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arXiv:cond-mat/0604236

What is a Cooper pair ?

Gerardo Ortíz, J. Dukelsky

Published Apr 9, 2006• 0 citations
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Abstract

Recently, the nature of Cooper pairs in the BCS-BEC crossover has regained attention due to the observation of a large fraction of preformed fermion pairs on the BCS side of the Feshbach resonance in ultracold atomic Fermi gases. While several theoretical explanations were proposed, the interpretations are still controversial. The root of the controversy is understanding what represents a Cooper pair in a correlated Fermi system. This paper discusses these issues at the most elementary level.

DOI
10.48550/arxiv.cond-mat/0604236

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Recently, the nature of Cooper pairs in the BCS-BEC crossover has regained attention due to the observation of a large fraction of preformed fermion pairs on the BCS side of the Feshbach resonance in ultracold atomic Fermi gases. While several theoretical explanations were proposed, the interpretations are still controversial. The root of the controversy is understanding what represents a Cooper pair in a correlated Fermi system. This paper discusses these issues at the most elementary level.
We study the superfluid state of atomic Fermi gases using a BCS-Bose-Einstein-condensation crossover theory. Our approach emphasizes noncondensed fermion pairs which strongly hybridize with their (Feshbach-induced) molecular boson counterparts. These pairs lead to pseudogap effects above Tc{T}_{c}Tc​ and non-BCS characteristics below. We discuss how these effects influence the experimental signatures of superfluidity.
The BCS-to-BEC crossover, as well as the nature of Cooper pairs, in superconducting and Fermi superfluid media is studied from the exact ground state wave function of the reduced BCS Hamiltonian. As the strength of the interaction increases, the ground state continuously evolves from a mixed system of quasifree fermions and pair resonances (BCS), to pair resonances and quasibound molecules (pseudogap), and finally to a system of quasibound molecules (BEC). A single unified scenario arises where the Cooper-pair wave function has a unique functional form. Several exact analytic expressions such as the binding energy and condensate fraction are derived. We compare our results with recent experiments in ultracold atomic Fermi gases.
We extend our previous investigations of fermionic condensation in broad Feshbach resonances by using the two-channel model developed for narrow Feshbach resonances. We investigate two crossovers: the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover by changing the sss-wave scattering length and the crossover from a narrow to a broad resonance by changing the atom-molecule coupling. At zero temperature we analyze, as a function of both atom-molecule coupling and sss-wave scattering length, the chemical potential, the energy gap, and the condensate fraction of atoms. In particular, we predict the contribution of Cooper pairs and preformed molecules to the total condensate density along the two crossovers.
The ability to control the interaction strength between atoms within strongly interacting Fermi gases by sweeping a magnetic field across a Feshbach resonance provides a powerful experimental system in which to study many-body physics. One example is the crossover from a Bose-Einstein condensate (BEC) regime, in which the atoms are strongly coupled into pairs, to the weak-coupling regime that mimics Bardeen-Cooper-Schrieffer (BCS) coupling of electrons in superconducting metals. Although behavior on either side of the resonance is fairly well understood, of immediate interest is to find out what happens in the BEC-BCS crossover regime. However, determining the relative contributions of atom pairing mechanisms is an experimental and theoretical challenge.
This thesis presents experiments probing physics in the crossover between Bose-Einstein condensation (BEC) and BCS superconductivity using an ultracold gas of atomic fermions. Scattering resonances in these ultracold gases (known as Feshbach resonances) provide the unique ability to tune the fermion-fermion interactions. The work presented here pioneered the use of fermionic Feshbach resonances as a highly controllable and tunable system ideal for studying the cusp of the BCS-BEC crossover problem. Here pairs of fermionic atoms have some properties of diatomic molecules and some properties of Cooper pairs. I present studies of a normal Fermi gas at a Feshbach resonance and the work required to cool the gas to temperatures where superfluidity in the crossover is predicted. These studies culminated in our observation of a phase transition at the cusp of the BCS-BEC crossover through condensation of fermionic atom pairs. I also discuss subsequent work that confirmed the crossover nature of the pairs in these condensates.