The equation of state of ultracold Bose and Fermi gases: a few examples

• Published in: New journal of physics Vol. 12; no. 10; p. 103026
• Main Authors: Nascimbène, Sylvain, Navon, Nir, Chevy, Frédéric, Salomon, Christophe
• Format: Journal Article
• Language: English
• Published: IOP Publishing 15-10-2010; Institute of Physics: Open Access Journals
• Subjects: Condensed Matter; Physics; Quantum Gases; many-body physics; quantum gases
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/12/10/103026

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 an 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. We compare our equation of state with an equation of state measured by the Tokyo group, that 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 3D 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.