Experimental Determination of Bose-Hubbard Energies

Abstract

We present the first experimental measurement of the ensemble averages of both the kinetic and interaction energies of the three-dimensional Bose--Hubbard model at finite temperature and various optical lattice depths across weakly to strongly interacting regimes, for an almost unit filling factor. The kinetic energy is obtained through Fourier transformation of a time-of-flight signal, and the interaction energy is measured using a newly developed atom-number-projection spectroscopy technique, by exploiting an ultra-narrow optical transition of two-electron atoms. The obtained experimental results can be used as benchmarks for state-of-the-art numerical methods of quantum many-body theory. As an illustrative example, we compare the measured energies with numerical calculations involving the Gutzwiller and cluster-Gutzwiller approximations, assuming realistic trap potentials and particle numbers at nonzero entropy (finite temperature); we obtain good agreement without fitting parameters. We also discuss the possible application of this method to temperature estimations for atoms in optical lattices using the thermodynamic relation. This study offers a unique advantage of cold atom system for `quantum simulators', because, to the best of our knowledge, it is the first experimental determination of both the kinetic and interaction energies of quantum many-body system.

arXiv comment22 pages, 20 figures

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Cited by in corpus (12)

• Tools for quantum simulation with ultracold atoms in optical lattices
• Observation of non-linearity of generalized King plot in the search for new boson
• Universal thermodynamics of an SU($N$) Fermi-Hubbard Model
• Recovering quantum correlations in optical lattices from interaction quenches
• Critical points of the three-dimensional Bose-Hubbard model from on-site atom number fluctuations
• Observation of slow relaxation due to Hilbert space fragmentation in strongly interacting Bose-Hubbard chains
• Current-feedback-stabilized laser system for quantum simulation experiments using Yb clock transition at 578 nm
• Measurement of total phase fluctuation in cold-atomic quantum simulators
• Exploring the Strongly-Interacting Regime of Effective Multi-Body Interactions in a Trapped Ultracold Atom System
• Evidence from on-site atom number fluctuations for a quantum Berezinskii-Kosterlitz-Thouless transition in the one-dimensional Bose-Hubbard model
• Finite temperature phase diagram of the extended Bose-Hubbard model in the presence of disorder
• Third quantization with Hartree approximation for open-system bosonic transport