Single atom laser in normal-superconductor quantum dots

We study a single-level quantum dot strongly coupled to a superconducting lead and tunnel coupled to a normal electrode which can exchange energy with a single-mode resonator. We show that such a system implements a single atom laser. We employ both a semiclassical treatment and a quantum master-equation approach to characterize the properties of this laser. In particular, we find that this system can be operated with efficiency approaching unity; that is, a single photon is emitted into the cavity for every Cooper pair participating in the charge current. We find also that lasing in the proposed setup is clearly identifiable in the transport properties: in the lasing state, the electrical current through the quantum dot is pinned to the maximum value achievable in this hybrid nanostructure, and hence, the onset of lasing can be detected simply by a current measurement.