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Optics and Spectroscopy

Relaxation in an entangled thermostat

В. Н. Горбачев, Andrew I. Trubilko

Published Jul 1, 2010• 0 citations
Publisher

Abstract

A generalized Lindblad equation is derived that describes the relaxation of two systems of an arbitrary physical nature in an entangled thermostat. The relaxation of an atom and a mode of the electromagnetic field selected by a high- Q cavity is considered as an example. Using the introduced collective operators for an atom and a mode, it is shown that the entangled state of the thermostat can lead to the coherent and squeezed state of the atom and the mode.

DOI
10.1134/s0030400x10070064

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A generalized Lindblad equation is derived that describes the relaxation of two systems of an arbitrary physical nature in an entangled thermostat. The relaxation of an atom and a mode of the electromagnetic field selected by a high- Q cavity is considered as an example. Using the introduced collective operators for an atom and a mode, it is shown that the entangled state of the thermostat can lead to the coherent and squeezed state of the atom and the mode.
A generalized Lindblad equation has been derived for describing the evolution of two dynamical systems interacting with a bath formed by two broadband modes of squeezed light in an entangled state. The transfer of quantum correlations, in particular, entanglement between the bath and dynamic systems, which are taken in the form of two electromagnetic field modes separated by two high- Q cavities, two atoms, and an atom and a mode, has been analyzed. It has been found that the entanglement of the bath is transferred both to two modes and to two atoms, which can form an almost perfect Einstein-Podolsky-Rosen pair. It has been shown that the interaction of the bath with the system consisting of an atom and a mode for which collective boson operators are introduced leads to the appearance of coherent and squeezed states.
It is shown that, in the Markov approximation, relaxation of two noninteracting atoms in the field of a common thermostat leads not only to decoherence but also to the opposite process of the entanglement of atomic states, which can take on a stationary value depending on the initial conditions. This region of initial conditions narrows as the mean number of photons in the thermostat increases. The main radiative mechanism destroying an arbitrary initial entanglement of atoms is interaction of each atom with its own thermostat independent of the other. All Markov relaxation models under consideration are based on the Lindblad equations.
A kinetic equation governing relaxation of a single two-level atom and a high- Q cavity mode in an entangled thermostat exhibiting quantum correlations is presented. Based on two kinds of collective operators, we demonstrate the possibility of the existence of dual squeezed states in this system. One kind of generator of collective operators corresponds to algebra obtained by polynomial deformation of the angular-momentum algebra, while the other kind corresponds to the Heisenberg-Weyl algebra. Squeezed states of the collective system are defined in terms of commutative relations for operators of the corresponding generator algebras. It is shown that quantum correlations in the system manifest themselves in two physical phenomena. The first one is the known entanglement-swapping protocol and is based on the projection measurement. In the other case, quantum correlations reveal themselves in the coherent scattering dynamics of an atom in the field of a standing light wave.
We derive a master equation describing the collective decay of two-level atoms inside a single mode cavity in the dispersive limit. By considering atomic decay in the collective thermostat, we found a decoherence-free subspace of the multiparticle entangled states of the WWW-like class. We present a scheme for writing and storing these states in collective thermostat.