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

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