Dynamic behaviour of Josephson-junction qubits: crossover between Rabi   oscillations and Landau-Zener transitions
  We study the dynamic behaviour of a quantum two-level system with periodically varying parameters by solving the master equation for the density matrix. Two limiting cases are considered: multiphoton Rabi oscillations and Landau-Zener transitions. The approach is applied to the description of the dynamics of superconducting qubits. In particular, the case of the interferometer-type charge qubit with periodically varying parameters (gate voltage or magnetic flux) is investigated. The time-averaged energy level populations are calculated as funtions of the qubit's control parameters. 
S.N. Shevchenko, A.S. Kiyko, A.N. Omelyanchouk, W. Krech