title: Analytic thermodynamics and thermometry of Gaudin-Yang Fermi gases.
abstract: We study the thermodynamics of a one-dimensional attractive Fermi gas (the Gaudin-Yang model) with spin imbalance. The exact solution has been known from the thermodynamic Bethe ansatz for decades, but it involves an infinite number of coupled nonlinear integral equations whose physics is difficult to extract. Here the solution is analytically reduced to a simple, powerful set of four algebraic equations. The simplified equations become universal and exact in the experimental regime of strong interaction and relatively low temperature. Using the new formulation, we discuss the qualitative features of finite-temperature crossover and make quantitative predictions on the density profiles in traps. We propose a practical two-stage scheme to achieve accurate thermometry for a trapped spin-imbalanced Fermi gas.
authors.affiliation: Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.
authors.forename: Erhai
authors.initials: E
authors.lastname: Zhao
authors.forename: Xi-Wen
authors.initials: XW
authors.lastname: Guan
authors.forename: W Vincent
authors.initials: WV
authors.lastname: Liu
authors.forename: M T
authors.initials: MT
authors.lastname: Batchelor
authors.forename: Masaki
authors.initials: M
authors.lastname: Oshikawa