Entanglement instability in the interaction of two qubits with a common non-Markovian environment

In this work we study the steady state entanglement between two qubits interacting asymetrically with a common non-Markovian environment. Depending on the initial two-qubit state, the asymmetry in the couplings between each qubit and the non-Markovian environment may lead to enhanced entanglement in the steady state of the system, measured in terms of the two-qubit concurrence. Our results indicate that, if a qubit-qubit interaction is also present, the two-qubit steady state concurrence is always favored by the symmetric or anti-symmetric coupling configuration. Although finite, the steady concurrence is predicted to be highly unstable in this regime as long as the interaction between the two qubits is larger than the couplings between each qubit and the non-Markovian reservoir.