Universal Phase Diagram and Scaling Functions of Imbalanced Fermi Gases
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ontribution for the JETP special issue in honor of L. P. Pitaevskii’s 85th birthday
Universal Phase Diagram and Scaling Functions of Imbalanced Fermi Gases1 B. Franka, J. Langa, and W. Zwergera,* a
Physik-Department, Technische Universität München, Garching, D-85748 Germany * e-mail: [email protected] Received April 9, 2018
Abstract—We discuss the phase diagram and the universal scaling functions of attractive Fermi gases at finite imbalance. The existence of a quantum multicritical point for the unitary gas at vanishing chemical potential μ and effective magnetic field h, first discussed by Nikolić and Sachdev, gives rise to three different phase diagrams, depending on whether the inverse scattering length 1/a is negative, positive or zero. Within a Luttinger–Ward formalism, the phase diagram and pressure of the unitary gas is calculated as a function of the dimensionless scaling variables T/μ and h/μ. The results indicate that beyond the Clogston–Chandrasekhar limit at (h/μ)c ≃ 1.09, the unitary gas exhibits an inhomogeneous superfluid phase with FFLO order that can reach critical temperatures near unitarity of ≃0.03TF. DOI: 10.1134/S1063776118110031
1. INTRODUCTION The experimental realization of stable, two-component Fermi gases near a Feshbach resonance, where the magnitude of the scattering length a can be tuned far beyond the average interparticle spacing, allows to explore the crossover from a Fermi superfluid of the BCS-type to a Bose–Einstein condensate of tightly bound pairs (for recent reviews of this subject, see [1– 3]). Of particular interest in this context is the unitary regime kF|a| ≫ 1. At first sight, the point at which the scattering length diverges is not expected to show any special features, because the ground state is a superfluid on both sides of the unitary point. This argument, however, misses a number of essential features: as pointed out by Nishida and Son [4], the unitary gas realizes a non-relativistic field theory which is both scale and conformally invariant. The additional symmetries have a number of nontrivial consequences, like a vanishing bulk viscosity [5] or a breathing mode at twice the trap frequency in the presence of a harmonic confinement [6]. The latter is due to a hidden SO (2, 1) symmetry first discussed for Bose gases in two dimensions [7]. Moreover, as shown by Nikolić and Sachdev [8], the unitary gas at zero density realizes a quantum multicritical point. It separates the onset transition from the vacuum to a finite density superfluid into two regimes where the flow is towards 1 The article is published in the original.
a weakly interacting gas of either Fermions or Bosons. The thermodynamics of a Fermi gas near unitarity is therefore governed by a novel strong coupling fixed point and associated universal scaling functions. In the following, we will discuss the consequences of this basic insight for the phase diagram and scaling functions of imbalanced Fermi gases at finite values of the chemical potential difference h = (μ↑ – μ↓)/2 (for reviews of this subject
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