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Acta Physica Polonica A

Resonance Superfluidity in a Quantum Degenerate Fermi Gas

S. J. J. M. F. Kokkelmans, Murray Holland, R. Walser, M. L. Chiofalo

Published Mar 1, 2002• 42 citations

Abstract

of Col or ado and Na ti onal Insti t ute of Standa rds and T echno lo gy Bo ul der, Col ora do 80 309-0440, U. S.A. and M. Chi of al o Scuol a No r mal e Superi ore, Pi azza dei Caval i eri 7, 56126 Pi sa, Ita l y W e consi der t he sup erÛuid ph ase transition that arises when a F eshbach resonance pairin g occurs in a dilute F ermi gas.T his is related to the phenomenon of sup ercondu cti v it y describ ed by the seminal Bardeen { Coop er{ Schrie ˜er theory .In supercondu ctivi ty , the phase transition is caused by a couplin g betw een pairs of electrons w ithin the medium.T his coupli ng is perturbative and leads to a critical temp erature T c w hich is small compared to the Fermi temp erature T F .Even high-T c sup erconductors typically ha ve a critical temp erature which is two orders of magnitude below T F .H ere w e describ e a resonance pairing mechanism in a quantum degenerate gas of potassium ( 4 0 K ) atoms w hich leads to sup erÛui di ty in a no vel regime | a regime that promises the unique opp ortunity to exp erimentally study the cross-over from the Bardeen À C oop er{Schrie˜er phase of w eakly-coupled fermions to the Bose{Einstei n condensate of strongly-boun d comp osite bosons.W e Ùnd that the transitio n to a superÛuid phase is possible at the high critical temp erature of about 0 :5 T F .I t should b e straightf orw ard to verif y this prediction, since these temp eratures can already be achieved exp erimentally .

DOI: 10.12693/aphyspola.101.387

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of Col or ado and Na ti onal Insti t ute of Standa rds and T echno lo gy Bo ul der, Col ora do 80 309-0440, U. S.A. and M. Chi of al o Scuol a No r mal e Superi ore, Pi azza dei Caval i eri 7, 56126 Pi sa, Ita l y W e consi der t he sup erÛuid ph ase transition that arises when a F eshbach resonance pairin g occurs in a dilute F ermi gas.T his is related to the phenomenon of sup ercondu cti v it y describ ed by the seminal Bardeen { Coop er{ Schrie ˜er theory .In supercondu ctivi ty , the phase transition is caused by a couplin g betw een pairs of electrons w ithin the medium.T his coupli ng is perturbative and leads to a critical temp erature T c w hich is small compared to the Fermi temp erature T F .Even high-T c sup erconductors typically ha ve a critical temp erature which is two orders of magnitude below T F .H ere w e describ e a resonance pairing mechanism in a quantum degenerate gas of potassium ( 4 0 K ) atoms w hich leads to sup erÛui di ty in a no vel regime | a regime that promises the unique opp ortunity to exp erimentally study the cross-over from the Bardeen À C oop er{Schrie˜er phase of w eakly-coupled fermions to the Bose{Einstei n condensate of strongly-boun d comp osite bosons.W e Ùnd that the transitio n to a superÛuid phase is possible at the high critical temp erature of about 0 :5 T F .I t should b e straightf orw ard to verif y this prediction, since these temp eratures can already be achieved exp erimentally .

We consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. This is related to the phenomenon of superconductivity described by the seminal Bardeen-Cooper-Schrieffer (BCS) theory. In superconductivity, the phase transition is caused by a coupling between pairs of electrons within the medium. This coupling is perturbative and leads to a critical temperature Tc which is small compared to the Fermi temperature TF. Even high-Tc superconductors typically have a critical temperature which is two orders of magnitude below TF. Here we describe a resonance pairing mechanism in a quantum degenerate gas of potassium (40K) atoms which leads to superfluidity in a novel regime--a regime that promises the unique opportunity to experimentally study the crossover from the BCS phase of weakly-coupled fermions to the Bose Einstein condensate of strongly-bound composite bosons. We find that the transition to a superfluid phase is possible at the high critical temperature of about 0.5TF. It should be straightforward to verify this prediction, since these temperatures can already be achieved experimentally.

Ce mémoire de thèse est divisé en deux parties. La première est consacrée à l étude de la superfluidité dans un gaz de fermions ultra-froids. En utilisant un gaz dégénéré de 6Li au voisinage d une résonance de Feshbach nous avons obtenu un superfluide fermionique et étudié son évolution en fonction de l énergie de liaison des paires. Afin de caractériser la transition BEC-BCS entre un condensat de Bose-Einstein de molécules et un état BCS de paires de Cooper faiblement liées, nous avons étudié l expansion du nuage en absence ou en présence d interactions. Nous avons ainsi extrait la distribution en impulsion du système et sondé son caractère hydrodynamique. La seconde partie concerne la conception et la réalisation d un montage expérimental de seconde génération. Par rapport à l ancien dispositif, ses principaux atouts sont un gain d un ordre de grandeur sur le nombre d atomes piégés, un bon accès optique, une grande stabilité et reproductibilité ainsi qu un taux de répétition cinq fois supérieur. La nouvelle expérience a déjà permis d atteindre le seuil de dégénérescence quantique du 7Li avec des performances très satisfaisantes et donne accès à la simulation de hamiltoniens de matière condensée avec des fermions ultra-froids.

I nst i tut e o f P hysi cs, A dam Mi cki ewi cz Uni versi ty Um ultowsk a 85, 61-61 4 Pozna¥ ( Recei ved Jul y 2, 2001)T w o-dim ension al ( d = 2 ) Penson À K olb mo del , i .e. t he ti ght-bindin g mo del with the pai r-hopp in g (intersite charge exchange ) interaction, is considered and the e˜ects of phase Ûuctuation s on the s -wave sup erconducti vi t y of this system are discussed w ithin the K osterlit z{T houl ess scenario.T he London penetration depth Ñ at T = 0 ; the K osterlitz-T houle ss critical temp erature T c , and the H artree{ Fock approximation critical temp erature T p are determined as a function of particle concentration and interaction.T he U emura typ e plots ( T c vs: Ñ À 2 ( 0) ) are derived.Beyond w eak coupli ng and for low concentrations they show the existence of universal scaling : T c ¿ 1=Ñ 2 ( 0) , as it w as previousl y found for the attractive H ubbard mo del and for the mo dels with intersite electron pairing.PAC S numb ers: 74.20.{z, 71.28.+ d, 74.25.H

a a U ni versit y of T ennessee , Kno xvi l le, T ennessee37996, U SA b Wro cl aw Uni versi ty of T echno lo gy, 50-370 Wro cl aw, Po l and Corr el at ions in partiall y Ùlled electron and comp osite fermion Landa u levels are studied numerically .I nsight into the nature of the correlations is obtained by using mo del pair pseudop oten tials.Energy spectra of a mo del short-range three-b ody repulsion are calculated.Mo ore{ Read ground state at the half -Ùllin g and its quasielec tron , quasihol e, magnetoroton, and pair-brea ki ng excitation s are all identiÙed.T he quasielectron /qu asihol e excitations are describ ed by a comp osite fermion mo del for Laughlin-correla ted electron pairs.C omparison of energy spectra and wavef unction overlaps obtained for di ˜erent pseudop otentials suggests that Ùnite-size e˜ects can b e imp ortant in numerical diagonal i zati on studies on a sphere.PAC S numb ers: 71.