Internal structure of a quantum soliton and classical excitations due to trap opening

TL;DR

This paper analytically investigates the internal quantum structure of matter wave solitons and the classical excitations resulting from trap opening, providing insights beyond mean field theory.

Contribution

It derives the internal correlation function of quantum solitons from Bethe ansatz and analyzes classical excitations in large particle number limits.

Findings

Quantum correlation function of particles in a soliton obtained from Bethe ansatz.

Classical excitations due to trap opening analyzed in the large particle number limit.

Abstract

We analytically solve two problems that may be useful in the context of the recent observation of matter wave bright solitons in a one-dimensional attractive atomic Bose gas. The first problem is strictly beyond mean field: From the Bethe ansatz solution we extract the internal correlation function of the particle positions in the quantum soliton, that is for a fixed center of mass position. The second problem is solved in the limit of a large number of particles, where the mean field theory is asymptotically correct: It deals with the number of excitations created by the opening of the trap, starting from a pure soliton in a weakly curved harmonic potential.