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arXiv:1808.06933 · New Journal of Physics

Equations of state from individual one-dimensional Bose gases

Francisco Salces-Carcoba, C J Billington, A Putra, Y Yue, Seiji Sugawa, I B Spielman

Published Nov 9, 2018• 21 citations
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Abstract

We trap individual 1D Bose gases and obtain the associated equation of state by combining calibrated confining potentials with in situ density profiles. Our observations agree well with the exact Yang–Yang 1D thermodynamic solutions under the local density approximation. We find that our final 1D system undergoes inefficient evaporative cooling that decreases the absolute temperature, but monotonically reduces a degeneracy parameter.

DOI
10.1088/1367-2630/aaef9b

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We trap individual 1D Bose gases and obtain the associated equation of state by combining calibrated confining potentials with in situ density profiles. Our observations agree well with the exact Yang–Yang 1D thermodynamic solutions under the local density approximation. We find that our final 1D system undergoes inefficient evaporative cooling that decreases the absolute temperature, but monotonically reduces a degeneracy parameter.
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By combining the thermodynamic Bethe ansatz and local density approximation, we investigate the Yang—Yang thermodynamics of interacting one-dimensional Bose gases with anisotropic transversal confinement. It is shown that with the increase of anisotropic parameter at low temperature, the Bose atoms are distributed over a wider region, while at high temperature the density distribution is not affected obviously. Both the temperature and transversal confinement can strengthen the local pressure of the Bose gases.
We investigate the behavior of a weakly interacting nearly one-dimensional trapped Bose gas at finite temperature. We perform in situ measurements of spatial density profiles and show that they are very well described by a model based on exact solutions obtained using the Yang-Yang thermodynamic formalism, in a regime where other, approximate theoretical approaches fail. We use Bose-gas focusing [I. Shvarchuck, Phys. Rev. Lett. 89, 270404 (2002)] to probe the axial momentum distribution of the gas and find good agreement with the in situ results.
We investigate theoretically the behavior of a one-dimensional interacting Bose-Fermi mixture with equal masses and equal repulsive interactions between atoms at finite temperature in the scheme of thermodynamic Bethe ansatz. Combining the Yang-Yang thermodynamic formalism with local-density approximation in a harmonic trap, we calculate the density distribution of bosons and fermions numerically by treating the radially and axially excited states as discrete and continuous ones, respectively. Our result from exactly solvable solutions may be used as a touchstone for one-dimensional interacting Bose-Fermi mixture for experimental data fitting where mean-field theoretical approaches fail.
After a brief historical introduction to Bose-Einstein condensation and Fermi degeneracy, we discuss theoretical results we have recentely obtained for trapped degenerate quantum gases by means of a thermal field theory approach. In particular, by using Gross-Pitaevskii and Bogoliubov-Popov equations, we consider thermodynamical properties of two Bosonic systems: a gas of Lithium atoms and a gas of Hydrogen atoms. Finally, we investigate finite-temperature density profiles of a dilute Fermi gas of Potassium atoms confined in a harmonic potential.
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.