1/f noise driven qubit dynamics in presence of a bosonic thermostat

Motivated by observations of distinct sources of noise in superconducting flux qubits over a wide frequency range, we analyze a qubit, a two level system, coupled to two microscopic sources of noise: 1/f low frequency noise and the Ohmic high frequency noise. The noise sources are treated as independent and characterized by different temperatures. We analyze the steady state regime of the resulting out-of-equilibrium dynamics focusing in particular on the effects of the interplay of the two types of noise on spectroscopic characteristics of the qubit. We calculate both analytically and numerically the steady state population of the qubit energy levels, relaxation and dephasing times and effective renormalization of the qubit's energy level splitting.