Dynamics of the attractive 1D Bose gas: analytical treatment from integrability

TL;DR

This paper provides analytical results for the zero-temperature dynamical correlations in the attractive 1D Bose gas using integrability techniques, offering predictions relevant for experiments in atomic gases and optical waveguides.

Contribution

It introduces a novel analytical approach combining Bethe Ansatz and determinant representations to study dynamical correlations in the attractive Lieb-Liniger model.

Findings

Analytical expressions for density and field operator correlations at zero temperature.

Quantitative predictions for experimental setups in atomic gases and optical waveguides.

Enhanced understanding of the dynamics in attractive 1D Bose gases.

Abstract

The physics of the attractive one-dimensional Bose gas (Lieb-Liniger model) is investigated with techniques based on the integrability of the system. Combining a knowledge of particle quasi-momenta to exponential precision in the system size with determinant representations of matrix elements of local operators coming from the Algebraic Bethe Ansatz, we obtain rather general analytical results for the zero-temperature dynamical correlation functions of the density and field operators. Our results thus provide quantitative predictions for possible future experiments in atomic gases or optical waveguides.