Competition Between Incoherent Pumping and Losses in a System of Two Interacting Qubits

We consider a model of two qubits, which interact through a Rotating Wave Approximation (RWA) potential; while the first qubit is incoherently pumped to its excited state, the second qubit loses its excitations by contact to a zero-temperature bath. We show that purely dissipative effects (and the help of the qubit-qubit interaction) can produce entangled stationary states. The steady state entanglement is significant when the interaction constant, and the pumping and dissipation rates are of the same order of magnitude. In this toy model, the entanglement of the system exists only when the two thermal baths are on and the qubits are coupled; if we turn off either the pumping or the dissipation these correlations disappear. We calculate and compare two quantifiers of non-classical correlations: the quantum discord [3] and the entanglement of formation, in the steady state. We find an analytical form for the conditions for which the steady-state qubit-qubit entanglement attains its maximum value Css..