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Physical Review Letters

Two-Color Photoassociation Spectroscopy of Ground State Rb2

Chin‐Chun Tsai, R. S. Freeland, J. M. M. J. Vogels, H. M. J. M. Boesten, BOUDEWIJN J. VERHAAR, Daniel J. Heinzen

Published Aug 18, 1997• 117 citations
Publisher

Abstract

We determine the energies of twelve vibrational levels lying within 20 GHz of the lowest dissociation limit of ${}^{85}{\mathrm{Rb}}_{2}$ with two-color photoassociation spectroscopy of ultracold ${}^{85}\mathrm{Rb}$ 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 ${}^{85}{\mathrm{Rb}}_{2}$ interaction parameters. The information obtained is sufficient to allow for quantitative calculations of arbitrary Rb ultracold collision properties.

DOI
10.1103/physrevlett.79.1245

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PHOTOASSOCIATION SPECTROSCOPY OF 85Rb2{^{85}}Rb_{2}85Rb2​ NEAR ITS DISSOCIATION LIMIT
We present results which probe the structure of 85Rb2{^{85}}Rb_{2}85Rb2​ very near its lowest dissociation limit. To obtain these results, we used two different variations of photoassociation spectroscopy of laser-cooled and trapped 85Rb{^{85}}Rb85Rb atoms. First, we have determined the positions of twelve of the highest vibrational levels of 85Rb2{^{85}}Rb_{2}85Rb2​, all bound by less than 0.7cm−10.7 cm^{-1}0.7cm−1, with two-color (free-bound-bound) photoassociation spectroscopy. The levels lie in an energy range for which singlet and triplet states are strongly mixed by the hyperfine interaction. We found that we could accurately describe these states with a novel coupled-channels inverse perturbation analysis. In a second experiment, we have carried out Zeeman-resolved photoassociation spectroscopy. This technique allowed us to probe the energy range in the lowest part of the electronic ground state continuum, which lies between the dissociation limits corresponding to different hyperfine states of the separated atoms. With this method, we have observed a Feshbach scattering resonance in the continuum for the first time, which we find can be tuned to zero energy with a magnetic field.
We report the first observation of the highest lying bound levels of the ground electronic state of ^85Rb2 by means of optical double resonance (free-bound-bound) photoassociation spectroscopy of colliding, laser-cooled ^85Rb atoms. Twelve levels with binding energies from 0.13 to 20 Ghz are observed. We carry out an inverse perturbation analysis of these levels that takes full account of the hyperfine-induced singlet-triplet mixing with a coupled channels approach. This analysis yields previously undetermined atomic interaction parameters that are crucial for the understanding of Rb ultracold collisions and Bose-Einstein condensates. Complete consistency is obtained with all previously measured cold collision properties of Rb. We gratefully acknowledge the support at Texas of the R. A. Welch Foundation, the NSF, and the Microgravity Science and Applications Division of NASA.
We describe a method that is well suited to analysis of the bound states of the alkali-metal dimers near their dissociation limit. The method combines inverse perturbation theory, coupled-channel bound-state theory, and the accumulated phase method to treat the short-range part of the molecular potentials. We apply this method to analyze the bound-state energies measured in a two-color photoassociation experiment in an ultracold 85Rb{}^{85}\mathrm{Rb}85Rb gas. This analysis yields information on the interactions between ultracold 85Rb{}^{85}\mathrm{Rb}85Rb atoms that is important to the understanding of ultracold Rb collisions and Bose-Einstein condensation.
The most accurate theoretical potentials available for the interaction of a pair of ground-state Rb atoms are used to evaluate their ultracold scattering properties. The close relation between the zero-energy scattering phase shifts and the number of bound states in the potential, by Levinson's theorem, is used to assign absolute values to the l = 0, 1 and 2 phase shifts. The number of bound states is compared with those resulting from detailed spectroscopic studies on the singlet potential and photoassociation results on the triplet potential. We review the scattering formulae needed to satisfy the Pauli principle for the fermion nuclei of 85Rb and 87Rb and their single unpaired electrons, for all possible initial hyperfine states. Scattering lengths are evaluated and their sensitivity to details of the asymptotic potentials is demonstrated.
The spectra of the high-lying vibrational levels of the Asp1Sigmasbspu+A\\sp1\\Sigma\\sbsp{u}{+}Asp1Sigmasbspu+ and 1sp3Sigmasbspg+1\\sp3\\Sigma\\sbsp{g}{+}1sp3Sigmasbspg+ singly excited states of both sp6rmLisb2\\sp6\\rm Li\\sb2sp6rmLisb2 and sp7rmLisb2\\sp7\\rm Li\\sb2sp7rmLisb2 are obtained via photoassociation of colliding ultracold atoms confined in a magneto-optical trap. The least bound state of the asp3Sigmasbspu+a\\sp3\\Sigma\\sbsp{u}{+}asp3Sigmasbspu+ ground state potential, obtained by two-photon photoassociative spectroscopy, is also presented for both sp7rmLisb2\\sp7\\rm Li\\sb2sp7rmLisb2 and sp6rmLisb2\\sp6\\rm Li\\sb2sp6rmLisb2. The vibrational levels have resolved hyperfine structure, whose relative energy splittings and transition strengths are accurately modeled. The photoassociative spectra are used to precisely determine both the singlet and triplet s-wave scattering lengths for both isotopes, which are important parameters in systems designed to observe quantum degenerate effects and Bose-Einstein condensation.
The formation of ultracold metastable RbCs molecules is observed in a double species magneto-optical trap through photoassociation below the 85 Rb(5S 1/2 ) + 133 Cs(6P 3/2 ) dissociation limit followed by spontaneous emission. The molecules are detected by resonance enhanced two-photon ionization. Using accurate quantum chemistry calculations of the potential energy curves and transition dipole moment, we interpret the observed photoassociation process as occurring at short internuclear distance, in contrast with most previous cold atom photoassociation studies. The vibrational levels excited by photoassociation belong to the 5th 0 + or the 4th 0 − electronic states correlated to the Rb(5P 1/2, 3/2 ) + Cs(6S 1/2 ) dissociation limit. The computed vibrational distribution of the produced molecules shows that they are stabilized in deeply bound vibrational states of the lowest triplet state. We also predict that a noticeable fraction of molecules is produced in the lowest level of the electronic ground state.