Spectrum and Dynamics of the BCS-BEC crossover from a few-body perspective

TL;DR

This paper provides a detailed few-body analysis of the BCS-BEC crossover in fermionic systems, revealing spectral structures and dynamics that inform experimental control of atom-molecule coherence.

Contribution

It offers the first accurate few-body solutions across the BCS-BEC crossover and analyzes the system's dynamics via Landau-Zener transitions during parameter ramps.

Findings

Spectral analysis reveals avoided crossings related to the crossover.

Dynamics modeled as a sequence of Landau-Zener transitions.

Proposes a ramping scheme to investigate atom-molecule coherence.

Abstract

The spectrum of two spin-up and two spin-down fermions in a trap is calculated using a correlated gaussian basis throughout the range of the BCS-BEC crossover. These accurate calculations provide a few-body solution to the crossover problem. This solution is used to study the time-evolution of the system as the scattering length is changed, mimicking experiments with Fermi gases near Fano-Feshbach resonances. The structure of avoiding crossings in the spectrum allow us to understand the dynamics of the system as a sequence of Landau-Zener transitions. Finally, we propose a ramping scheme to study atom-molecule coherence.