State-selected rubidium-87 molecules were created at rest in a dilute Bose-Einstein condensate of rubidium-87 atoms with coherent free-bound stimulated Raman transitions. The transition rate exhibited a resonance line shape with an extremely narrow width as small as 1.5 kilohertz. The precise shape and position of the resonance are sensitive to the mean-field interactions between the molecules and the atomic condensate. As a result, we were able to measure the molecule-condensate interactions. This method allows molecular binding energies to be determined with unprecedented accuracy and is of interest as a mechanism for the generation of a molecular Bose-Einstein condensate.

We probe s-wave collisions of laser-cooled 85 Rb͑ f 2, m f 22͒ atoms with Zeeman-resolved photoassociation spectroscopy. We observe that these collisions exhibit a magnetically tunable Feshbach resonance, and determine that this resonance tunes to zero energy at a magnetic field of 164 6 7 G. This result indicates that the self-interaction energy of an 85 Rb Bose-Einstein condensate can be magnetically tuned. We also demonstrate that Zeeman-resolved photoassociation spectroscopy provides a useful new tool for the study of ultracold atomic collisions. [S0031-9007(98)06510-7]

On the basis of recently measured Rb 2 bound-state energies and continuum properties, we predict magnetically-induced Feshbach resonances in collisions of ultracold rubidium atoms. The resonances make it possible to control the sign and magnitude of the effective particle-particle interaction in a Rb Bose condensate by tuning a bias magnetic field. For the case of 85 Rb they occur at field values in the range where these atoms can be magnetostatically trapped. For 87 Rb they are predicted to occur at negative field values.

We determine the energies of twelve vibrational levels lying within 20 GHz of the lowest dissociation limit of 85 Rb 2 with two-color photoassociation spectroscopy of ultracold 85 Rb atoms. The levels lie in an energy range for which singlet and triplet states are mixed by the hyperfine interaction. We carry out a coupled channels bound state analysis of the level energies, and derive accurate values for 85 Rb 2 interaction parameters. The information obtained is sufficient to allow for quantitative calculations of arbitrary Rb ultracold collision properties. [S0031-9007(97)03822-2] PACS numbers: 32.80.Pj, 34.20.Cf An important reason for the interest in Bose-condensed, magnetically trapped alkali vapors [1-3] is that it is possible to understand many of their properties from first principles, starting with known atomic interactions. This close contact between theory and experiment requires accurate atomic interaction parameters such as elastic scattering lengths and inelastic collision cross sections. In principle these quantities can be computed from the atomic interaction potentials. Substantial progress has been made, for example, in the determination of Li [4-6], Na [7-9], and Rb [10-13] scattering lengths. Unfortunately, it has still not been possible to calculate many important collision properties because of uncertainties in the potential parameters.In this Letter, we present new results that eliminate most of these uncertainties for Rb. We measure the energies of twelve of the highest bound vibrational levels of ground state 85 Rb 2 with two-color ultracold atom photoassociation spectroscopy. As illustrated in Fig. 1, ultracold 85 Rb atoms collide in the presence of two laser fields of frequency n 1 and n 2 . Resonances observed at specific values of the frequency difference n 2 2 n 1 directly provide the level energies. We analyze the level energies with an inverse perturbation approach with coupled channels bound states, and obtain both singlet and triplet parameters. Two-color photoassociation spectroscopy has previously been used to obtain a single ground state level of Li 2 [5], and evidence for ground state levels of Na 2 [14]. Our work differs from this in that we obtain a much more complete spectrum, assignment, and analysis.A unique aspect of our work is that we obtain a molecular spectrum for levels with binding energies comparable to the atomic hyperfine splitting. In this range singlet (S 0) and triplet (S 1) states are strongly mixed by the hyperfine interaction V hf a͑I 1 ? S 1 1 I 2 ? S 2 ͒, so that molecular quantum numbers ͑S, I͒ are not good. Here S S 1 1 S 2 , I I 1 1 I 2 , and S i and I i are the electronic and nuclear spins of the two atoms (i 1, 2), respectively. Atomic quantum numbers ( f 1 , f 2 , with f i S i 1 I i ) are not good either, since these states are mixed at short range by the exchange interaction. Only the total spin quantum number F, with F f 1 1 f 2 S 1 I, is good at all internuclear distances. Adiabatic molecular potentials for 85 Rb 2 with the pure triplet (F 6...

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