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arXiv:math-ph/0509060 · Communications in Mathematical Physics

Mott Transition in Lattice Boson Models

Roberto Fernández, Jürg Martin Fröhlich, Daniel Ueltschi

Published May 8, 2006• 18 citations
arXivHTMLPDF
DOI
10.1007/s00220-006-0038-9

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arXiv:2010.14352•Physical Review Letters•Jan 26, 2021•17 citations
Rotational states for trapped bosons in an optical lattice are studied in the framework of the Hubbard model. Critical frequencies are calculated and the main parameter regimes are identified. Transitions are observed from edge superfluids to vortex lattices with Mott insulating cores, and subsequently to lattices of interstitial vortices. The former transition coincides with the Mott transition. Changes in symmetry of the vortex lattices are observed as a function of lattice depth. Predictions for experimental signatures are presented.
We numerically studied Bose–Fermi mixtures in one-dimensional optical lattices using a modified Bose–Fermi–Hubbard model. We derived the modified Bose–Fermi–Hubbard model in a tight-binding approximation, retaining the terms which were usually ignored. Quantum Monte Carlo simulations were then performed on the model to demonstrate a bosonic Mott transition of the Bose–Fermi mixtures. This gives another scenario of the fermion-induced decoherence of bosons observed in some experiments.
We present a joint experimental and theoretical analysis to assess the adiabatic experimental preparation of ultracold bosons in optical lattices aimed at simulating the three-dimensional Bose-Hubbard model. Thermometry of lattice gases is realized from the superfluid to the Mott regime by combining the measurement of three-dimensional momentum-space densities with ab initio quantum Monte Carlo (QMC) calculations of the same quantity. The measured temperatures are in agreement with isentropic lines reconstructed via QMC for the experimental parameters of interest, with a conserved entropy per particle of S/N=0.8(1)k_{B}. In addition, the Fisher information associated with this thermometry method shows that the latter is most accurate in the critical regime close to the Mott transition, as confirmed in the experiment. These results prove that equilibrium states of the Bose-Hubbard model-including those in the quantum-critical regime above the Mott transition-can be adiabatically prepared in cold-atom apparatus.