Atomic and molecular matter fields in periodic potentials

This paper deals with the conversion between atoms and molecules in optical lattices. We show that in the absence of collisional interaction, the atomic and molecular components in different lattice wells combine into states with macroscopic condensate fractions, which can be observed as a strong diffraction signal, if the particles are abruptly released from the lattice. The condensate population, and the diffraction signal are governed not only by the mean number of atoms or molecules in each well, but by the precise amplitudes on state vector components with different numbers of particles. We discuss ways to control these amplitudes and to maximize the condensate fraction in the molecular formation process.Comment: Invited talk at 'Quantum Challenges', Falenty, Poland, Sep. 2003. Submitted to J. Mod. Op

Bose-Einstein condensates in spatially periodic potentials

Introduction Bose-Einstein condensation in trapped dilute gases 1, 2, 3 was observed only recently. Nevertheless, the experimental developments in this field have advanced rapidly, and the properties of condensates in different circumstances have become a matter of practical interest. In this work we study the influence of a spatially periodic external potential on the properties of a Bose-Einstein condensate, as reported elsewhere in more detail 4 . Such a periodic potential may be induced by a far-off resonant laser field, and with present trapped condensates it is possible to have a condensate extending over many periods of such a field. The proposed periodic potential could be realized by a simple rearrangement of the laser field in the experiments with an optically trapped condensate 5 . The present study of condensates in periodic potentials both serves to generalize studies of single atom behaviour in such periodic potentials<F