity-intensity correlation function varies dramatically with the carrier frequency of the stochastic field. For appropriate choices of the parameters, the fluorescent emission of the atom is antibunched for all time. The absorption spectral features also deviate significantly from those of the monochromatically driven atom. By appropriately tuning the stochastic field, one finds that a sharp peak (absorption) or hole (gain) can occur at line center and the probe beam can be amplified at either the lower-frequency Rabi sideband or the higher-frequency sideband and the inversionless gain can be enhanced.
The calculation is given of the spectral distribution of resonance fluorescence from an atom that is driven near a j=12j=\frac{1}{2}j=21​ to j=12j=\frac{1}{2}j=21​ transition by a monochromatic, xxx-polarized electric field and that is subject to radiation damping only. In accordance with Mollow's results for a two-level system, the power spectrum of the scattered radiation corresponding to the xxx component of the dipole moment contains a coherent part for all driving-field intensities. The coherent part is absent in the fluorescence radiation corresponding to the yyy and zzz components of the dipole moment. For weak driving fields all power scattered by these latter components is present in a narrow Lorentzian. Consistent with energy conservation, the width of the Lorentzian corresponds to the probability of excitation of the atom out of its ground level due to the presence of the driving field. For strong driving fields the power spectra corresponding to the xxx component and to the yyy or zzz component mainly differ in the heights and widths of their central incoherent band and their Rabi-precession-frequency-shifted side bands.
We study the correlation between photons in the fluorescence light scattered from an atom driven by an intense bichromatic field having one strong and one weak component, with or without the use of frequency filters in front of the photodetectors. Depending on the filters used and on the spectral components selected, we predict signals corresponding either to bunching or to antibunching, and modulations at the driving field Rabi frequencies as well as at their sum and difference. In contrast with the case of monochromatic driving, the antibunching can occur between photons emitted into different (as well as the same) lines of the fluorescence spectrum.
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 dynamical behavior of an atom interacting with a coherent and a chaotic field is investigated. Langevin equations describing the time dependent behavior of the dipole moment and population inversion are numerically integrated using Monte-Carlo techniques. The model can account for a finite correlation time for the chaotic component. Results on fluctuations in the fluorescence intensity from an ensemble of two-level atoms and the power spectra of these intensity fluctuations are presented. The effect of detuning the pump field from the resonant frequency of the two-level atoms on the fluctuations in fluorescence is studied. The effect of field fluctuations on the macroscopic polarization produced by the atoms is also reported. The fluctuation behavior of the atomic fluorescence is found to be very sensitive to the correlation time of the stochastic component.