Ultra-cold molecules in an atomic Bose-Einstein condensate

This thesis is about photoassociation of Bose-condensed 87Rb. Most importantly we report that state selected 87Rb₂ molecules were created at rest in a condensate of 87Rb using two-photon photoassociation. Additionally, we have identified three weakly bound states of the 87Rb₂ $S+u3$, potential for the |1, −1⟩ + |1, − 1⟩ collisional channel. The binding energies of these states are 529.4 ± .07, 636.0094 ± .0012, and 24.24 ± .01 MHz respectively. We have also carried out a detailed study of the density dependence of the shift and width of the two-photon lineshape. This shift and width is modeled using the theory of Bohn and Julienne [34] and in addition to the precise measurement of binding energy we also report the first measurement of an atom molecule scattering length, a_am, which we conclude is −180 ± 150 a₀, and the inelastic collision rate, K_inel < 8 × 10−11 cm−3/s.; Stimulated Raman free bound coupling in an atomic Bose-Einstein condensate may lead to the formation of a molecular condensate. In order to evaluate this possibility we present a many-body quantum mean field theory of a Bose-Einstein condensate that includes a density dependent coherent coupling between atoms and molecules. This theory yields two coupled equations, one for the evolution of atomic condensate amplitude and one for the evolution of molecular condensate amplitude. The nature of the atomic-molecular condensate evolution is shown to depend on six, model parameters including the coherent coupling, given by $cn$. The other five parameters can be interpreted as light-shifts and incoherent loss rates. We present a calculation intended to estimate the values of these six parameters for the 87Rb − 87Rb ₂ system. Based on the results of this calculation we identify two locations in the 87Rb₂ spectrum where coherent transfer of population from atomic condensate to molecular condensate is plausible. Finally, we examine the credibility of the theoretical model used to estimate the six parameters used by the mean field theory. By comparing the measured Stark shifts of two-color resonances with predictions based on our theoretical model we conclude that the model is satisfactory for the v = 37 level of the $S+u3$ potential.; This work also describes the experimental details of stabilizing a Coherent 899-01 Ti:Saphire laser and the experimental methods important to executing photoassociation in a time-averaged-orbiting potential (TOP) trap.