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arXiv:quant-ph/0502181 · Physical Review E

Control of local relaxation behavior in closed bipartite quantum systems

Harry Schmidt, Günter Mahler A

Published Jul 19, 2005• 11 citations
arXivHTMLPDF

Abstract

We investigate the decoherence of a spin- 1/2 subsystem weakly coupled to an environment of many spins- 1/2 with and without mutual coupling. The total system is closed, its state is pure, and evolves under Schrödinger dynamics. Nevertheless, the considered spin typically reaches a quasistationary equilibrium state. Here we show that this state depends strongly on the coupling to the environment on the one hand and on the coupling within the environmental spins on the other. In particular we focus on spin star and spin ring-star geometries to investigate the effect of intra-environmental coupling on the central spin. By changing the spectrum of the environment, its effect as a bath on the central spin is also changed and may even be adjustable to some degree. We find that the relaxation behavior is related to the distribution of the energy eigenstates of the total system. For each of these relaxation modes, there is a dual mode for which the resulting subsystem approaches an inverted state occupation probability (negative temperature).

DOI
10.1103/physreve.72.016117

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We investigate the decoherence of a spin- 1/2 subsystem weakly coupled to an environment of many spins- 1/2 with and without mutual coupling. The total system is closed, its state is pure, and evolves under Schrödinger dynamics. Nevertheless, the considered spin typically reaches a quasistationary equilibrium state. Here we show that this state depends strongly on the coupling to the environment on the one hand and on the coupling within the environmental spins on the other. In particular we focus on spin star and spin ring-star geometries to investigate the effect of intra-environmental coupling on the central spin. By changing the spectrum of the environment, its effect as a bath on the central spin is also changed and may even be adjustable to some degree. We find that the relaxation behavior is related to the distribution of the energy eigenstates of the total system. For each of these relaxation modes, there is a dual mode for which the resulting subsystem approaches an inverted state occupation probability (negative temperature).
We investigate a two-level system in contact with a larger quantum environment, often consisting of many two-level systems itself (spin environment) which may or may not interact. The total system is considered to be closed. The environment typically is in a canonical state with a given temperature initially. Depending on the precise spectral structure of the environment and the type of coupling between both systems, the smaller part may relax to a canonical state with the same temperature as the environment (i.e., thermal relaxation) or to some other quasiequilibrium state (nonthermal relaxation). The type of (quasi)equilibrium state can be related to the distribution of certain properties of the energy eigenvectors of the total system. We examine these distributions for several abstract and concrete (spin environment) Hamiltonian systems; the significant aspect of these distributions can be related to the relative strength of the local and interaction parts of the Hamiltonian.
We investigate a two-level system in resonant contact with a larger environment. The environment typically is in a canonical state with a given temperature initially. Depending on the precise spectral structure of the environment and the type of coupling between both systems, the smaller part may relax to a canonical state with the same temperature as the environment (i.e., thermal relaxation) or to some other quasiequilibrium state (nonthermal relaxation). The type of (quasi)equilibrium state can be related to the distribution of certain properties of the energy eigenvectors of the total system. We examine these distributions for several abstract and concrete (spin environment) Hamiltonian systems; the significant aspect of these distributions can be related to the relative strength of the local and interaction parts of the Hamiltonian.
We discuss the quantum dynamics of an isolated composite system consisting of weakly interacting many-body subsystems. We focus on one of the subsystems, S, and study the dependence of its quantum correlations and decoherence rate on the state of the weakly-coupled complementary part E, which represents the environment. As a theoretical laboratory, we consider a composite system made of two stacked quantum Ising chains, locally and homogeneously weakly coupled. One of the chains is identified with the subsystem S under scrutiny, and the other one with the environment E. We investigate the behavior of S at equilibrium, when the global system is in its ground state, and under out-of-equilibrium conditions, when the global system evolves unitarily after a quench of the coupling between S and E. When S develops quantum critical correlations in the weak-coupling regime, the associated scaling behavior crucially depends on the quantum state of E, whether it is characterized by short-range correlations (analogous to those characterizing disordered phases in closed systems), algebraically decaying correlations (typical of critical systems), or long-range correlations (typical of magnetized ordered phases). In particular, different scaling behaviors, depending on the state of E, are observed for the decoherence of the subsystem S, as demonstrated by the different power-law divergences of the decoherence susceptibility that quantifies the sensitivity of the coherence to the interaction with E.
A low-temperature model system consisting of a central spin coupled to a spin-bath is studied to determine whether interaction among bath spins has an effect on central spin dynamics. In the absence of intra-environmental coupling, decoherence of the central spin is fast and irreversible. Strong intra-environmental interaction results in an effective decoupling of the central spin from the bath and suppression of decoherence. Weaker intra-environmental coupling reduces but does not eliminate decoherence. We argue that similar suppression of decoherence should be observed for electronic states of He impurities in silicon or diamond.
We derive the exact reduced dynamics of a central two-qubit system in a spin star configuration. The exact evolution of the reduced system density matrix is obtained and we compute the limit of an infinite number of environment spins. Initially pure states of the central system evolve into mixed ones and we determine the decoherence-free states of the model. The long-time behavior is studied, partial decoherence is shown to be a result of the coupling of the qubits to the environment, and entanglement evolution of the central system is investigated.
We study the entanglement evolution in a weakly coupled bipartite system with a large energy level difference under the influence of spin-star environments. The subsystems can be coupled to a pure state or a thermal equilibrium state spin-star environment. Our results show that, in the case of the coupling strength being less than the energy level difference of the subsystems (weakly coupled), the spin-star environment can always be used to assist the entanglement generation of the bipartite system.