Theory of damped Rabi oscillations

Rabi oscillations with decays to the outside world as well as internal relaxations are theoretically studied. The density-matrix equations of motion are exactly solved by extending the Torrey method based on Laplace transform technique, and then general solutions involving different decay processes are obtained. The special solution describing damped Rabi oscillations is successively explained on the remarkable features of a Josephson phase qubit demonstrated by Yu. In addition, a new technique is proposed for determining all the relaxation rates including an internal relaxation rate gamma(10) and the pure dephasing rate gamma(phi) by using the decay rates of damped oscillating solutions with different decay processes.