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DYNAMICS OF ENTANGLEMENT IN OPTICAL CAVITIES

J. M. Herazo

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The dynamics of one two-level atoms coupled to a lossy electromagnetic cavity, in the dispersive regime, is analyzed. A Lie algebraic technique is employed to find an analytic expression for the density operator and the linearized entropies of all systems and subsys- tems involved. Despite the infinite number of levels of the cavity electromagnetic field, which is initially prepared in a coherent state, it is shown that concurrence can be used to characterize entanglement

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The dynamics of one two-level atoms coupled to a lossy electromagnetic cavity, in the dispersive regime, is analyzed. A Lie algebraic technique is employed to find an analytic expression for the density operator and the linearized entropies of all systems and subsys- tems involved. Despite the infinite number of levels of the cavity electromagnetic field, which is initially prepared in a coherent state, it is shown that concurrence can be used to characterize entanglement
We examine the dynamics of bipartite quantum entanglement between a two-level atom and the electromagnetic field. We begin with the Jaynes-Cummings model with a single field mode and examine in detail the exact time evolution of entanglement, including cases where the atomic state is initially mixed and the atomic transition is detuned from resonance. We then explore the effects of other nearby modes by calculating the exact time evolution of entanglement in more complex systems with two, three, and five field modes. For these cases we can obtain exact solutions which include the strong-coupling regime. Finally, we consider the entanglement of a two-level atom with the infinite collection of modes present in the intracavity field of a Fabre-Perot cavity. In contrast to the usual treatment of atom-field interactions with a continuum of modes using the Born-Markov approximation, our treatment in all cases describes the full non-Markovian dynamics of the atomic subsystem under general couplings. Only when an analytic expression for the infinite mode case is desired do we need to make a weak coupling assumption which at late times approximates Markovian dynamics.
We describe the unitary dynamics and the entanglement properties of a system where a cavity field mode is resonantly coupled to one or two two-level atoms that are strongly driven in the cavity by a coherent field. The cavity field and one atom prepared in pure states always entangle, except when atoms are maximally polarized. The entanglement is maximum for atoms in the upper or lower state and for interaction times in the strong coupling regime. Two atoms, though correlated via the cavity field, do not entangle if the field is not accessible to measurements as in the microwave domain. However, in the optical regime, a null measurement of the cavity field can conditionally prepare an atom pair in a maximally entangled state.
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.
We investigate the entanglement dynamics in a quantum system consisting of three two-level atoms resonantly coupled to a single mode cavity in the presence of phase decoherence. With the help of the dynamical algebraic method, we obtain an analytical solution of the present system. The influence of phase decoherence on the entanglement of the system is studied. We find that the entanglement between the cavity field and any atom will be destroyed completely by phase decoherence as the system evolves. However, there is long-lived entanglement (or stationary state entanglement) of arbitrary two atoms, that is, the entanglement of atoms is more robust against phase decoherence than that of the atom-field system.