Atom-molecule coherence in a one-dimensional system

TL;DR

This paper investigates a one-dimensional fermionic atom-molecule system, revealing a low-energy coherence between molecules and atoms, a spin gap, and unique correlation decay behaviors, with exact solutions at a special Luther-Emery point.

Contribution

It introduces a detailed model of atom-molecule coherence in 1D, identifying a Luther-Emery point with exact solutions and elucidating the nature of correlations and excitations.

Findings

Coherence develops between molecule and fermion Luttinger liquids at low energy.

A spin excitation gap opens in the spectrum.

At the Luther-Emery point, the system is described by noninteracting pseudofermions.

Abstract

We study a model of one-dimensional fermionic atoms that can bind in pairs to form bosonic molecules. We show that at low energy, a coherence develops between the molecule and fermion Luttinger liquids. At the same time, a gap opens in the spin excitation spectrum. The coherence implies that the order parameters for the molecular Bose-Einstein Condensation and the atomic BCS pairing become identical. Moreover, both bosonic and fermionic charge density wave correlations decay exponentially, in contrast with a usual Luttinger liquid. We exhibit a Luther-Emery point where the systems can be described in terms of noninteracting pseudofermions. At this point, we provide closed form expressions for the density-density response functions.