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Physical Review A

Aspects of the dynamics of a two-level atom dispersively coupled to a damped and driven field mode

J. G. Peixoto de Faria, Maria Carolina Nemes

Published Jun 18, 2004• 16 citations
Publisher

Abstract

We give a fully analytical description of the dynamics of an atom dispersively coupled to a field mode in a dissipative environment fed by an external source. The competition between the unitary atom field (which leads to entanglement) and the dissipative field-environment couplings are investigated in detail. We find the time evolution of the global atom-field system for any intial state and we show that the atom-field steady state is, at most, classically correlated. For a chosen initial state, we evaluate the purity loss of the global system and of atomic and field subsystems as a function of time. We find that the source will tend to compensate for the dissipation of the field intensity and to accelerate decoherence of the global and atomic states. A result pertinent to quantum information is the quantification of concurrence during the dissipative dynamics. An analytical expression for the time evolution of the concurrence is given.

DOI
10.1103/physreva.69.063812

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We give a fully analytical description of the dynamics of an atom dispersively coupled to a field mode in a dissipative environment fed by an external source. The competition between the unitary atom field (which leads to entanglement) and the dissipative field-environment couplings are investigated in detail. We find the time evolution of the global atom-field system for any intial state and we show that the atom-field steady state is, at most, classically correlated. For a chosen initial state, we evaluate the purity loss of the global system and of atomic and field subsystems as a function of time. We find that the source will tend to compensate for the dissipation of the field intensity and to accelerate decoherence of the global and atomic states. A result pertinent to quantum information is the quantification of concurrence during the dissipative dynamics. An analytical expression for the time evolution of the concurrence is given.
We give a fully description of the dynamics of an atom dispersively coupled to a field mode in a dissipative environment fed by an external source. The competition between the unitary atom-field (which leads to entanglement) and the dissipative field-environment couplings are investigated in detail. We find the time evolution of the global atom-field system for any initial state and we show that atom-field steady state is at most classically correlated. For an initial state chosen, we evaluate the purity loss of the global system and of atomic and field subsystems as a function of time. We find that the source will tend to compensate for the dissipation of the field intensity and to accelerate decoherence of the global and atomic states. Moreover, we show that the degree of entanglement of the atom-field state, for the particular initial state chosen, can be completely quantified by concurrence. Analytical expression for time evolution of the concurrence is given.
The analytical description of the dynamics of a nonlinear atom-field system described by a diagonal f -deformed Jaynes-Cummings model for a chosen initial state is obtained. The purity loss of the global system, and the atomic and field subsystems are discussed. Information on entanglement between the field and matter is studied by comparing the results for mutual entropy, which is a measure of the total correlation, and the negativity as a measure of the amount of entanglement. It is found that the nonlinearity of the dissipation tends to accelerate the decoherence of the global, field, and atomic states. In addition, we find that the so-called entanglement sudden death can occur when both of the nonlinearity couplings between the cavity field and the dissipation are combined. Subject Index: 061
We consider two two-level atoms, interacting with two independent dissipative cavities, each of which is driven by an external source. The two cavity fields are both initially prepared in the coherent states, and the two two-level atoms are initially prepared in the singlet state |Ψ − ⟩ = (|eg⟩ – |ge⟩)/√2. We investigate the influence of the damping constant κ, the intensity of the external sources F, and the relative difference of the atomic couplings r on the entanglement between the two atoms. In the dispersive approximation, we find that the entanglement between the two atoms decreases with the time evolution, and the decreasing rate of entanglement depends on the values of F/κ, κ/ω, and r. For the given small values of F/κ and κ/ω, on the one hand, the increasing of r favors entanglement decreasing of the atomic system, on the other hand, when r → 1 the entanglement decreasing becomes slower. With the increasing of the value of κ/ω, the influence of r on the decreasing rate of entanglement becomes smaller, and gradually disappears for the big value of κ/ω.
We study the dynamics of a collection of two-level atoms interacting with a single mode of a quantized field in a dissipative cavity in the dispersive regime. The quantized mode is driven by a classical driving field. The steady-state density matrix is obtained. The influence of the driving field on the quantized driven field and on atomic properties in both the dissipative and the lossless cases is studied. The atomic decoherence time in the dissipative-driven case is obtained. We show that the external driving field strongly suppresses the atomic coherence (in comparison with the dissipative cavity without the driving field).
We present the time evolution of a two-level atom interacting dispersively with an electromagnetic field in a dissipative cavity. We investigate the influence of dissipation on the entanglement of the two subsystems (atom+field).(\mathrm{atom}+\mathrm{field}).(atom+field). Simple but realistic, the model displays several nontrivial quantum features, which emerge when an environment is taken into account: the cavity is shown to have practically no influence in the coherence properties of the field from the qualitative point of view. On the other hand, although the atom is not directly coupled to the cavity modes, its coherent properties are strongly influenced by dissipation both qualitatively as well as quantitatively.
We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, comprising a first subsystem (a harmonic oscillator) coupled to a driven and damped second subsystem (another harmonic oscillator). We choose initial states whose dynamics is confined to a couple of two-level systems, and show that the maximum value of entanglement between the two subsystems, as measured by concurrence, depends on the dissipation rate to the coupling-constant ratio and the initial state. While in a related model the entropy of the first subsystem (a two-level system) never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model.