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Journal of Experimental and Theoretical Physics

Relaxation of an atom and a cavity mode in an entangled environment

В. Н. Горбачев, Andrew I. Trubilko

Published Feb 1, 2009• 7 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776109020022

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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.
Parametric interaction of a pair of cavity fields in a near-resonantly driven atomic system is described by a bilinear Hamiltonian that decouples from atomic flip operators and is proportional to the population difference between dressed states. For proper choice of parameters, the parametric interaction is enhanced by at least two orders compared to the dispersively dressed cases. Although spontaneous emission is fed into the cavity fields, destructive interference occurs in the fluctuations of a pair of collective modes. As a result of the two factors, perfect squeezing and Einstein–Podolsky–Rosen entanglement in the output occur when the cavity relaxation rates are much larger than in the dispersive case. The mechanism is applicable to a great variety of multilevel systems and has experimental advantages in the cavity QED generation of squeezed and entangled states of light.
The interaction of a two-level atom with a single mode of the radiation field is examined. The cavity mode is damped by coupling to a reservoir in a squeezed state, and the atom is also driven by an external laser field. A master equation for the atomic density operator in the bad-cavity limit is derived. The effect of the squeezing in the stationary population inversion and in the resonance spectrum of the light emitted by the atom into the background modes is studied. The results are compared with the numerical solution of the full master equation for the atom-plus-cavity mode-density operator.
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 discuss the generation and evolution of a macroscopic entanglement light with a subthreshold non-degenerate parametric oscillator, coupled to a vacuum reservoir. The four-level atoms driven by two classical fields interact with the parametric oscillator. The master equation for the cavity modes of the scheme is derived and analyzed, the entanglement properties of the two-mode light generated by this scheme inside and outside the cavity is studied. We show that the light produced by this system is strongly entangled with time evolution inside and outside a cavity.
We propose an experimental setup, feasible with present day technology, involving two highquality- factor cavities, one Ramsey zone and a two-level atom which interacts with them. The dynamics in the cavities is modeled by a dissipative dispersive Jaynes-Cummings model. Analytical expresions for the evolution superoperator in each part of the proposed setup and for the concurrence between the atom and the first cavity are given, and the pairwise entanglement of the subsystems is calculated numerically. We consider initial separable states given by the tensor product of a superposition of the two atomic relevant states and coherent states for the fields. We show that for realistic model parameters (including dissipation), when the dissipation rates are smaller than the dispersive frequencies (the ratio between the squared vacuum Rabi frequencies and the detunings), the final state of the cavity fields remains entangled.
Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level atom. For the two-mode case, the initial field is a pair coherent state or a two-mode squeezed vacuum. Effects due to nonlinearity, intensity-dependent interaction and detuning on the dynamics are discussed and compared with those of the single-mode case.