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

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.

New version of figure 1b

References in corpus (5)

• Monte Carlo study of two-dimensional Bose-Hubbard model
• Interference pattern and visibility of a Mott insulator
• Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition
• Quantum Monte Carlo study of confined fermions in one-dimensional optical lattices
• Numerical simulations of strongly correlated fermions confined in 1D optical lattices

Cited by in corpus (7)

• Supersolids in one dimensional Bose Fermi mixtures
• Adiabatic dynamics of an inhomogeneous quantum phase transition: the case of z > 1 dynamical exponent
• Signatures of the superfluid to Mott insulator transition in cold bosonic atoms in a one dimensional optical lattice
• State diagram for continuous quasi-one dimensional systems in optical lattices
• Counterflow of lattice polarons in harmonically confined optical lattices
• Interaction-Induced Gradients Across a Confined Fermion Lattice
• The Bose-Hubbard polaron from weak to strong coupling