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Journal of Experimental and Theoretical Physics

Broadband radiation transport in an optically dense gas in the presence of an RF field

К. А. Баранцев, A. N. Litvinov, Е. Н. Попов

Published Jul 1, 2017• 2 citations
Publisher

Abstract

The theory of transport of fluctuating double-frequency optical radiation in a gas of three-level atoms in the presence of rf radiation forming a closed excitation circuit has been generalized. The theory is based on the quantum kinetic equations for the atomic density matrix, which are solved together with the wave equations for classical electromagnetic fields. After averaging over the radiation fluctuation ensemble, a transition is made to equations for atomic-field correlation functions and transport equations for the spectral density of fields.

DOI
10.1134/s1063776117070159

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The theory of transport of fluctuating double-frequency optical radiation in a gas of three-level atoms in the presence of rf radiation forming a closed excitation circuit has been generalized. The theory is based on the quantum kinetic equations for the atomic density matrix, which are solved together with the wave equations for classical electromagnetic fields. After averaging over the radiation fluctuation ensemble, a transition is made to equations for atomic-field correlation functions and transport equations for the spectral density of fields.
This work is devoted to generalization of the semi-classical theory of interaction of broadband laser radiation with the atomic gas at the room temperature in the cell in the case of the closed excitation contour. The atomic density matrix equations and spectrum and correlations transport equations have been derived for excitation by fluctuating field with Gaussian statistics. It is shown that the spatial oscillations of radiation intensity and atomic density matrix can be excited. It was found that such medium can serve as a filter of incoherent part of the radiation.
The Markov model of spontaneous emission of an atom localized in a spatial region with a broadband electromagnetic field with zero photon density is considered in the conditions of coupling of the electromagnetic field with the broadband field of a neighboring space. The evolution operator of the system and the kinetic equation for the atom are obtained. It is shown that the field coupling constant affects the rate of spontaneous emission of the atom, but is not manifested in the atomic frequency shift. The analytic expression for the radiative decay constant for the atom is found to be analogous in a certain sense to the expression for the decay constant for a singly excited localized ensemble of identical atoms in the conditions when the effect of stabilization of its excited state by the Stark interaction with the vacuum broadband electromagnetic field is manifested. The model is formulated based on quantum stochastic differential equations of the non- Wiener type and the generalized algebra of the Ito differential of quantum random processes.
The effect of field fluctuations on the motion of a two-level atom in resonant laser radiation is investigated theoretically. The internal motion of the atom is treated quantum mechanically (optical Bloch equations); the translational motion, which is coupled to the internal motion, is treated classically (Ehrenfest's theorem); and the fluctuating radiation is treated as a classical electromagnetic wave with stochastic phase (phase-diffusion model). An expression for the radiation force and equations of motion for the ensemble-averaged Bloch vector are derived and used to calculate (i) the radiation force in a plane running wave, (ii) the steady-state radiation force in a general standing wave, and (iii) the dissipative force in a plane standing wave in the limit of strong phase fluctuations. In case (iii) it is found that the atomic velocity is damped when the radiation is tuned above resonance, which is opposite to the case of a weak coherent standing wave, in which damping occurs for radiation tuned below resonance. It is shown that fluctuations have a substantial effect on the radiation force only when the spectral width of the radiation approaches or exceeds the spontaneous emission rate.
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 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.
Generalized single-atom Maxwell-Bloch equations for optically dense media are derived taking into account noncooperative radiative atom-atom interactions. Applying a Gaussian approximation and formally eliminating the degrees of freedom of the quantized radiation field and of all but a probe atom leads to an effective time-evolution operator for the probe atom. The mean coherent amplitude of the local field seen by the atom is shown to be given by the classical Lorentz-Lorenz relation. The second-order correlations of the field lead to terms that describe relaxation or pump processes and level shifts due to multiple scattering or reabsorption of spontaneously emitted photons. In the Markov limit a nonlinear and nonlocal single-atom density matrix equation is derived. To illustrate the effects of the quantum corrections, we discuss amplified spontaneous emission and radiation trapping in a dense ensemble of initially inverted two-level atoms and the effects of radiative interactions on intrinsic optical bistability in coherently driven systems.