Measuring the equation of state of trapped ultracold bosonic systems in an optical lattice with in-situ density imaging

Abstract

We analyze quantitatively how imaging techniques with single-site resolution allow to measure thermodynamical properties that cannot be inferred from time-of-light images for the trapped Bose-Hubbard model. If the normal state extends over a sufficiently large range, the chemical potential and the temperature can be extracted from a single shot, provided the sample is in thermodynamic equilibrium. When the normal state is too narrow, temperature is low but can still be extracted using the fluctuation-dissipation theorem over the entire trap range as long as the local density approximation remains valid, as was recently suggested by Qi Zhou and Tin-Lun Ho [arXiv:0908.3015]. However, for typical present-day experiments, the number of samples needed is of the order of 1000 in order to get the temperature at least $10\%$ accurate, but it is possible to reduce the variance by 2 orders of magnitude if the density-density correlation length is short, which is the case for the Bose-Hubbard model. Our results provide further evidence that cold gases in an optical lattices can be viewed as quantum analog computers.

8 pages, 10 figures

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Probing the Superfluid to Mott Insulator Transition at the Single Atom Level
• The ALPS project release 1.3: open source software for strongly correlated systems
• Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices
• Experimental demonstration of single-site addressability in a two-dimensional optical lattice
• Suppression of Density Fluctuations in a Quantum Degenerate Fermi Gas
• On-site number statistics of ultracold lattice bosons

Cited by in corpus (13)

• Cooling in strongly correlated optical lattices: prospects and challenges
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• Finite temperature study of bosons in a two dimensional optical lattice
• Superfluid to normal phase transition in strongly correlated bosons in two and three dimensions
• Quantum Criticality from in-situ Density Imaging
• Schwinger-Keldysh approach to out of equilibrium dynamics of the Bose Hubbard model with time varying hopping
• Thermometry of cold atoms in optical lattices via artificial gauge fields
• Revealing the Condensate and Non-Condensate Distributions in the Inhomogeneous Bose-Hubbard Model
• Seeing Hofstadter's Butterfly in Atomic Fermi Gases
• Boson Core Compressibility
• Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity
• Probing Phases and Quantum Criticality using Deviations from the Local Fluctuation-Dissipation Theorem
• Efficiency for preforming molecules from mixtures of light Fermi and heavy Bose atoms in optical lattices: the strong-coupling-expansion method