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arXiv:0803.0364 · Physical Review B

Induced decoherence and entanglement by interacting quantum spin baths

Cheng-Yan Lai, Jo-Tzu Hung, Chung‐Yu Mou, Pochung Chen

Published May 13, 2008• 48 citations
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Abstract

The reduced dynamics of a single qubit or two qubits coupled to an interacting quantum spin bath modeled by an $XXZ$ spin chain is investigated. By using the method of a time-dependent density matrix renormalization group $(t\text{-DMRG})$, we go beyond the uniform coupling central spin model and nonperturbatively evaluate the induced decoherence and entanglement. It is shown that both the decoherence and the entanglement strongly depend on the phase of the underlying spin bath. We show that in general, spin baths can induce entanglement for an initially disentangled pair of qubits. Furthermore, when the spin bath is in the ferromagnetic phase because the qubits directly couple to the order parameter, the reduced dynamics shows an oscillatory type behavior. On the other hand, only for the paramagnetic and the antiferromagnetic phases do the initially entangled states suffer from an entanglement sudden death. By calculating the concurrence, the finite disentanglement time is mapped out for all of the phases in the phase diagram of the spin bath.

DOI
10.1103/physrevb.77.205419

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The reduced dynamics of a single qubit or two qubits coupled to an interacting quantum spin bath modeled by an XXZXXZXXZ spin chain is investigated. By using the method of a time-dependent density matrix renormalization group (t-DMRG)(t\text{-DMRG})(t-DMRG), we go beyond the uniform coupling central spin model and nonperturbatively evaluate the induced decoherence and entanglement. It is shown that both the decoherence and the entanglement strongly depend on the phase of the underlying spin bath. We show that in general, spin baths can induce entanglement for an initially disentangled pair of qubits. Furthermore, when the spin bath is in the ferromagnetic phase because the qubits directly couple to the order parameter, the reduced dynamics shows an oscillatory type behavior. On the other hand, only for the paramagnetic and the antiferromagnetic phases do the initially entangled states suffer from an entanglement sudden death. By calculating the concurrence, the finite disentanglement time is mapped out for all of the phases in the phase diagram of the spin bath.
We investigate the reduced dynamics of single or two qubits coupled to an interacting quantum spin bath modeled by a XXZ spin chain. By using the method of time‐dependent density matrix renormalization group (t‐DMRG), we evaluate nonperturbatively the induced decoherence and entanglement. We find that the behavior of both decoherence and entanglement strongly depend on the phase of the underlying spin bath. We show that spin baths can induce entanglement for an initially disentangled pair of qubits. We observe that entanglement sudden death only occurs in paramagnetic phase and discuss the effect of the coupling range.
We investigate the reduced dynamics of two qubits coupled to an interacting quantum spin bath modeled by a XXZ spin chain. By using the method of time-dependent density matrix renormalization group (t-DMRG), it is shown that when the spin bath is in an ordering state, the reduced dynamics of qubits strongly depends on the range of the spin chain that qubits coupled to. Only for ordering spin baths, both decoherence and entanglement show qualitatively different behaviors when the coupling range changes. In particular, In particular, we find that in the parametic regime where there is no ordering in the bath, the coupling range is irrelevant. On the other hand, for ordering spin baths, when the coupling range increases from local coupling to infinite range coupling, the reduced dynamics of qubits exhibits a transition in which initially entangled states no longer suffers from the entanglement sudden death when the coupling range is large.
We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, XYXYXY, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the XYXYXY models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.
We examine the influence of environmental interactions on simple quantum systems by obtaining the exact reduced dynamics of a qubit coupled to a one-dimensional spin bath. In contrast to previous studies, both the qubit-bath coupling and the nearest-neighbor intrabath couplings are taken as the spin-flip XXXXXX type. We first study the Rabi oscillations of a single qubit with the spin bath prepared in a spin coherent state, finding that nonresonance and finite intrabath interactions have significant effects on the qubit dynamics. Then we discuss the bath-induced decoherence of the qubit when the bath is initially in the ground state and show that the decoherence properties depend on the internal phases of the spin bath. By considering two independent copies of the qubit-bath system, we finally probe the disentanglement dynamics of two noninteracting entangled qubits. We find that entanglement sudden death appears when the spin bath is in its critical phase. We show that the single-qubit decoherence factor is an upper bound for the two-qubit concurrence.
The decoherence and entanglement dynamics of two interacting qubits coupled through Heisenberg XY interactions to a spin bath in thermal equilibrium are studied. The exact form of the reduced density matrix is derived for finite and infinite numbers of environmental spins. It is shown that decoherence can be minimized at low bath temperatures and strong coupling between the qubits. Some initial product states evolve into entangled ones, initially entangled states lose completely or partially their entanglement. The relation between the fidelity and the concurrence is also investigated.
We obtain exact dynamics of a two-qubit central spin model (CSM) consisting of two interacting qubits homogeneously coupled to a spin bath via the XXZXXZXXZ-type coupling, with the bath initially prepared in linear superpositions of the symmetric Dicke states. Using the interaction picture Hamiltonian with respect to the non-spin-flipping part of the model, we derive a sequence of equations of motion within each magnetization sector satisfied by the probability amplitudes of the time-evolved state. These equations of motion admit analytical solutions for the single-qubit CSM in which one of the two central qubits decouples from the rest of the system. Based on this, we provide a quantitative interpretation to the observed collapse-revival phenomena in the single-qubit Rabi oscillations when the bath is prepared in the spin coherent state. We then study the disentanglement and coherence dynamics of two initially entangled noninteracting qubits when the two qubits interact with individual baths or with a common bath. For individual baths, the coherent dynamics is found to be positively correlated to the single-qubit purity dynamics, and entanglement sudden disappearance and revivals are observed in both cases. The entanglement creation of two initially separable qubits coupled to a common bath is also studied and collapse and revival behaviors in the entanglement dynamics are observed. Choosing the equally weighted state and the WWW-class states as the bath initial states, we finally study the dynamics of entanglement between two individual bath spins and demonstrate the entanglement sharing mechanism in such a system.