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

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.

References in corpus (5)

• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• The Unitary Fermi Gas: From Monte Carlo to Density Functionals
• Renormalisation Flow and Universality for Ultracold Fermionic Atoms
• BCS-BEC crossover and quantum phase transition for 6Li and 40K atoms across Feshbach resonance
• Derivation of hydrodynamics for the gapless mode in the BEC-BCS crossover from the exact one-loop effective action

Cited by in corpus (1)

• Properties of the single-site reduced density matrix in the Bose-Bose resonance model in the ground state and in quantum quenches