Landau‐Zener transition for association of an atomic Bose‐Einstein condensate with interparticle elastic interactions included.

From atomic to molecular Bose-Einstein condensates: a physically realizable term-crossing model for cold atom association

Using an exact third-order NL di®erential equation for the molecular state probability, we develop a variational approach which enables us to construct highly accurate analytic approximations describing time dynamics of the coupled atom-molecular system in each of the interaction regimes. We show that the approximation describing time evolution of the molecular state probability both in the weak interaction limit and in the large detuning regime of the strong interaction limit can be written as a sum of two distinct terms; the ¯rst one, being a solution to a limit ¯rst-order NL equation, e®ectively describes the process of the molecule formation while the second one, being a scaled solution…

Fermi-type interaction in molecular and atomic Hamiltonians. Application to molecular systems and Bose-Einstein condensates.

International audience; We present a simple prescription to build phenomenological Hamiltonians describing Fermi-type interactions and apply the developed formalism to two distinct physical systems. First, in a very simple way, we derive equations describing time dynamics of two coherently coupled Bose-Einstein condensates. Further, for bent XY2 molecules, we reproduce all the experimental data with an excellent precision.

Landau-Zener Transition for Association of an Atomic Bose-Einstein Condensate With Inter-Particle Elastic Interactions Included

International audience; We study strong coupling limit of the non-linear Landau-Zener transition at coherent photo- and magneto-association of cold atoms, focusing on the role of the elastic interspecies scatterings. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a nontrivial version of the strained parameter method which enables us to construct a highly accurate and simple analytic approximation describing time dynamics of the coupled atom-molecular system.