Synchronization in the BCS Pairing Dynamics as a Critical Phenomenon

TL;DR

This paper investigates the dynamical transitions in a Fermi gas with time-dependent pairing, revealing critical phenomena akin to phase transitions between synchronized and dephased states.

Contribution

It introduces a detailed analysis of the transition from synchronized to dephased pairing oscillations, highlighting the critical behavior and phase transition nature in the BCS dynamics.

Findings

Transition from phase-locked to dephased oscillations as coupling varies

Identification of a second transition where pairing amplitude vanishes

Both transitions exhibit continuous (second-order) critical behavior

Abstract

Fermi gas with time-dependent pairing interaction hosts several different dynamical states. Coupling between the collective BCS pairing mode and individual Cooper pair states can make the latter either synchronize or dephase. We describe transition from phase-locked undamped oscillations to Landau-damped dephased oscillations in the collisionless, dissipationless regime as a function of coupling strength. In the dephased regime, we find a second transition at which the long-time asymptotic pairing amplitude vanishes. Using a combination of numerical and analytical methods we establish a continuous (type II) character of both transitions.