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Physical Review A

Effects of detuning and fluctuations on fluorescence radiation from a strongly driven three-level atom: Some analytical results

S. V. Lawande, Richard D’Souza, Ravinder Rupchand Puri

Published Oct 1, 1987• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.36.3228

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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.
We study fluorescence from a three-level atom in a cascade configuration driven by two coherent fields and damped by a broadband squeezed vacuum. Under the conditions that one or both of these fields are intense, a secular approximation is invoked to derive an analytical solution of the relevant master equation. When the two fields are in exact resonance with their respective transitions, expressions for the fluorescent spectra show a narrowing of the central peak for some specific values of the parameters of the squeezed vacuum and the phases between the driving fields and the squeezed vacuum. We also present analytical expressions for second-order intensity correlations. The inhibition of fluorescence in a squeezed vacuum is reflected in the quantum-jump-like behavior shown by these correlations.
A system of N identical superimposed two-level atoms (the Dicke model) interacting with one another and driven by a fluctuating laser field of finite phase and amplitude bandwidths is considered. An exact master equation for the phase-averaged reduced atomic density operator is derived using the theory of multiplicative stochastic processes. It is shown that in the absence of amplitude fluctuations, this equation admits an exact steady-state solution. The exact solution is further used to obtain and analyse the behaviour of the phase-averaged atomic observables and atomic correlation functions in the steady state. The principal results of our analysis is that the phase fluctuations tend to smooth the discontinuities in the observables and the correlation functions found in the non-fluctuating case. Further, including the amplitude fluctuations as well we derive in the high-field limit a Markovian master equation for the density operator averaged over the ensembles of both phase and amplitude fluctuations. The quantum regression theorem is used to derive and discuss exact analytical expressions for the fluorescent spectrum and the second-order intensity correlation function for a system of two interacting atoms.
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.
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.
Time-dependent features of the fluorescence radiation from a strongly driven three-level atom in a Raman configuration are studied applying the Eberly-W\'odkiewicz counting-rate definition of the spectrum. Using our earlier formalism, where we assume that one or both of the driving fields are intense, we obtain analytical expressions for the time-dependent fluorescence spectra. We have also studied the influence on the transient spectrum of the initial preparation of the atom in three different dressed states.