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.

4 pages, 2 figures; published version (v2)

References in corpus (8)

• Phase diagram of a two-component Fermi gas with resonant interactions
• Phase diagram of a strongly interacting polarized Fermi gas in one dimension
• Thermodynamics of the Spin Luttinger-Liquid in a Model Ladder Material
• Quasi-one-dimensional polarized Fermi superfluids
• Phase Transitions and Pairing Signature in Strongly Attractive Fermi Atomic Gases
• Exact quantum Monte Carlo study of one dimensional trapped fermions with attractive contact interactions
• Theory of quasi-one dimensional imbalanced Fermi gases
• Universal temperature dependence of the magnetization of gapped spin chains

Cited by in corpus (33)

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• Spin-Imbalance in a One-Dimensional Fermi Gas
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• Asymptotic correlation functions and FFLO signature for the one-dimensional attractive spin-1/2 Fermi gas
• Universality in one-dimensional fermions at finite temperature: Density, pressure, compressibility, and contact
• Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems
• Quantum Criticality of 1D Attractive Fermi Gas
• Wilson ratio of Fermi gases in one dimension
• Critical behaviours of contact near phase transitions
• Thermodynamics, contact and density profiles of the repulsive Gaudin-Yang model
• Two interacting fermions in a 1D harmonic trap: matching the Bethe ansatz and variational approaches
• Universal Tomonaga-Luttinger liquid phases in one-dimensional strongly attractive SU(N) fermionic cold atoms
• Integrable quenches in the Hubbard model
• Thermodynamics, spin-charge separation and correlation functions of spin-1/2 fermions with repulsive interaction
• Quantum criticality and universal scaling of strongly attractive spin-imbalanced Fermi gases in a 1D harmonic trap
• Exactly solvable models and ultracold Fermi gases
• Analytical thermodynamics of a strongly attractive three-component Fermi gas in one dimension
• Collective modes as a probe of imbalanced Fermi gases
• Critical phenomena in one dimension from a Bethe ansatz perspective
• Dimensional Crossover in a Spin-imbalanced Fermi gas
• Magnetism of one-dimensional strongly repulsive spin-1 bosons with antiferromagnetic spin exchange interaction
• Universality class of quantum criticality for strongly repulsive spin-1 bosons with antiferromagnetic spin-exchange interaction
• Yang-Yang method for the thermodynamics of one-dimensional multi-component interacting fermions
• Thermodynamics of one-dimensional SU(4) and SU(6) fermions with attractive interactions
• Effects of interaction and polarization on spin-charge separation: A time-dependent spin-density-functional theory study
• Hartree-Fock-Bogoliubov theory of trapped one-dimensional imbalanced Fermi systems
• Thermodynamics and spin-charge separation of one-dimensional strongly repulsive three-component fermions
• Low temperature specific heat of 1D multicomponent systems at commensurate- incommensurate phase transition point
• Trapped imbalanced fermionic superfluids in one dimension: A variational approach
• The properties of Tonk-Girardeau Gas at Finite Temperature and Comparison with Polarized Free Fermions
• Universal logarithmic temperature dependence of magnetic susceptibility of one-dimensional electrons at critical values of magnetic field
• Quantum Criticality of one-dimensional multicomponent Fermi Gas with Strongly Attractive Interaction