Normal State of Highly Polarized Fermi Gases: Simple Many-Body Approaches

Abstract

We consider the problem of a single # atom in the presence of a Fermi sea of " atoms, in the vicinity of a Feshbach resonance. We calculate the chemical potential and the effective mass of the # atom using two simple approaches: a many-body variational wave function and a T-matrix approximation. These two methods lead to the same results and are in good agreement with existing quantum Monte Carlo calculations performed at unitarity and, in one dimension, with the known exact solution. Surprisingly, our results suggest that, even at unitarity, the effect of interactions is fairly weak and can be accurately described using single particle-hole excitations. We also consider the case of unequal masses. DOI: 10.1103/PhysRevLett.98.180402 PACS numbers: 05.30.Fk, 03.75.Ss, 71.10.Ca, 74.72.ÿh The investigation of ultracold Fermi gases with two unbalanced hyperfine states (which we shall denote as " and # ) has been through an impressive expansion last year. This subfield is of great interest both on practical and on theoretical grounds. Indeed, on one hand, it is related to other fields of physics, namely, superconductivity, astrophysics, and high-energy physics, where similar situations arise [1]. On the other hand, the additional parameter provided by the population imbalance should provide a tool to deepen our understanding of the Bose-Einstein condensation (BEC)-BCS crossover in these systems and contribute to improving our control of many-body theory. This recent activity has been started by striking experimental results [2] which have given rise to a considerable number of theoretical works [3]. Experiments performed on trapped systems have observed equal density superfluid states as well as partially and fully polarized regions.The analysis of the T 0 phase separation requires the knowledge of the properties of both the superfluid and the partially polarized normal phase [4 -6]. This has been developed in the recent work of Lobo et al. [6], where, at unitarity, the properties of the partially polarized phase have been obtained by calculating through a quantum Monte Carlo (QMC) approach the parameters which characterize a single # atom immersed in a Fermi sea of " atoms, with density n " k 3 F =62 . In this way, they were able to obtain very good agreement with experimental results.Here we consider the general problem of a single # atom in a completely polarized " atom Fermi sea. The " -# interaction is characterized by an s-wave scattering length a, whose value can be tuned via a Feshbach resonance from the BEC (1=k F a 1) to the BCS (1=k F a ÿ1) limits. The Fermi gas is ideal due to the suppression of higher angular momentum scattering at low temperatures. This problem is a much simpler one than the case of two equal spin populations in the BEC-BCS crossover, although still quite nontrivial due to the absence of a small parameter in the strongly interacting regime. It is the simplest realization of the moving impurity problem, and it bears a strong similarity with other old, famous, and notoriously difficult...

Thermodynamics of Ultracold Fermi Gases

“…The normal phase is then merely described, in most of the parameter range, as a mixture of ideal Fermi gases of majority atoms and Fermi polarons. The polaron e ective masses extracted from our data are in agreement with the most advanced theories [83,84,85,86].…”

“…This`impurity' problem is much simpler than the general problem with macroscopic atom numbers in both spin states. Up to now all theories give the same value for A(δ 1 ) within less than 1% [83,85,178,84,86], and are in agreement with the MIT measurement [82] (see Fig.5.1).…”

Metastability and coherence of repulsive polarons in a strongly interacting Fermi mixture

“…The [24,35] or molecule [23,36,37] properties. The quasiparticle parameters for the polaron (energy E + and E − , residue Z, effective mass) and the molecule properties can be found either variationally, or diagrammatically using the ladder approximation.…”

“…Previous treatments [12,23,24,27,[35][36][37] were based on a universal scattering amplitude, describing broad Feshbach resonances. To include effects of the finite effective range we employ a many-body T-matrix given by [38,39] an energy-dependent length parameter, with a bg , ∆B, B 0 , and δ µ being the background scattering length, the width, the center, and the relative magnetic moment of the Feshbach resonance.…”

“…Far away from resonance this simplifies to a mean-field shift proportional to a. The lower branch E − of the system (green line) corresponds to the attractive polaron, which has recently received a great deal of attention theoretically [4,15,[23][24][25] as well as experimentally [16,17,26]. This polaronic branch remains the ground state of the system until a critical interaction strength is reached, where the system energetically prefers to form a bosonic molecule by binding the impurity to an atom taken from the Fermi sea [23,25,27].…”