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

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.

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• Path Integral Molecular Dynamics for Bosons
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• Optimized Configuration Interaction Approach for Trapped Multiparticle Systems Interacting Via Contact Forces
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• Energy level splitting for weakly interacting bosons in a harmonic trap
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• Path integral molecular dynamics for thermodynamics and Green's function of ultracold spinor bosons
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• Phase-space localization at the lowest Landau level
• On the direct diagonalization method for a few particles trapped in harmonic potentials
• Enhanced strong interaction effect in synthetic spin-orbit coupling with mixed spin symmetry