Qubit decoherence due to a Josephson bifurcation amplifier trapped in one of

We investigate the relaxation of a superconducting flux qubit for the case when its detector, the Josepshon bifurcation amplifier, remains latched in one of its two (meta)stable states. We observe a qualitatively different behavior for the two different attractors, and interpret the result as the combined effect of the amplitude of the detector's response to external driving and the effective curvature of the detector's basins of attraction in a rotating frame, in the proximity of the stable points. We address the question of the proper version of detailed balance for the qubit.