Fermi-Bose mapping for one-dimensional Bose gases

TL;DR

This paper reviews the Fermi-Bose mapping in one-dimensional Bose gases, highlighting its broad applicability to various interaction regimes, nonequilibrium states, and excited states, especially in the context of recent experimental realizations.

Contribution

It demonstrates the generality of the Fermi-Bose mapping, extending its validity to time-dependent, excited, and Lieb-Liniger gases beyond the Tonks-Girardeau limit.

Findings

Fermi-Bose mapping applies to nonequilibrium wavefunctions.

It provides the entire spectrum of excited states.

Applicable to Lieb-Liniger gases with contact interactions.

Abstract

One-dimensional Bose gases are considered, interacting either through the hard-core potentials or through the contact delta potentials. Interest in these gases gained momentum because of the recent experimental realization of quasi-one-dimensional Bose gases in traps with tightly confined radial motion, achieving the Tonks-Girardeau (TG) regime of strongly interacting atoms. For such gases the Fermi-Bose mapping of wavefunctions is applicable. The aim of the present communication is to give a brief survey of the problem and to demonstrate the generality of this mapping by emphasizing that: (i) It is valid for nonequilibrium wavefunctions, described by the time-dependent Schr\"odinger equation, not merely for stationary wavefunctions. (ii) It gives the whole spectrum of all excited states, not merely the ground state. (iii) It applies to the Lieb-Liniger gas with the contact interaction, not merely to the TG gas of impenetrable bosons.