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The ultracold molecular conversion rate occurring in an adiabatic rampthrough a Fano-Feshbach resonance is studied and compared in two statisticalmodels. One model, the so-called stochastic phase space sampling (SPSS)[E.Hodbyet al., PRL.94 120402(2005)] evaluates the overlap of two atomic distributionsin phase space by sampling atomic pairs according to a phase-space criterion.The other model, the chemical equilibrium theory(ChET)[S.Watabe and T.Nikuni,PRA.77 013616(2008)] considers atomic and molecular distributions in the limitof the chemical and thermal equilibrium. The present study applies SPSS andChET to a prototypical system of K+K K2 in all the symmetry combinations,namely Fermi-Fermi, Bose-Bose, and Bose-Fermi cases. To examine implications ofthe phase-space criterion for SPSS, the behavior of molecular conversion isanalyzed using four distinct geometrical constraints. Our comparison of theresults of SPSS with those of ChET shows that while they appear similar in mostsituations, the two models give rise to rather dissimilar behaviors when thepresence of a Bose-Einstein condensate (BEC) strongly affects the moleculeformation.

Stochastic and equilibrium pictures of the ultracold FFR molecular conversion rate