Relaxation of interacting atoms in an external random field

Iosif B. Khriplovich

Sergey V. Bozhokin, Vladislav Gennadievich Malyshkin

Abstract A fluorescence dynamics of a cold atomic cloud, laser–cooled to a very low temperature, optically excited by a short laser impulse is calculated by applying non–stationary Schrödinger equation to the system of atoms and electromagnetic field. The solution gives fluorescence time–relaxation dependence, with relaxation time distribution depending on the system itself and external electromagnetic field applied. The distribution of the relaxation rates changes, when an external electric field affecting the atomic ensemble is applied. To analyze the relaxation process a novel Radon–Nikodym approach is applied: the relaxation curve is not piece–wise interpolated, but instead is converted to a matrix, the eigenvalues of which provide relaxation rate distribution. In contrasts to the random matrix theory, where the weights, corresponding to an eigenvalue, are considered equal, in this work the weight, corresponding to an individual eigenvalue, is determined by the Lebesgue integral quadrature weights.

Pier A. Mello, Pedro Pereyra, Narendra Kumar

Victor A. Mikhailov, Nikolay V. Troshkin

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.S. Davydov