The time evolution of an entangled bi-partite qubit interacting with two independent photon baths in isolated cavities is not unitary. It is shown that the bi-partite qubit oscillates between pure and mixed states, and that the initial entanglement is lost and recovered in time by time as a consequence of its interaction with the baths.
We analyze the time-evolution of a pair of atoms that are initially entangled and are each of them in an independent isolated QED cavity. The cavities are assumed to contain a radiation bath of a given number of photons. The sudden death and recovering of entanglement are studied in terms of the concurrence introduced by Hill and Wootters. This last gives the value 1 for maximal entanglement and 0 for unentangled systems. We find that the entanglement of the bipartite atomic systems depends on the number of photons in the cavities when the radiation bath is assumed to be in a Fock state.
We investigate a system of two interacting qubits having one of them isolated and the other coupled to a thermal reservoir. We consider two different models of system-reservoir interaction: i) a model, in which the master equation is derived taking into account the interaction between the two subsystems (qubits), ii) a naive model, in which the master equation consists of a dissipative term added to the unitary evolution term. We study the dynamics of quantities such as bipartite entanglement, quantum discord and the linear entropy of the isolated qubit for both strong and weak coupling regimes (qubit-qubit interaction) as well as for different temperatures of the reservoir. We find significant disagreements between the results obtained from the two models even in the weak coupling regime. For instance, we show that according to the phenomenological model, the isolated qubit would approach a maximally mixed state more slowly for higher temperatures (unphysical result), while the microscopic model predicts the opposite behaviour (correct result).
We examine the time evolution of entanglement between two qubits of a system of four qubits. The system is composed of two separate cavities each containing a single two-level atom. The qubits of the system are the two atoms and the two cavity modes. We show that during the transfer of an initial entanglement from atoms to the cavity modes, an additional entanglement is induced between the atoms and the cavity modes. Thus, during the evolution, the system effectively behaves as a six qubit system. In addition, we study the entanglement evolution for an imperfect matching of the atoms to the cavity modes. We show that the imperfect matching can force a stable entangled state to evolve in time and may produce a continuous entanglement in time.
A complete treatment of the entanglement of two-level systems, which evolves through the contact with a thermal bath, must include the fact that the system and the bath are not fully separable. Therefore, quantum coherent superpositions of system and bath states, which are almost never fully included in theoretical models, are invariably present when an entangled state is prepared experimentally. We show their importance for the time evolution of the entanglement of two qubits coupled to independent baths. In addition, our treatment is able to handle slow and low-temperature thermal baths.
We discuss the ground state entanglement of a bi-partite system, composed by a qubit strongly interacting with an oscillator mode, as a function of the coupling strength, the transition frequency and the level asymmetry of the qubit. This is done in the adiabatic regime in which the time evolution of the qubit is much faster than the oscillator one. Within the adiabatic approximation, we obtain a complete characterization of the ground state properties of the system and of its entanglement content.
We discuss the ground state entanglement of a bi-partite system, composed by a qubit strongly interacting with an oscillator mode, as a function of the coupling strength, the transition frequency and the level asymmetry of the qubit. This is done in the adiabatic regime in which the time evolution of the qubit is much faster than the oscillator one. Within the adiabatic approximation, we obtain a complete characterization of the ground state properties of the system and of its entanglement content.