  We show how a pair of superconducting qubits coupled to a microwave cavity
mode can be used to engineer a single-atom laser that emits light into a
non-classical state. Our scheme relies on the dressing of the qubit-field
coupling by periodic modulations of the qubit energy. In the dressed basis, the
radiative decay of the first qubit becomes an effective incoherent pumping
mechanism that injects energy into the system, hence turning dissipation to our
advantage. A second, auxiliary qubit is used to shape the decay within the
cavity, in such a way that lasing occurs in a squeezed basis of the cavity
mode. We characterize the system both by mean-field theory and exact
calculations. Our work may find applications in the generation of squeezing and
entanglement in circuit QED, as well as in the study of dissipative many-body
phase transitions.
