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

Creation and destruction of the coherence for quantum systems in regular and stochastic fields

Alexander V. Gorokhov

Published Jul 11, 2006• 0 citations
Publisher

Abstract

The problem of the coherent states generation with definite parameters for multilevel quantum systems is investigated. The interaction with external environment and stochastic fields can destroy of the coherence. The competition of these processes is considered on a base of Fokker - Planck Equations approach, deriving from master equation for the density matrix of the system. Examples of the coherent states dynamics for two-level atoms in an external stochastic field in the nonideal resonator are considered. Average over the realizations of stochastic fields is performed for the case of white gaussian noise and Kubo - Anderson process. Explicit formulas for transition probabilities, longitudinal and transversal relaxation times and shape of radiation line are obtained.

DOI
10.1117/12.696856

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The problem of the coherent states generation with definite parameters for multilevel quantum systems is investigated. The interaction with external environment and stochastic fields can destroy of the coherence. The competition of these processes is considered on a base of Fokker - Planck Equations approach, deriving from master equation for the density matrix of the system. Examples of the coherent states dynamics for two-level atoms in an external stochastic field in the nonideal resonator are considered. Average over the realizations of stochastic fields is performed for the case of white gaussian noise and Kubo - Anderson process. Explicit formulas for transition probabilities, longitudinal and transversal relaxation times and shape of radiation line are obtained.
The problem of the coherent state generation with definite parameters for multilevel quantum systems is investigated. The interaction with external environment and stochastic fields can destroy the coherence. The competition of these processes is considered on the basis of the Fokker-Planck equations approach, derived from the master equation for the density matrix of the system. Examples of the coherent states dynamics for two-level atoms in an external stochastic field in a nonideal resonator are considered. Average over the realizations of stochastic fields is performed for the case of the white Gaussian noise and the Kubo-Anderson process. Explicit formulas for probability and shape of radiation line are obtained.
Relaxation of a motionless three-level atom with a non-equidistant spectrum in a photon heat bath and an external stochastic field is investigated. In the Markovian approximation of the relaxation processes a master equation for the reduced density matrix is derived by making use of the averaging over realizations of the stochastic field. The master equation is solved exactly. The correlation functions, the shapes of the radiation lines, the intensity correlation and photon number spectrums are calculated for the V, Ξ and Λ atoms and realizations of the stochastic field by a delta-correlated and a Kubo-Anderson processes.
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.
The problem of the coherent generation of the entanglement photon pairs by an ensemble of the two-level atoms passing through the cavity is studied. The dependence of the generation rate of the photon pairs as a function of the coherent states of the atomic stream is established. Considering that the flying time of the atoms passing through the cavity is less than decay time, a new method of the elimination of atomic variables from the system is proposed. The master equation for multimode cavity electromagnetic field is obtained. Using the Fokker–Planck equations, the steady state solution of this master equation is studied. The quantum properties of the multimode electromagnetic field are analyzed, using the non-diagonal P representation for su (1,1) symmetry.
We develop a formally exact master equation to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over stochastic processes generally results in decoherence effects in closed system dynamics, in addition to the unitary evolution. We then show that, for an important class of problems in which the Hamiltonian is proportional to a Gaussian random process, the 2nd-order master equation yields exact dynamics. The general formalism is applied to study the examples of a two-level system, two atoms in a stochastic magnetic field and the heating of a trapped ion, where we find phenomena such as decoherence-induced disentanglement.