Multiphoton transitions between energy levels in a phase-biased   Cooper-pair box
  We investigated both theoretically and experimentally dynamic features of a phase-biased charge qubit consisting of a single-Cooper-pair transistor closed by a superconducting loop. The effective inductance of the qubit was probed by a high-quality tank circuit. In the presence of a microwave power, with a frequency of the order of the qubit energy level separation, an alteration of the qubit inductance was observed. We demonstrate that this effect is caused by the redistribution of the qubit level population. The excitation of the qubit by one-, two-, and three-photon processes was detected. Quantitative agreement between theory and experimental data was found. 
V.I.Shnyrkov, Th.Wagner, D.Born, S.N.Shevchenko, W.Krech,   A.N.Omelyanchouk, E.Il'ichev, H.-G.Meyer