《普通物理学》课程教学资源（参考资料）SalomonBEC

Ultra-cold Fermi Gases From Molecular Bose-Einstein Condensation to BCS Pairing CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE Bose-E condensate Fermi sea College de france Thomas Bourdel, Julien Cubizolles, K Magalhaes Servaas Kokkelmans, Dima Petrov, Gora Shlyapnikov Christophe Salomon Laboratoire Kastler Brossel, Ecole Normale Superieure, Paris Orsay, 20 novembre 2003

Ultra-cold Fermi Gases From Molecular Bose-Einstein Condensation to BCS Pairing Ultra-cold Fermi Gases From Molecular Bose-Einstein Condensation to BCS Pairing Thomas Bourdel, Julien Cubizolles, K. Magalhaes Servaas Kokkelmans, Dima Petrov, Gora Shlyapnikov Christophe Salomon Laboratoire Kastler Brossel, Ecole Normale Supérieure, Paris, Orsay, 20 novembre 2003 Collège de France

Molecular Bose-Einstein Condensate and Fermi Superfluidity Two component Fermi gas at very low temperature s-wave interaction, scattering length a a>0 a<0 Molecular bec Fermi superfluid See Science news tocus Feshbach resonance August 8th, 2003

Molecular MolecularBBose-Einstein ose-EinsteinCondensate CondensateaandndFermi Superfluidity Fermi Superfluidity Two component Fermi gas at very low temperature s-wave interaction, scattering length a a > 0 a < 0 Molecular BEC ? Fermi superfluid ? See Science news focus, Feshbach August 8th, 2003 resonance

Outline o Basics of dilute trapped Bose and Fermi gases Search for superfluidity in Fermi gas o Study of Li Feshbach resonance Measurement of the interaction energy near a feshbach resonance Fermions in the strongly interacting regime O Formation of ultra-cold long-lived molecules near Feshbach resonance Reversible process between Fermi and Bose gases 2, Li2 dimer molecules o Bose-Einstein condensation of molecules ○ Perspectives

Outline Outline Basics of dilute trapped Bose and Fermi gases Study of 6Li Feshbach resonance - Measurement of the interaction energy near a Feshbach resonance - Fermions in the strongly interacting regime Search for superfluidity in Fermi gas Formation of ultra-cold long-lived molecules near Feshbach resonance Reversible process between Fermi and Bose gases 40K2 , 6Li2 dimer molecules Bose-Einstein condensation of molecules Perspectives

Bose-Einstein Condensation in Atomic Gases o Bose-Einstein condensate SCiENCE Rubidium Bose enhancement ho (0.83 O 1995 E. Cornell /C. Wieman W. Ketterle o Rb Na LiH *He K. Cs. Yb K. Li dimers of fermions Sodium

Bose -Einstein Condensation in Atomic Bose -Einstein Condensation in AtomicGases Gases Bose-Einstein condensate Rubidium Bose enhancement MI T T>Tc T<Tc T<<Tc Sodium (0.8 3 N)1/3 T = C k B h ω Rb, Na, Li, H, *He, K, Cs, Yb, K 2, Li2: dimers of fermions 1995 E. Cornell /C. Wieman, W. Ketterle

Prix nobel de physique 1997 S Chu, C. Cohen Tannoudji, W. Phillips Manipulation d'atomes par laser Prix nobel de physique 2001 E. Cornell, W. Ketterle, C. Wieman Condensation de bose-Einstein colueadzs

Prix Nobel de physique 1997 S. Chu, C. Cohen Tannoudji, W. Phillips Manipulation d’atomes par laser Prix Nobel de physique 2001 E. Cornell, W. Ketterle, C. Wieman Condensation de Bose-Einstein

Quantum Statistics O Bose-Einstein statistics(1924) O Fermi-Dirac statistics (1926 Bose-Einstein condensate Fermi sea E Bose enhancement Pauli Exclusion ho 083N T<7、ho k。(6N)0 superfluid He, dilute gases, le. electrons in metals, atoms excitons neutron stars

Quantum Statistics Quantum Statistics 3He, electrons in metals, atoms, neutron stars, … Fermi-Dirac statistics (1926) E F Fermi sea Pauli Exclusion T << T = ( 6 N ) F 1/ 3 k B h ω Bose-Einstein statistics (1924) Bose-Einstein condensate Bose enhancement (0.8 3 N)1/3 T = C k B h ω superfluid 4He, dilute gases, excitons

Gaseous condensates: orders of magnitude Dilute gaz at temperature T' confined in harmonic trap :∷∷ V(7)=-mr Condensation threshold 「no: central density N=1.202/2)3 kg7>加3=2612 h 2zmk t Liquid helium Gaseous condensates 1027 atoms/m 1019 atoms/m n013=10AT~1K 1/3=05mT~1uK

1 2 2 ( ) 2 V r = mω r G Gaseous GaseousCondensates Condensates: orders : ordersofofmagnitude magnitude Dilute gaz at temperature T confined in harmonic trap : Condensation threshold: n0 : central density 3 1.202 Bk T N ω   =     = 3 0n λ = 2.612 Bk T  =ω 2 B h mk T λ π = Liquid Helium : 1027 atoms/m3 n0-1/3 = 10 Å T ~1 K Gaseous condensates: 1019 atoms/m3 n0-1/3 = 0.5 µm T ~1 µK

Magnetic trapping of neutral atoms local minimum of spin polarization Trap depth I mK E=-1B=+团z The magnetic energy creates a potential well for the center of mass motion of the atoms For loading a magnetic trap 109 atomes. 1 cm3 100μuK aser cooling n入3≈106 Photo: Bell labs melasse optique

Magnetic Magneticttrapping rappingooffnneutral eutralatoms atoms E B B G G = −µ. = + µ G G local minimum of B G + spin polarization Trap depth : 1 mK The magnetic energy creates a potential well for the center of mass motion of the atoms For loading a magnetic trap: Laser cooling : nλ3 ≈ 10−6 Photo: Bell Labs 109 atomes, 1 cm3 100 µK mélasse optique

Visualisation du nuage atomique CCD Dependance spatiale de absorption d'un faisceau laser sonde par le nuage Mesure in situ: distribution en position ou apres temps de vol: distribution en impulsion

Mesure in situ: distribution en position ou après temps de vol: distribution en impulsion

Interest of dilute Bose and fermi gases 1) Low density, low energy 1012-1015acm3,T~1010e-1K.EFem~10K Atom-atom interactions described by a small number of parameters Scattering length, density, tunability of interactions TWO-body, three-body interactions Flexibility of trapping parameters 2) Simplicity of detection by optical imaging Comparison between experiments and predictions of many-body theories Gross-Pitaevski eq, Bose-Hubbard model, Mott insulator transition Link with other fields of physics, condensed matter, solid-state physics nuclear physics, astrophysics Fermi systems Fermi pressure Inhibition of collisions, Modification of spontaneous emission rate Mixtures of Bose-Fermi systems Search for a bcs transition

Interest Interestof dilute of diluteBose and Bose andFFermi gases ermi gases 1) Low density, low energy 1012 -1015 at/cm3, T~ 10-10 eV~1 µK. EFermi ~ 10 µK Atom-atom interactions described by a small number of parameters Scattering length, density,..tunability of interactions Two-body, three-body interactions Flexibility of trapping parameters 2) Simplicity of detection by optical imaging Comparison between experiments and predictions of many-body theories Gross-Pitaevski eq., Bose-Hubbard model, Mott insulator transition,… Link with other fields of physics, condensed matter, solid-state physics nuclear physics, astrophysics,…. Fermi systems Fermi pressure Inhibition of collisions, Modification of spontaneous emission rate Mixtures of Bose-Fermi systems Search for a BCS transition