Stationary entanglement in strongly coupled qubits

The dynamics of two superconducting flux qubits coupled to each other and to a common bath is discussed. We focus on the case in which the qubit-qubit coupling strength dominates over the respective qubit transition frequencies. We derive the master equation including collective effect by modeling the bath as one-dimensional open space in this ultrastrong coupling regime, and find that the coupling greatly modifies both the coherent and the incoherent dynamics of the system, giving rise to qualitatively different properties. By analyzing the steady-state and the dynamics governed by the master equation, we show that ground-state entanglement and maximum coherence between the two qubits can be induced by the environment alone. By employing in addition a single external driving field, both the entangled antisymmetric and symmetric collective states can be populated and preserved with high fidelity. Similarly, entangled states can be prepared using adiabatic passage techniques using two external fields. Our results could find applications in entangling quantum gates and quantum memories free from the decoherence.