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Laser Physics

Normal state of highly polarized Fermi gases: The bound state

R. Combescot, S. Giraud, X. Leyronas

Published Feb 2, 2010• 1 citation
Publisher

Abstract

We consider a highly polarized Fermi gas with a single ↓ atom within a Fermi sea of ↑ atoms. We extend a preceding many-body analysis to the case where a bound state is formed between the ↓ atom and an ↑ atom.
DOI
10.1134/s1054660x10050038

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We present a full many-body analysis of the problem of a single ↓ atom resonantly interacting with a Fermi sea of ↑ atoms. A series of successive approximations permits us to clarify the quite mysterious agreement between Monte Carlo results and approximate calculations taking only into account single particle-hole excitations. We show that it results from a nearly perfect destructive interference of the contributions of states with more than one particle-hole pair. Our treatment provides, at the same time, an essentially exact solution to this problem.
We present an analytical treatment of a single ↓-atom within a Fermi sea of ↑-atoms, when the interaction is strong enough to produce a bound state, dressed by the Fermi sea. Our method makes use of a diagrammatic analysis, with the involved diagrams taking only into account at most two particle-hole pairs excitations. The agreement with existing Monte Carlo results is excellent. In the BEC limit our equation reduces exactly to the Skorniakov and Ter-Martirosian equation. We present results for ↑- and ↓-atoms with different masses, which is of interest for experiments in progress.
We consider a single atom within a Fermi sea of atoms. We elucidate by a full many-body analysis the quite mysterious agreement between Monte Carlo results and approximate calculations taking only into account single particle-hole excitations. It results from a nearly perfect destructive interference of the contributions of states with more than one particle-hole pair. This is linked to the remarkable efficiency of the expansion in powers of hole wave vectors, the lowest order leading to perfect interference. Going up to two particle-hole pairs gives an essentially perfect agreement with known exact results. Hence our treatment amounts to an exact solution of this problem.
We consider a dense ultracold Fermi gas in the presence of a Feshbach resonance. We investigate how the threshold for bound state formation, which is just at the Feshbach resonance for a dilute gas, is modified due to the presence of the Fermi sea. We make use of a preceding framework of handling this many-body problem. We restrict ourselves to the simple case where the chemical potential μ is negative, which allows us to cover in particular the classical limit where the effect is seen to disappear. We show that, within a simple approach where basically only the effect of Pauli exclusion is included, the Fermi sea produces a large shift of the threshold, which is of the order of the width of the Feshbach resonance. This is in agreement with very recent experimental findings.
We consider the problem of a single downward arrow atom in the presence of a Fermi sea of upward arrow atoms, in the vicinity of a Feshbach resonance. We calculate the chemical potential and the effective mass of the downward arrow 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.