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Optics and Spectroscopy

Correlations of a single atom and a resonance mode and their manifestation in some physical phenomena

В. Н. Горбачев, Andrew I. Trubilko

Published Apr 1, 2014• 1 citation
Publisher

Abstract

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.

DOI
10.1134/s0030400x14040122

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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.
The general kinetic equation for an isolated two-level atom and a high- Q cavity mode in a heat bath exhibiting quantum correlations (entangled bath) is applied to the analysis of the squeezed states of the collective system. Two types of collective operators are introduced for the analysis: one is based on bosonic commutation relations, and the other, on the commutation relations of the algebra obtained by a polynomial deformation of the angular momentum algebra. On the basis of these relations, formulas for observables are constructed that identify squeezed states in the system. It is shown that, under certain conditions, the collective system exhibits dual squeezing within the relations for boson operators, as well as for the operators constructed from the angular momentum algebra. Such squeezing is demonstrated under a projective measurement of an atom and for an entanglement swapping protocol. In the latter case, when measuring two initially independent atomic systems, depending on the type of measurement, two cavity modes collapse into a nonseparable state, which is described either by a nonseparability relation based on boson operators or by a relation based on the operators of the algebra of the quasimomentum of the collective system consisting of these two modes.
Collective operators corresponding to two different algebras have been introduced for a simple system consisting of a single two-level atom and a high-quality cavity mode. The generators of the first algebra satisfy boson commutation relations, whereas the generators of the second algebra have been obtained by polynomial deformation of su(2) algebra. It has been shown that dual squeezed states identified using the considered commutation relations can be observed in the system placed in an entangled bath with quantum correlations.
The master equation is derived for an atom and a single high-Q cavity mode interacting with the bath modes produced by a two-mode broadband source based on two degenerate optical parametric oscillators. The relaxation superoperator, found in the resonant and dispersive limits, contains new terms describing correlations between the atom and the cavity mode. Collective coherent states are introduced to show that squeezed states of the atom-cavity subsystem are generated via interaction with an entangled environment. It is shown that a correlated initial state of the atom and the cavity mode manifests itself in two cavity QED phenomena: spontaneous atomic emission in the strong-coupling regime and population inversion in the Jaynes-Cummings model.
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.