Quantum quench phase diagrams of an s-wave BCS-BEC condensate

TL;DR

This paper investigates the long-term behavior of an s-wave BCS-BEC condensate after detuning quenches, revealing three distinct asymptotic phases and developing an exact method to predict the final state based on initial conditions.

Contribution

It provides the first exact phase diagrams for the asymptotic states of a two-channel fermionic condensate beyond the weak coupling limit.

Findings

Identifies three main asymptotic phases with distinct order parameter behaviors.

Develops a method to predict the final state from initial and final detunings.

Shows modifications in relaxation mechanisms outside the weak coupling regime.

Abstract

We study the dynamic response of an s-wave BCS-BEC (atomic-molecular) condensate to detuning quenches within the two channel model beyond the weak coupling BCS limit. At long times after the quench, the condensate ends up in one of three main asymptotic states (nonequilibrium phases), which are qualitatively similar to those in other fermionic condensates defined by a global complex order parameter. In phase I the amplitude of the order parameter vanishes as a power law, in phase II it goes to a nonzero constant, and in phase III it oscillates persistently. We construct exact quench phase diagrams that predict the asymptotic state (including the many-body wavefunction) depending on the initial and final detunings and on the Feshbach resonance width. Outside of the weak coupling regime, both the mechanism and the time dependence of the relaxation of the amplitude of the order parameter in phases I and II are modified. Also, quenches from arbitrarily weak initial to sufficiently strong final coupling do not produce persistent oscillations in contrast to the behavior in the BCS regime. The most remarkable feature of coherent condensate dynamics in various fermion superfluids is an effective reduction in the number of dynamic degrees of freedom as the evolution time goes to infinity. As a result, the long time dynamics can be fully described in terms of just a few new collective dynamical variables governed by the same Hamiltonian only with "renormalized" parameters. Combining this feature with the integrability of the underlying (e.g. the two channel) model, we develop and consistently present a general method that explicitly obtains the exact asymptotic state of the system.