Beyond Gross-Pitaevskii equation for 1D gas: quasiparticles and solitons

TL;DR

This paper investigates excitations in a 1D repulsive Bose gas across interaction strengths using hydrodynamics, comparing results with exact solutions and discussing the method's applicability to different excitation types.

Contribution

It introduces a hydrodynamic approach to study both particle and hole excitations in a 1D Bose gas, highlighting its strengths and limitations compared to exact models.

Findings

Hydrodynamics agrees well with exact solutions for particle excitations.

Discrepancies observed for hole excitations, especially for short-wavelength structures.

Hydrodynamics effectively describes long-wavelength phonons and has limited applicability for narrow solitons.

Abstract

Describing properties of a strongly interacting quantum many-body system poses a serious challenge both for theory and experiment. In this work, we study excitations of one-dimensional repulsive Bose gas for arbitrary interaction strength using a hydrodynamic approach. We use linearization to study particle (type-I) excitations and numerical minimization to study hole (type-II) excitations. We observe a good agreement between our approach and exact solutions of the Lieb-Liniger model for the particle modes and discrepancies for the hole modes. Therefore, the hydrodynamical equations find to be useful for long-wave structures like phonons and of a limited range of applicability for short-wave ones like narrow solitons. We discuss potential further applications of the method.