Unravelling the dynamics of entanglement in a non-Markovian bath

Abstract

We analyse the dynamics of quantum correlations between two qubits coupled to a linear chain of oscillators. The qubits undergo an effective open-system dynamics in the presence of a non-Markovian reservoir, constituted by the chain's vibrations. The model is amenable to an analytical solution when the chain is initially in a thermal state. We study the dynamics of the qubits concurrence starting from a separable state and assuming that the chain spectrum is gapped. 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 excitation. 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 identifies the resources of an environment for realising quantum coherent dynamics of open systems.