Effective Field Theory for Atom-Molecule Systems II: Stationary Solutions and Bogoliubov Excitations in Atom-Molecule Systems

TL;DR

This paper develops theoretical methods for Bose-Einstein condensates near Feshbach resonances, incorporating atom-molecule coupling, and analyzes how this affects Bragg scattering spectra, aligning with experimental observations.

Contribution

It introduces a formalism for atom-molecule systems near Feshbach resonances, including Bogoliubov excitations, and applies it to Bragg scattering, revealing significant spectral shifts.

Findings

Significant shift in Bragg spectra peak at large scattering lengths

Formalism matches experimental results by Papp et al.

Differences from structureless atom models are pronounced at moderate and large scattering lengths

Abstract

We formulate the basic theoretical methods for Bose-Einstein Condensation of atoms close to a Feshbach resonance, in which the tunable scattering length of the atoms is described using a system of coupled atom and molecule fields. These include the Thomas-Fermi description of the condensate profile, the c-field equations, and the Bogoliubov-de Gennes equations, and the Bogoliubov excitation spectrum for a homogenous condensed system. We apply this formalism to the special case of Bragg scattering from a uniform condensate, and find that for moderate and large scattering lengths, there is a dramatic difference in the shift of the peak of the Bragg spectra, compared to that based on a structureless atom model. The result is compatible with the experimental results of Papp et al. [S. B. Papp et al., Phys. Rev. Lett., 101(13):135301, Sep 2008].