Synchronization in the BCS pairing dynamics as a critical phenomenon.

Area of Science:

• Condensed Matter Physics
• Quantum Dynamics
• Many-Body Systems

Background:

• Fermi gases exhibit complex dynamics under time-dependent interactions.
• The interplay between collective modes and individual quantum states is crucial for understanding emergent phenomena.

Purpose of the Study:

• To investigate the dynamical states of a Fermi gas with a time-dependent pairing interaction.
• To characterize the transitions between synchronized and dephased Cooper pair oscillations.
• To determine the nature of these transitions as a function of coupling strength.

Main Methods:

• Employed a combination of numerical simulations and analytical techniques.
• Studied the collisionless, dissipationless regime of the Fermi gas.
• Analyzed the coupling between the Bardeen-Cooper-Schrieffer (BCS) pairing mode and individual Cooper pair states.

Main Results:

• Observed a transition from phase-locked undamped oscillations to Landau-damped dephased oscillations with increasing coupling strength.
• Identified a second transition in the dephased regime where the long-time asymptotic pairing amplitude vanishes.
• Established that both transitions are continuous (type II).

Conclusions:

• The dynamics of Fermi gases with time-dependent pairing interactions are rich and exhibit distinct phase transitions.
• The coupling strength critically governs the transition between coherent and incoherent pairing dynamics.
• The continuous nature of these transitions provides insights into the fundamental behavior of interacting quantum systems.