Nonequilibrium dynamics of ultracold Fermi superfluids

Abstract

The aim of this mini review is to survey the literature on the study of nonequilibrium dynamics of Fermi superfluids in the BCS and BEC limits, both in the single channel and dual channel cases. The focus is on mean field approaches to the dynamics, with specific attention drawn to the dynamics of the Ginzburg-Landau order parameters of the Fermi and composite Bose fields, as well as on the microscopic dynamics of the quantum degrees of freedom. The two approaches are valid approximations in two different time scales of the ensuing dynamics. The system is presumed to evolve during and/or after a quantum quench in the parameter space. The quench can either be an impulse quench with virtually instantaneous variation, or a periodic variation between two values. The literature for the order parameter dynamics, described by the time-dependent Ginzburg-Landau equations, is reviewed, and the works of the author in this area highlighted. The mixed phase regime in the dual channel case is also considered, and the dual order parameter dynamics of Fermi-Bose mixtures reviewed. Finally, the nonequilibrium dynamics of the microscopic degrees of freedom for the superfluid is reviewed for the self-consistent and non self-consistent cases. The dynamics of the former can be described by the Bogoliubov de-Gennes equations with the equilibrium BCS gap equation continued in time and self -consistently coupled to the BdG dynamics. The latter is a reduced BCS problem and can be mapped onto the dynamics of Ising and Kitaev models. This article reviews the dynamics of both impulse quenches in the Feshbach detuning, as well as periodic quenches in the chemical potential, and highlights the author's contributions in this area of research. I. INTRODUCTIONStudies of the coherent quantum dynamics of closed many body systems have gained considerable interest in the last two decades. This interest has been brought about by such states becoming experimentally accessible using ultracold atoms, cooled to near absolute zero temperatures by the use of optical molasses [1] , evaporative cooling [2], laser culling [3] , cavity QED methods [4] , and other experimental techniques. The experimental realization of the Bose Einstein condensate by Cornell, Ketterle and Weiman in 1995 [2] , as well as the realization of the Bosonic Superfluid Mott-Insulator transition by Greiner et. al. in 2002 [5] (theoretically predicted by Jaksch et. al. in 1998 [6] ), motivated strong theoretical interest in the coherent dynamics of ultracold bosons. Previously, the regimes where fermionic coherent dynamics can be realized were unattainable in either solid state systems or with ultracold atoms. The difficulties for ultracold atoms were eventually circumvented by experiments performed over the first decade of the 21 st century. Studies of fermionic atoms gained momentum after these experiments realized pure fermionic BCS states [7] , as well as the BCS-BEC crossover that was predicted theoretically a decade earlier [8] . The formation of Fermi superfluids were realized ...