Detecting quantum phase localization using Arnold tongue

Abstract

The dynamical phase localization of a single qubit in a dissipative bath is investigated. We show that phase preference persists in the long time limit only for a non-Markovian evolution with a finite detuning implying that non-Markovianity is required for phase localization. The maximum of the shifted phase distribution exhibits an Arnold tongue like feature where the phase localized and phase delocalized regions are distinctly separated. We show the formation of Arnold tongue using the relative entropy of coherence as well. From our work we propose that Arnold tongue can be used to detect dynamical phase localization even when there is no synchronization present in the system.