One Dimensional Gas of Bosons with Feshbach Resonant Interactions

TL;DR

This paper explores the unique properties of a one-dimensional bosonic gas with Feshbach resonant interactions, revealing multiple regimes and complex excitation spectra, including roton-like minima and ground state instabilities.

Contribution

It introduces a detailed analysis of the resonant bosonic gas, highlighting novel regimes and spectral features not present in non-resonant systems, and discusses the limitations of current theoretical tools.

Findings

Existence of three distinct regimes depending on density and interaction parameters.

Development of a roton-like minimum in the excitation spectrum at higher densities.

Identification of ground state instability as the minimum dips below the Fermi energy.

Abstract

We present a study of a gas of bosons confined in one dimension with Feshbach resonant interactions, at zero temperature. Unlike the gas of one dimensional bosons with non-resonant interactions, which is known to be equivalent to a system of interacting spinless fermions and can be described using the Luttinger liquid formalism, the resonant gas possesses novel features. Depending on its parameters, the gas can be in one of three possible regimes. In the simplest of those, it can still be described by the Luttinger liquid theory, but its Fermi momentum cannot be larger than a certain cutoff momentum dependent on the details of the interactions. In the other two regimes, it is equivalent to a Luttinger liquid at low density only. At higher densities its excitation spectrum develops a minimum, similar to the roton minimum in helium, at momenta where the excitations are in resonance with the Fermi sea. As the density of the gas is increased further, the minimum dips below the Fermi energy, thus making the ground state unstable. At this point the standard ground state gets replaced by a more complicated one, where not only the states with momentum below the Fermi points, but also the ones with momentum close to that minimum, get filled, and the excitation spectrum develops several branches. We are unable so far to study this new regime in detail due to the lack of the appropriate formalism.