Non-Markovianity of qubit evolution under the action of spin environment (original) (raw)
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Entanglement dynamics in systems of qubits with Markov environments
Physica Scripta, 2009
Entanglement dynamics in representative examples of Markov open quantum systems with qualitatively different dynamics are studied. Rings of qubits with thermal or dephasing local environment are used to study the qualitative properties of the entanglement dynamics depending on the interqubit interaction, type of environment and the initial state. It is demonstrated that the effect of the local environment is manifested as an exponential decrease of the entanglement superimposed on the entanglement dynamics in the isolated system.
Two coupled qubits interacting with a thermal bath: A comparative study of different models
A B S T R A C T We investigate the dynamics of two interacting two-level systems (qubits) having one of them isolated and the other coupled to a large number of modes of the quantized electromagnetic field (thermal reservoir). We consider two different models of system–reservoir interaction: (i) a " microscopic " model, according to which the corresponding master equation is derived taking into account the interaction between the two subsystems (qubits); (ii) a naive " phenomenological " model, in which such interaction is neglected in the derivation of the master equation. We study the dynamics of quantities such as bipartite entanglement, quantum discord and the linear entropy of the isolated qubit in both the strong and weak coupling regimes of the inter-qubit interaction. We also consider 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).
Non-Markovian Entanglement Dynamics in the Presence of System-Bath Coherence
Physical Review Letters, 2010
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.
Non-Markovian qubit dynamics in a thermal field bath: Relaxation, decoherence and entanglement
2004
We study the non-Markovian dynamics of a qubit made up of a two-level atom interacting with an electromagnetic field (EMF) initially at finite temperature. Unlike most earlier studies where the bath is assumed to be fixed, we study the coherent evolution of the combined qubit-EMF system, thus allowing for the back-action from the bath on the qubit and the qubit on the bath in a self-consistent manner. In this way we can see the development of quantum correlations and entanglement between the system and its environment, and how that affects the decoherence and relaxation of the system. We find non-exponential decay for both the diagonal and non-diagonal matrix elements of the qubit's reduced density matrix in the pointer basis. From the diagonal elements we see the qubit relaxes to thermal equilibrium with the bath. From the non-diagonal elements, we see the decoherence rate beginning at the usually predicted thermal rate, but changing to the zero temperature decoherence rate as the qubit and bath become entangled. These two rates are comparable, as was shown before in the zero temperature case [C. Anastopoulos and B. L. Hu, Phys. Rev. A 62 ]. On the entanglement of a qubit with the EMF under this type of resonant coupling we calculated, for the qubit reduced density matrix, the fidelity and the von Neumann entropy, which is a measure of the purity of the density matrix. The present more accurate non-Markovian calculations predict lower loss of fidelity and purity as compared with the Markovian results. Generally speaking, with the inclusion of quantum correlations between the qubit and its environment, the non-Markovian processes tend to slow down the drive of the system to equilibrium, prolonging the decoherence and better preserving the fidelity and purity of the system.
Entanglement dynamics of two independent qubits in environments with and without memory
Physical Review A, 2008
A procedure to obtain the dynamics of NNN independent qudits ($d$-level systems) each interacting with its own reservoir, for any arbitrary initial state, is presented. This is then applied to study the dynamics of the entanglement of two qubits, initially in an extended Werner-like mixed state with each of them in a zero temperature non-Markovian environment. The dependence of the entanglement dynamics on the purity and degree of entanglement of the initial states and on the amount of non-Markovianity is also given. This extends the previous work about non-Markovian effects on the two-qubit entanglement dynamics for initial Bell-like states [B. Bellomo \textit{et al.}, Phys. Rev. Lett. \textbf{99}, 160502 (2007)]. The effect of temperature on the two-qubit entanglement dynamics in a Markovian environment is finally obtained.
Non-Markovian thermalization of entangled qubits
Arxiv preprint quant-ph/0604030, 2006
Matthias Jakob and Michael Nölle ARC Seibersdorf Research GmbH, Tech Gate Vienna, Donau-City-Str. 1, A-1220 Vienna, Austria (Dated: February 1, 2008) We study the decoherence properties of an entangled bipartite qubit system, represented by two two-level atoms that ...
Entanglement dynamics of two qubits in a common bath
Physical Review A, 2012
We derive a set of hierarchical equations for qubits interacting with a Lorentz-broadened cavity mode at zero temperature, without using the rotating-wave, Born, and Markovian approximations. We use this exact method to reexamine the entanglement dynamics of two qubits interacting with a common bath, which was previously solved only under the rotating-wave and single-excitation approximations. With the exact hierarchy equation method used here, we observe significant differences in the resulting physics, compared to the previous results with various approximations. Double excitations due to counter-rotating-wave terms are also found to have remarkable effects on the dynamics of entanglement. PACS numbers: 03.65.Ta, 03.65.Ud, 03.65.Yz
Entanglement dynamics of coupled qubits and a semi-decoherence free subspace
Physics Letters A, 2010
We study the entanglement dynamics and relaxation properties of a system of two interacting qubits in the two cases (I) two independent bosonic baths and (II) one common bath, at temperature T. The entanglement dynamics is studied in terms of the concurrence C(t) between the two spins and of the von Neumann entropy S(t) with respect to the bath, as a function of time. We prove that the system does thermalize. In the case (II) of a single bath, the existence of a decoherence-free (DFS) subspace makes entanglement dynamics very rich. We show that when the system is initially in a state with a component in the DFS the relaxation time is surprisingly long, showing the existence of semi-decoherence free subspaces. The equilibrium state in this case is not the Gibbs state. The entanglement dynamics for the single bath case is also studied as a function of temperature, coupling strength with the environment and strength of tunneling coupling. The case of the mixed state is finally shown and discussed.
Journal of Physics A: Mathematical and Theoretical, 2010
We explore various aspects of the quantum entanglement dynamics of systems of two, three and four qubits interacting with an environment at zero temperature in a non-Markovian regime, as described by the paradigmatic model recently studied by Bellomo, Lo Franco, and Compagno [Bellomo et al. Phys. Rev. Lett. 99 (2007) 160502]. We consider important families of initial states for the alluded systems. The average, typical entanglement evolution associated with each of these families is determined, and its relation with the evolution of the global degree of mixedness of the multi-qubit system is explored. For three and four qubits we consider the family of initial states equivalent under local unitary transformations to the |GHZ and |W states, and compare their average behavior with the average behavior exhibited by initial maximally entangled twoqubits states. Furthermore, in the case of two qubits, the evolution of other manifestations of entanglement, related to measurable quantities, is also investigated. In particular, we consider the Mintert-Buchleitner concurrence lower bound and an entanglement indicator based upon the violation of local uncertainty relations.