Adiabatic approximation in the ultrastrong-coupling regime of a system   consisting of an oscillator and two qubits
  We present a system composed of two flux qubits and a transmission-line resonator. Instead of using the rotating wave approximation (RWA), we analyse the system by the adiabatical approximation methods under two opposite extreme conditions. Basic properties of the system are calculated and compared under these two different conditions. Energy-level spectrum of the system in the adiabatical displaced oscillator basis is shown, and the theoretical result is compared with the numerical solution. 
Ping Yang, Zhi-Ming Zhang
quant-ph physics.optics