Synchronization in the BCS pairing dynamics as a critical phenomenon

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.