Dressed-state master equation for two strongly coupled two-level atoms with long-lived entanglement
We derive a dressed-state master equation in Lindblad form for two strongly coupled two-level atoms. The resulting decay dynamics are governed by Lindblad operators that couple different dressed states. We show that the eigenvalues and eigenvectors of the Liouvillian can be obtained in a compact form, since each off-diagonal element in the dressed-state basis constitutes an eigenvector. Depending on the interatomic distance and the atomic transition frequency, the decay exhibits two well-separated time scales. On short times, the system relaxes into a pair of states, one of which is a transient, maximally entangled state. On longer times, this intermediate entanglement irreversibly decays into a separable steady state. Our results demonstrate that the intrinsic decay mechanism can transiently generate maximal entanglement, an effect that is not captured without the dressed-state master-equation formalism.