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arXiv:1304.4625 · Physical Review A

Thermodynamics of strongly correlated one-dimensional Bose gases

Andreas Vogler, Ralf Labouvie, Felix Stubenrauch, Giovanni Barontini, Vera Guarrera, Herwig Ott

Published Sep 11, 2013• 54 citations
arXivHTMLPDF

Abstract

We investigate the thermodynamics of one-dimensional (1D) Bose gases in the strongly correlated regime. To this end, we prepare ensembles of independent 1D Bose gases in a two-dimensional optical lattice and perform high-resolution in situ imaging of the column-integrated density distribution. Using an inverse Abel transformation we derive effective one-dimensional line-density profiles and compare them to exact theoretical models. The high resolution allows for a direct thermometry of the trapped ensembles. The knowledge about the temperature enables us to extract thermodynamic equations of state such as the phase-space density, the entropy per particle, and the local pair-correlation function.

DOI
10.1103/physreva.88.031603

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We investigate the thermodynamics of one-dimensional (1D) Bose gases in the strongly correlated regime. To this end, we prepare ensembles of independent 1D Bose gases in a two-dimensional optical lattice and perform high-resolution in situ imaging of the column-integrated density distribution. Using an inverse Abel transformation we derive effective one-dimensional line-density profiles and compare them to exact theoretical models. The high resolution allows for a direct thermometry of the trapped ensembles. The knowledge about the temperature enables us to extract thermodynamic equations of state such as the phase-space density, the entropy per particle, and the local pair-correlation function.
Ultracold Bose gases in one-dimensional optical lattices constitute an important benchmark problem in the study of strongly interacting many-body quantum phases. Here we present a combined experimental and theoretical study of their phase-coherence properties over a wide range of lattice depths. Experimentally, we extract the single-particle correlation function directly from the measured momentum distribution. Theoretically, we perform tensor-network simulations of the Bose-Hubbard model that incorporate all relevant experimental parameters. For deep lattices well within the Mott insulator regime, the experimental results are in good agreement with the expected zero-temperature behavior, with only small temperature-dependent corrections. As the lattice depth is reduced, finite-temperature effects become increasingly important. We find that the experimental data are quantitatively described by an effective temperature extracted from the tensor-network simulations, and that this effective temperature decreases markedly with increasing lattice depth. Rather than indicating actual cooling, we interpret this behavior as evidence of inhibition of thermalization caused by the formation of Mott domains that suppress heat transport. Counterintuitively, the inhibition of thermalization favors the preparation of an effectively low-entropy quantum gas in the trap center for large lattice depths.
We calculate the density profiles and density correlation functions of the one-dimensional Bose gas in a harmonic trap, using the exact finite-temperature solutions for the uniform case, and applying a local density approximation. The results are valid for a trapping potential which is slowly varying relative to a correlation length. They allow a direct experimental test of the transition from the weak coupling Gross-Pitaevskii regime to the strong coupling, \'fermionic\' Tonks-Girardeau regime. We also calculate the average two-particle correlation which characterizes the bulk properties of the sample, and find that it can be well approximated by the value of the local pair correlation in the trap center.
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Understanding the effect of correlations in interacting many-body systems is one of the main challenges in quantum mechanics. While the general problem can only be addressed by approximate methods and numerical simulations, in some limiting cases, it is amenable to exact solutions. I will present a family of exact solutions for strongly interacting 1D quantum gases in arbitrary external potential, valid for bosons, multicomponent fermions and mixtures. It allows us to obtain experimental observables such as the density profiles and momentum distribution at all momentum scales, beyond the Luttinger liquid approach. It also predicts the exact quantum dynamics at all the times, including the small oscillation regime yielding the collective modes of the system and the large quench regime where the system parameters are changed considerably. The solution can be extended to describe finite-temperature conditions, spin, and magnetization effects. In particular I will present large-size calculations of the frequency- and momentum-resolved spectral function of strongly repulsive lattice bosons and a symmetry-breaking exact solution for a Bose-Bose mixture. Our approach directly describes the experiments with trapped ultracold atoms where the strongly correlated regime in one dimension has been achieved.
We describe a powerful method for determining the equation of state of an ultracold gas from in situ images. The method provides a measurement of the local pressure of a harmonically trapped gas and we give several applications to Bose and Fermi gases. We obtain the grand-canonical equation of state of a spin-balanced Fermi gas with resonant interactions as a function of temperature (Nascimbène et al 2010 Nature 463 1057). We compare our equation of state with an equation of state measured by the Tokyo group (Horikoshi et al 2010 Science 327 442), which reveals a significant difference in the high-temperature regime. The normal phase, at low temperature, is well described by a Landau Fermi liquid model, and we observe a clear thermodynamic signature of the superfluid transition. In a second part, we apply the same procedure to Bose gases. From a single image of a quasi-ideal Bose gas, we determine the equation of state from the classical to the condensed regime. Finally, the method is applied to a Bose gas in a three-dimensional optical lattice in the Mott insulator regime. Our equation of state directly reveals the Mott insulator behavior and is suited to investigate finite-temperature effects.