Low-density, one-dimensional quantum gases in a split trap

TL;DR

This paper provides an exact analysis of one-dimensional quantum gases in a split harmonic trap, exploring their ground states, soliton solutions, and experimental implications for both fermionic and bosonic systems.

Contribution

It offers exact solutions for degenerate quantum gases in a split trap, including ground states and solitons, using the Fermi-Bose mapping theorem, advancing understanding of such systems.

Findings

Exact many-particle ground-state wave-functions derived

Identification of soliton-like solutions in the system

Comparison between bosonic and fermionic behaviors

Abstract

We investigate degenerate quantum gases in one dimension trapped in a harmonic potential that is split in the centre by a pointlike potential. Since the single particle eigenfunctions of such a system are known for all strengths of the central potential, the dynamics for non-interacting fermionic gases and low-density, strongly interacting bosonic gases can be investigated exactly using the Fermi-Bose mapping theorem. We calculate the exact many-particle ground-state wave-functions for both particle species, investigate soliton-like solutions, and compare the bosonic system to the well-known physics of Bose gases described by the Gross-Pitaevskii equation. We also address the experimentally important questions of creation and detection of such states.