Atom-atom interactions U(r At low temperature only s wave collisions ik.r tan o(k) a k->0 The magnitude and sign of a depend sensitively on the detailed a: scattering length shape of long range potential al-1 a 100 nm 4Th a 6(-) a>0: effective repulsive interaction a<0, effective attractive interaction
Atom-atom Atom-atomiinteractions nteractions The magnitude and sign of a depend sensitively on the detailed shape of long range potential r U(r) At low temperature, only s wave collisions . 0 0 ( ) tan ( ) lim ik r ikr k a r e e r k a k ψ δ → = − = − G G G a: scattering length |a|~1 à 100 nm 2 1 2 1 2 4 ( ) ( ) a V r r r r m π − = − δ G G = G G a > 0 : effective repulsive interaction a < 0 : effective attractive interaction
Control of interactions in a condensate Condensate dynamics described by gross-Pitaevski equation △+(G)+Ng()v(F)=v(F) 4ha g a: scattering length △ 004-0.020002004C a varies typically between I and 100 nanometers Bohr radius: 0, 05 nm)
2 2 ( ) ( ) ( ) ( ) 2 V r Ng r r r m ψ ψ µψ − ∆ + + = = G G G G a : scattering length 2 4 a g m π = = Condensate dynamics described by Gross-Pitaevski equation : scattering scattering length -0.04 -0.02 0 0.02 0.04 6 6 C C ∆ Control of Control of interactions in a condensate interactions in a condensate W(r) r 6 6 −C r/ |a| varies typically between 1 and 100 nanometers (Bohr radius : 0,05 nm)