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arXiv:0807.2202 · Physical Review A

Long-lived spin entanglement induced by a spatially correlated thermal bath

Dara P. S. McCutcheon, Ahsan Nazir, Sougato Bose, Andrew J. Fisher

Published Aug 28, 2009• 46 citations
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Abstract

We investigate how two spatially separated qubits coupled to a common heat bath can be entangled by purely dissipative dynamics. We identify a dynamical time scale associated with the lifetime of the dissipatively generated entanglement and show that it can be much longer than either the typical single-qubit decoherence time or the time scale on which a direct exchange interaction can entangle the qubits. We give an approximate analytical expression for the long-time evolution of the qubit concurrence and propose an ion trap scheme in which such dynamics should be observable.

DOI
10.1103/physreva.80.022337

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We investigate how two spatially separated qubits coupled to a common heat bath can be entangled by purely dissipative dynamics. We identify a dynamical time scale associated with the lifetime of the dissipatively generated entanglement and show that it can be much longer than either the typical single-qubit decoherence time or the time scale on which a direct exchange interaction can entangle the qubits. We give an approximate analytical expression for the long-time evolution of the qubit concurrence and propose an ion trap scheme in which such dynamics should be observable.
We use numerically exact iterative path integral methods to investigate the decoherence and entanglement dynamics of a tunneling pair of two coupled qubits (spins) system interacting with a dissipative bath. We find that decoherence is generally accompanied by the destruction of entanglement, although the specifics of this destruction depend sensitively on the parameters of the Hamiltonian (qubit-qubit coupling and/or energy bias), the strength of dissipation, the temperature, and the choice of initial condition. We also observe that dissipation can in some cases generate a substantial amount of entanglement. Finally, if an entangled eigenstate exists which does not couple to the environment, the long-time entanglement can significantly exceed the value corresponding to the Boltzmann equilibrium state.
We solve the time evolution for most general density matrix for 2‐qubits under the interaction with a common heat bath and investigate the time evolution for a particularly interesting entangled state where we provide a scheme to enhance or concentrate entanglement using common heat bath interaction. The correspondence between the entanglement dynamics and energy exchange of the system with the environment is discussed under that situation. Entanglement sudden death, decoherence free entanglement and entanglement enhancement are shown to be dependent on the energy exchange of the system with the environment.
We analyze the dynamics of quantum correlations between two qubits coupled to a linear chain of oscillators. The chain mediates interactions between the qubits and acts as a non-Markovian reservoir. The model is amenable to an analytical solution when the initial state of the chain is Gaussian. We study the dynamics of the qubits' concurrence starting from a separable state and assuming that the chain spectrum is gapped and the chain is initially in a thermal state. We identify three relevant regimes that depend on the strength of the qubit-chain coupling in relation to the spectral gap. These are (i) the weak-coupling regime, where the qubits are entangled at the asymptotics, (ii) the strong-coupling regime, where the concurrence can exhibit collapses followed by revivals with exponentially attenuated amplitude, and (iii) the thermal damping regime, where the concurrence rapidly vanishes due to the chain's thermal excitations. In all cases, if entanglement is generated, this occurs after a finite time has elapsed. This time scale depends exponentially on the qubits' distance and is determined by the spectral properties of the chain. Entanglement irreversible decay, on the other hand, is due to the dissipative effect induced by the coupling with the chain and is controlled by the coupling strength between the chain and qubits. This study unravels the basic mechanisms leading to entanglement in a non-Markovian bath and allows one to identify the key resources for realizing quantum coherent dynamics of open systems.
We demonstrate an exact mapping of a class of models of two interacting qubits in thermal reservoirs to two separate problems of spin–boson-type systems. Based on this mapping, exact numerical simulations of the qubits dynamics can be performed, beyond the weak system–bath coupling limit and the Markovian approximation. Given the time evolution of the system population and coherences, we study as an application the dynamics of entanglement between the pair of qubits immersed in boson thermal baths, showing a rich phenomenology, including an intermediate oscillatory behavior, the entanglement sudden birth, sudden death and revival. We find that the occurrence of entanglement sudden death in this model depends on the portion of the zero and double excitation states in the subsystem initial state. In the long-time limit, analytic expressions are presented at weak system–bath coupling, for a range of relevant qubit parameters.
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.
Creation of entangled states of quantum systems with low decoherence rates is a cornerstone in practical implementation of quantum computations. Processes of separate dephasing in each qubit in experimentally feasible systems is commonly accepted to destroy entanglement. In this work, we consider a system of two strongly coupled qubits that interact with dephasing reservoirs. We demonstrate that interaction with dephasing reservoirs can contribute to the formation of a long-lived mixed entangled state with nonzero concurrence. The weight of the subradiant state in this mixed state tends toward unity if the dephasing rate is much larger than the radiative rate and less than the coupling constant between qubits. The lifetime of this state is proportional to the exponent of the ratio of the coupling constant to environmental temperature and can be, by orders of magnitude, larger than the system's characteristic dephasing and dissipation times. Therefore, high dephasing, along with strong coupling, contributes to the creation of an entangled state with a long lifetime. This result paves the way for creation of long-lived entangled states.