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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

The Fokker-Planck equation for relaxation of a system of two dipole-dipole interacting atoms

Victor A. Mikhailov, Nikolay V. Troshkin, Anton M. Trunin

Published Apr 21, 2016• 1 citation
Publisher

Abstract

The relaxation of a pair of dipole-dipole interacting two-level atoms with parallel dipole moments in a large dissipative system is studied on the basis of the generalized coherent states method. The Fokker-Planck equation and its exact solution are obtained. Explicit formulas for two-time correlation functions are given. The influence of the magnitude of the interaction on the shape of the radiation line is investigated.

DOI
10.1117/12.2229712

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The relaxation of a pair of dipole-dipole interacting two-level atoms with parallel dipole moments in a large dissipative system is studied on the basis of the generalized coherent states method. The Fokker-Planck equation and its exact solution are obtained. Explicit formulas for two-time correlation functions are given. The influence of the magnitude of the interaction on the shape of the radiation line is investigated.
This work is devoted to the description of the interaction between n-level atom and a large dissipative system (heat bath). SU(n)-group coherent states as useful and convenient basis are employed. Fokker-Planck-like equations for (rho) - symbol of reduced density matrix taking into account possible squeezed fluctuations of heat bath are derived. New formulas for correlators of the transition operators between levels of system are obtained and influence of squeezing on the shape of radiation lines is discussed.
A generalized second-order Fokker-Planck equation is derived for a single two-level atom in a cavity driven by an external classical field without using system size expansion or any truncation. Effects of detuning, as well as atomic and cavity decays, are incorporated in this Fokker-Planck equation. This equation is used to study atomic inversion and the second-order intensity correlation function of light in the bad-cavity limit by adiabatically eliminating the field variables. Several novel features in atomic inversion and intensity correlations that arise due to atomic and cavity detuning are discussed. Curves are presented to illustrate the behavior.
Relaxation of a three-level atom with non-equidistant spectrum interacting with a thermostat and an external stochastic field is studied. The master equation for the reduced density matrix and its solution in the first order of the perturbation theory are obtained. Using quantum regression theorem, explicit formulas for two-time correlation functions and shapes of radiation lines are derived for all types of three-level atoms and the following stochastic processes: a delta-correlated process and a Kubo-Anderson process. The influence of stochastic perturbations of atom’s energy levels and damping constants of adjacent transitions on width of radiation lines is shown.
A quantum treatment of a coherently driven cavity with a medium of two-level atoms is given. The system displays both absorptive and dispersive bistability. Quantum fluctuations are included via a Fokker-Planck equation in a generalized PPP representation, after adiabatic elimination of the atomic variables. The transmitted spectrum and correlation function is calculated in a linearized (Gaussian) approximation. In the limit of large detuning and radiative damping, the quantum fluctuations are identical to those of a simple nonlinear polarizability theory. An analysis is given of the nonclassical statistical properties of the intensity-correlation spectrum.
A theoretical analysis is developed for the spectrum of the light scattered by two two-level atoms driven near resonance by an external coherent electromagnetic field. The atoms are assumed to relax to equilibrium with the driving field as a result of radiation damping. The explicit dependence of the coherent dipole-dipole interactions on the distance between the two atoms is taken into account. For the case of two two-level atoms with a fixed distance smaller than a wavelength, an analytical result for the resonance fluorescence line shape is obtained, and the result is compared to previous work.>