Asymptotic geometric phase and purity for phase qubit dispersively coupled to lossy LC circuit

► The model of a current biased Josephson phase qubit, strongly coupled to loss LC circuit, is considered. ► Analytical descriptions of the geometric phase (GP) of this model, in the dispersive limit, are studied. ► The GP and purity depend on the dissipation which leads to the GP death phenomenon. ► Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP.