Mesoscopic superpositions of Tonks-Girardeau states and the Bose-Fermi mapping

TL;DR

This paper investigates the evolution of excited states in a one-dimensional ultracold bosonic gas in a double-well potential as interactions vary, revealing conditions for unique mesoscopic superpositions beyond traditional mappings.

Contribution

It characterizes the transition from NOON states to NOON Tonks-Girardeau states and identifies when these states appear outside the Bose-Fermi mapping predictions.

Findings

Identification of conditions for NOON Tonks-Girardeau states to appear.

Analysis of the relation between excited states and the Bose-Fermi mapping.

Insights into the spectrum evolution with interaction tuning.

Abstract

We study a one dimensional gas of repulsively interacting ultracold bosons trapped in a double-well potential as the atom-atom interactions are tuned from zero to infinity. We concentrate on the properties of the excited states which evolve from the so-called NOON states to the NOON Tonks-Girardeau states. The relation between the latter and the Bose-Fermi mapping limit is explored. We state under which conditions NOON Tonks-Girardeau states, which are not predicted by the Bose-Fermi mapping, will appear in the spectrum.