Post-adiabatic Hamiltonian for low-energy excitations in a slowly time-dependent BCS-BEC crossover

TL;DR

This paper derives a Hamiltonian that captures the slow, non-adiabatic dynamics of a BCS-BEC crossover in fermionic gases, including leading post-adiabatic effects during Feshbach resonance sweeps.

Contribution

It introduces a novel post-adiabatic Hamiltonian framework that accounts for non-zero sweep rates in the BCS-BEC crossover, extending previous adiabatic models.

Findings

Derived a post-adiabatic effective Hamiltonian for the crossover

Applied path integral and stationary phase methods for narrow resonances

Mapped molecular mode dynamics onto a bosonic Hamiltonian

Abstract

We develop a Hamiltonian that describes the time-dependent formation of a molecular Bose-Einstein condensate (BEC) from a Bardeen-Cooper-Schrieffer (BCS) state of fermionic atoms as a result of slowly sweeping through a Feshbach resonance. In contrast to many other calculations in the field (see e.g. [1-4]), our Hamiltonian includes the leading post-adiabatic effects that arise because the crossover proceeds at a non-zero sweep rate. We apply a path integral approach and a stationary phase approximation for the molecular zero momentum background, which is a good approximation for narrow resonances (see e.g. [5, 6]). We use two-body adiabatic approximations to solve the atomic evolution within this background. The dynamics of the non-zero momentum molecular modes is solved within a dilute gas approximation and by mapping it onto a purely bosonic Hamiltonian. Our main result is a post-adiabatic effective Hamiltonian in terms of the instantaneous bosonic (Anderson-)Bogoliubov modes, which holds throughout the whole resonance, as long as the Feshbach sweep is slow enough to avoid breaking Cooper pairs.