Canonical Trajectories and Critical Coupling of the Bose-Hubbard Hamiltonian in a Harmonic Trap

TL;DR

This paper uses Quantum Monte Carlo simulations and the Local Density Approximation to analyze the phase diagram and density profiles of the Bose-Hubbard model in a harmonic trap, clarifying the relationship with uniform system critical points.

Contribution

It maps canonical trajectories of the trapped Bose-Hubbard model onto the uniform phase diagram and clarifies how these relate to critical couplings and Mott insulator lobes.

Findings

Trajectories do not generally intersect Mott lobes tips.

Density profiles from QMC agree with LDA results.

Provides insights for comparing trapped system experiments with uniform system simulations.

Abstract

Quantum Monte Carlo (QMC) simulations and the Local Density Approximation (LDA) are used to map the constant particle number (canonical) trajectories of the Bose Hubbard Hamiltonian confined in a harmonic trap onto the $(\mu/U,t/U)$ phase diagram of the uniform system. Generically, these curves do not intercept the tips of the Mott insulator (MI) lobes of the uniform system. This observation necessitates a clarification of the appropriate comparison between critical couplings obtained in experiments on trapped systems with those obtained in QMC simulations. The density profiles and visibility are also obtained along these trajectories. Density profiles from QMC in the confined case are compared with LDA results.