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Journal of Nonlinear Optical Physics & Materials

FREE ATOM IN STRONG AMPLITUDE-MODULATED LIGHT

Anatoly I. Burshtein, Andrey Sivachenko

Published Oct 1, 1996• 2 citations
Publisher

Abstract

The population and phase relaxation in TLS induced by resonant radiation with stochastic amplitude was studied within the framework of sudden modulation theory. Kinetics and stationary light absorption as well as resonance fluorescence were calculated for light with complex and real amplitude. Although the latter is a very popular model of the former, it was shown to be inappropriate at strong interaction. The real (Rayleigh) light has complex amplitude random in magnitude and phase and changing in time as a Markovian chain, correlated or non-correlated. With respect to atom response to light of medium power, the analytically studied non-correlated field was shown to be similar to strongly correlated, “stochastic” field opened to only numerical inspection.

DOI
10.1142/s0218863596000593

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•Jan 1, 1998•0 citations
The population and phase relaxation in TLS induced by resonant radiation with stochastic amplitude was studied within the framework of sudden modulation theory. Kinetics and stationary light absorption as well as resonance fluorescence were calculated for light with complex and real amplitude. Although the latter is a very popular model of the former, it was shown to be inappropriate at strong interaction. The real (Rayleigh) light has complex amplitude random in magnitude and phase and changing in time as a Markovian chain, correlated or non-correlated. With respect to atom response to light of medium power, the analytically studied non-correlated field was shown to be similar to strongly correlated, “stochastic” field opened to only numerical inspection.
The response of a TLS to waves, phase- and frequency-modulated by a purely Markovian process, is calculated rigorously. The spectrum of luminescence characterised by two rates of phase relaxation Gamma 1 and Gamma 2 , rather than one, as in the case of phase diffusion ( Gamma 2 =4 Gamma 1 ), is found. Saturation of TLS and its absorption of light at arbitrary correlation between successive values of its randomly and suddenly varying frequency are determined. The probability of light absorption at any strength of its interaction with TLS and at any rate of frequency modulation is found for uncorrelated frequency change.
The nature of resonance emission of light, which appears as a mixture of (coherent) resonance scattering and (incoherent) resonance fluorescence, is considered. The basic conceptual elements which distinguish the scattering and fluorescence components for the linear excitation limit are developed in terms of a simple formulation whereby a molecule interacts with a coherent Lorentzian light pulse which increases exponentially with time for t<0 and is turned off at t = 0. These results together with the ideas, currently existing in the literature, that stochastic modulation of a molecule by its medium is essential for the appearance of fluorescence provide the basis for the further formulation of a theory which does not require the ad hoc introduction of a random potential. The theory developed considers the microscopic origins of manifest stochastic modulation effects in terms of a bath potential for the molecule–medium (bath) degrees of freedom. This potential, termed the sudden potential, is associated with the change in interaction with the medium that a molecule experiences upon intramolecular state transitions which are induced by external interactions (e.g., by light). Development of the reduced molecule–field density operator leads naturally to a separation of terms which describes scattering and (the propensity for) fluorescence. Critical to the theory is a four-time correlation function for the bath (sudden) potential. The difficulties inherent in defining absorption (spectrum) resonances and the corresponding distinctions between resonance and relaxed emission are discussed. Implications are considered for the further understanding of experimental results on molecular excitation dynamics in the gas phase and in supersonic jets. Sources of stochastic modulation other than material media are mentioned. In particular, the possibility is suggested of the pervasive existence of stochastic modulation through interaction of a molecule with the vacuum state of the radiation field. This raises questions concerning the fundamental relations between quantum mechanics and thermodynamics.
On the basis of a stochastic model of Burshtein et al. (1967) which assumes the phases, frequencies and/or amplitudes of the radiation field to constitute a randomly time-varying jump-like Markoff process, a generalisation of Mollow's theory (1975) of the dynamic Stark effect is formulated leading to predictions for the resonant scattering spectrum for a two-level atom quite similar to those published in the work of Agarwal (1976), of Eberly (1976) and of Kimble et al. (1977) who use a different approach. Apparently, the general form of the resonant scattering spectrum in a modulated radiation field depends less strongly on the particular stochastic model of the laser light than might be expected.
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.
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.
We have investigated the interaction between bichromatic optical fields and atomic transitions. We have considered both the interaction of a saturating bichromatic field in the form of a 100% amplitude-modulated field resonantly interacting with a single atomic transition as well as the interaction of a pair of 100% amplitude-modulated fields with two coupled atomic transitions. In our studies of a single atomic transition resonantly excited by a 100% amplitude-modulated field we have used a fully quantum-electrodynamical analysis to model the Autler-Townes effect induced by a bichromatic optical field. We find that the effect induced by a bichromatic field is markedly different from the effect produced by a monochromatic exciting field. We have derived analytic expressions for the bichromatic Autler-Townes absorption spectrum. The absorption spectrum consists of equally spaced lines spaced by the modulation frequency. The linewidths of neighboring lines alternate as functions of the field strength. Experimentally, we observed this spectrum for both resonant and detuned 100% amplitude-modulated driving fields by monitoring the absorption of a weak monochromatic field as it was tuned about the resonance frequency of the 3²P₃/₂(F = 3, mF = 3) ↔ 4²D₅/₂(F = 4, mF = 4) transition while driving the 3²S₁/₂(F = 2, mF = 2) ↔ 3²P₃/₂(F = 3, mF = 3) transition with a saturating 100% amplitude-modulated field. We found excellent agreement between our predicted and measured spectra. We then investigated the resonant interaction between a pair of 100% amplitude-modulated fields and two atomic transitions sharing a common atomic level. We considered both a three-level atomic cascade system and a three-level atomic lambda system. We examined the effect that the relative phase between the two modulations has on the rate at which the modulated fields are absorbed. We find that the saturated time-averaged field absorption exhibits parametric resonances in both the cascade and lambda systems. The time-averaged absorption is strongly dependent upon the relative phase of modulation between the two fields and for certain phase differences the time-averaged absorption can be enhanced over the maximum saturated absorption experienced by cw fields of the same time-averaged intensities. We also find that the stationary atomic response exhibits periodic oscillations and for the cascade system periodic two-photon inversions of up to 40% can be achieved. We further find dark absorption resonances as a function of phase in the lambda system. We analyze the results from the point of view of semi-classical adiabatic dressed states.