Decoherence of a driven quantum system interacting with environment through many degrees of freedom

We present a comprehensive approach for the study of decoherence of an ac-field-driven multilevel quantum system interacting with environment through many degrees of freedom. In this approach, the system is described by a reduced density operator and the environment is characterized by a number of spectral densities. The reduced density operator is governed by a master equation in which the effect of ac fields and leakage to non-computational states are included. The approach is applied to investigate decoherence of a SQUID flux qubit with a two-dimensional (2D) potential coupled to environment through its control and readout circuits. The calculated relaxation time agrees well with experimental result when the potential is quasi one-dimensional (1D). Effects of the second degree of freedom, which is frozen in a quasi-1D system, on relaxation and decoherence times are examined systematically by varying circuit parameters.