Decoherence and Entanglement Dynamics of Coupled Qubits

TL;DR

This paper investigates how two coupled qubits lose or maintain entanglement over time in different environmental conditions, revealing long-lived entanglement in decoherence-free subspaces and non-Gibbs equilibrium states.

Contribution

It provides a detailed analysis of entanglement dynamics in coupled qubits with independent and common baths, highlighting the role of decoherence-free subspaces and non-thermal equilibrium states.

Findings

Existence of semi-decoherence free subspaces prolongs entanglement.

System thermalizes but equilibrium states can differ from Gibbs states.

Entanglement dynamics depend on temperature, coupling, and initial states.

Abstract

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.