Landau-Zener-St\"uckelberg-Majorana lasing in circuit QED
  We demonstrate amplification (and attenuation) of a probe signal by a driven two-level quantum system in the Landau-Zener-St\"{u}ckelberg-Majorana regime by means of an experiment, in which a superconducting qubit was strongly coupled to a microwave cavity, in a conventional arrangement of circuit quantum electrodynamics. Two different types of flux qubit, specifically a conventional Josephson junctions qubit and a phase-slip qubit, show similar results, namely, lasing at the working points where amplification takes place. The experimental data are explained by the interaction of the probe signal with Rabi-like oscillations. The latter are created by constructive interference of Landau-Zener-St\"{u}ckelberg-Majorana (LZSM) transitions during the driving period of the qubit. A detailed description of the occurrence of these oscillations and a comparison of obtained data with both analytic and numerical calculations are given. 
P. Neilinger, S. N. Shevchenko, J. Bog\'ar, M. Reh\'ak, G. Oelsner, D.   S. Karpov, U. H\"ubner, O. Astafiev, M. Grajcar and...
cond-mat.supr-con