Quadratic-nonlinear Landau-Zener transition for association of an atomic Bose-Einstein condensate with inter-particle elastic interactions included

• Published in: The European physical journal. D, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2010-02, Vol.56 (3), p.421-429
• Main Authors: Ishkhanyan, A., Sokhoyan, R., Suominen, K. A., Leroy, C., Jauslin, H. R.
• Format: Article
• Language: English
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Atomic; Atomic and molecular collision processes and interactions; Atomic and molecular physics; Classical and quantum physics: mechanics and fields; Exact sciences and technology; Laser-modified scattering and reactions; Level crossing and optical pumping; Matter waves; Molecular; Molecular properties and interactions with photons; Nonlinear Dynamics; Optical and Plasma Physics; Photon interactions with molecules; Physical Chemistry; Physics; Physics and Astronomy; Quantum Information Technology; Quantum Physics; Scattering of atoms, molecules and ions; Spectroscopy/Spectrometry; Spintronics
• ISSN: 1434-6060; 1434-6079
• DOI: 10.1140/epjd/e2009-00310-7

We study the strong coupling limit of a quadratic-nonlinear Landau-Zener problem for coherent photo- and magneto-association of cold atoms taking into account the atom-atom, atom-molecule, and molecule-molecule elastic scattering. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct a highly accurate and simple analytic approximation describing the time dynamics of the coupled atom-molecule system. We show that the approximation describing time evolution of the molecular state probability can be written as a sum of two distinct terms; the first one, being a solution to a limit first-order nonlinear equation, effectively describes the process of the molecule formation while the second one, being a scaled solution to the linear Landau-Zener problem (but now with negative effective Landau-Zener parameter as long as the strong coupling regime is considered), corresponds to the remaining oscillations which come up when the process of molecule formation is over.