Theory of damped coherent oscillations in superconducting phase qubits

This paper presents a theoretical study of quantum coherent oscillations between superconducting phase qubits with decay to the outside world as well as spontaneous relaxation and pure dephasing. We propose methods for measuring relaxation constants, which are necessary for analyzing decoherence processes in coupled superconducting phase qubits. Exact solutions for probability-density equations of motion are obtained by using the Torrey method. As a result, the pure dephasing rate and the longitudinal relaxation rate can be determined by using the decay constants of the solutions. We also estimate the longitudinal relaxation time and the pure dephasing time in applying the methods to experimental results for a system consisting of two phase qubits demonstrated by McDermott.