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arXiv:0806.4852 · Journal of Physics A Mathematical and Theoretical

Dissipation and entanglement dynamics for two interacting qubits coupled to independent reservoirs

M Scala, Rosanna Migliore, A Messina

Published Oct 1, 2008• 52 citations
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Abstract

We derive the master equation of a system of two coupled qubits by taking into account their interaction with two independent bosonic baths. Important features of the dynamics are brought to light, such as the structure of the stationary state at general temperatures and the behaviour of the entanglement at zero temperature, showing the phenomena of sudden death and sudden birth as well as the presence of stationary entanglement for long times. The model here presented is quite versatile and can be of interest in the study of both Josephson junction architectures and cavity-QED.

DOI
10.1088/1751-8113/41/43/435304

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We derive the master equation of a system of two coupled qubits by taking into account their interaction with two independent bosonic baths. Important features of the dynamics are brought to light, such as the structure of the stationary state at general temperatures and the behaviour of the entanglement at zero temperature, showing the phenomena of sudden death and sudden birth as well as the presence of stationary entanglement for long times. The model here presented is quite versatile and can be of interest in the study of both Josephson junction architectures and cavity-QED.
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We investigate the entanglement dynamical behavior of two coupled qubits via a Heisenberg XX interaction, which are connected with two independent finite temperature heat baths. By numerical simulations of the quantum master equation, it is found that the interesting phenomena of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. We also show that two critical temperatures T 1 (determining that the quantum state is entangled or separable) and T 2 (where maximal stationary entanglement can be observed) exist, and stationary entanglement exhibits a non-monotonic behavior as a function of the finite temperature noise strength. These results enlarge the domain of the reasonable experimental temperature where stationary entanglement can be observable.
The reduced dynamics of two interacting qubits coupled to two independent bosonic baths is investigated. The one-excitation dynamics is derived and compared with that based on the resolution of appropriate non-Markovian master equations. The Nakajima-Zwanzig and the time-convolutionless projection operator techniques are exploited to provide a description of the non-Markovian features of the dynamics of the two-qubit system. The validity of such approximate methods and their range of validity in correspondence to different choices of the parameters describing the system are brought to light.
By analytically solving the Lindblad form of the master equation, we investigate entanglement dynamics of two qubits coupled via the XY interaction, where each qubit is interacting with an independent reservoir with the squeezing parameters and squeezing angles. In the weak-squeezed reservoir, we show that the entanglement sudden death and entanglement sudden birth will happen for various entangled states. Some initial product states evolve into entangled ones, initially entangled states lose completely or partially their entanglement. The effects of varying the degree of entanglement of the initial states, the spin chain system parameters and different values of the degree of squeezing on the sudden death, revival and birth times are analyzed in detail. We also see that the steady state concurrence appears in the squeezed dissipative environments, which is affected by both the system parameters and the degree of squeezing.
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 discuss the evolution of entanglement for a system of two two-level atoms interacting with a common reservoir at finite temperature. The Markovian master equation is used to describe the evolution of entanglement measured by concurrence. The phenomena of sudden birth and sudden death of entanglement are discussed. It is shown that entanglement sudden death is a standard feature when the reservoir has finite temperature. Entanglement sudden birth, which is the result of the collective behaviour of atoms, appears only for a sufficiently small mean number of photons of the reservoir (sufficiently low temperatures), and it gradually diminishes as the temperature increases. The results are illustrated for the system prepared in the Werner state.