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