Quantum correlations and degeneracy of identical bosons in a 2D harmonic trap

TL;DR

This paper analyzes the spectral properties, degeneracies, and correlation effects of a few bosons in a 2D harmonic trap with finite-range interactions, revealing how degeneracies break and wave functions develop holes in strong interactions.

Contribution

It provides analytic expressions for degeneracies and their breaking, and studies the evolution of correlations and wave functions in a 2D bosonic system with finite-range interactions.

Findings

Degeneracy of low-energy states is independent of particle number in noninteracting and weakly interacting regimes.

Strong interactions cause wave functions to develop holes to avoid particle overlap, similar to Tonks-Girardeau gas.

Density profiles, pair correlations, and fragmentation are analyzed for systems with 2 to 4 bosons.

Abstract

We consider a few number of identical bosons trapped in a 2D isotropic harmonic potential and also the $N$-boson system when it is feasible. The atom-atom interaction is modelled by means of a finite-range Gaussian interaction. The spectral properties of the system are scrutinized, in particular, we derive analytic expressions for the degeneracies and their breaking for the lower-energy states at small but finite interactions. We demonstrate that the degeneracy of the low-energy states is independent of the number of particles in the noninteracting limit and also for sufficiently weak interactions. In the strongly interacting regime, we show how the many-body wave function develops holes whenever two particles are at the same position in space to avoid the interaction, a mechanism reminiscent of the Tonks-Girardeau gas in 1D. The evolution of the system as the interaction is increased is studied by means of the density profiles, pair correlations and fragmentation of the ground state for $N=2$, $3$, and $4$ bosons.