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Physical Review A

Coupled singlet-triplet analysis of two-color cold-atom photoassociation spectra

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

Published Mar 8, 2000• 23 citations
Publisher

Abstract

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 ${}^{85}\mathrm{Rb}$ gas. This analysis yields information on the interactions between ultracold ${}^{85}\mathrm{Rb}$ atoms that is important to the understanding of ultracold Rb collisions and Bose-Einstein condensation.

DOI
10.1103/physreva.61.043407

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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.
We determine the energies of twelve vibrational levels lying within 20 GHz of the lowest dissociation limit of 85Rb2{}^{85}{\mathrm{Rb}}_{2}85Rb2​ with two-color photoassociation spectroscopy of ultracold 85Rb{}^{85}\mathrm{Rb}85Rb 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 85Rb2{}^{85}{\mathrm{Rb}}_{2}85Rb2​ interaction parameters. The information obtained is sufficient to allow for quantitative calculations of arbitrary Rb ultracold collision properties.
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.
A theoretical analysis of photoassociation in ultracold metastable helium has been undertaken for the 2(^3)S1 + 2(^3)S1 to 2(^3)S1 + 2(^3)P transition. A full multichannel calculation is presented for two aspects of the system, a) the accurate calculation of energies for the bound vibrational levels of the dimer; and b) the non-perturbative calculation of the photoassociation line shapes allowing for abitrary laser intensity and detuning. A strong emphasis is placed on the accuracy of the calculations, and the elimination of approximations that have been used in previous investigations. The results indicate that full multichannel calculations are required rather than approximate single-channel calculations in some important situations, and are especially useful for making assignments between experiment and theory. Bound levels have been previously measured from the photoassociation of cold metastable thermal gases to energies close to the three asymptotes j = 0, 1, 2 of the 2(^3)S1 → 2(^3)Pj atomic transition. Previous analysis of these measurements was made using either approximate accumulated phase techniques based on long-range single-channel potentials, or using multichannel calculations and long-range potentials. Because accurate short-range electronic potentials have been calculated only recently, this thesis presents the first multichannel calculation for the levels near the j = 1, 2 asymptotes. The new short-range potentials had previously been used in an approximate single-channel calculation, but this type of calculation ignores the effects of non-adiabatic and Coriolis couplings. Presented here are the binding energies calculated from a fully multichannel technique which includes these couplings, and some differences of up to 10% from the single-channel calculations are observed. The detailed knowledge of the bound wave functions is then exploited to determine a set of observability criteria that produce a near unique assignment of theoretical levels to experimental observations. From these unique assignments, a 1% correction to the short-range electronic potentials has been implemented that significantly improves the agreement between theory and experiment. Experimental measurements have previously been made of line shifts in the photoassociation spectra of vibrational levels in the 0+u long-range potential that asymptotes to 2(^3)S1 + 2(^3)P0 and their variation with laser intensity. These results were previously analysed by performing an approximate second-order perturbative calculation of the line shift that is valid only for low laser intensities. In this thesis a completely non-perturbative calculation of the spectra and line shapes for abitrary laser intensity is presented for photoassociation to the levels probed in experiment. The techniques of dressed state formalism and a modified radiative coupling are employed to properly treat the laser coupling for large interatomic separations. These calculations produce resonance profiles superimposed on a very significant background, a feature that is not seen in photoassociation calculations of other atomic species. From the calculated line shapes, the line shifts and line widths were determined for varying intensity and a small nonlinear intensity-dependence of up to 2.5% was found for the line shift. The effects of invoking the dipole approximation for the laser coupling for the long-range molecular system are analysed by solving the equations using the complete laser coupling that does not assume the dipole approximation. Important differences are obtained between the profiles with and without the dipole approximation, and the photoassociation resonances are found to be more discernible at larger intensities when the complete laser coupling is used.
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.
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.
Photoassociation is the process in which two colliding atoms absorb a photon to form an excited molecule. The development of laser-cooling techniques for producing gases at ultracold (<1mK)(<1\phantom{\rule{0.3em}{0ex}}\mathrm{mK})(<1mK) temperatures allows photoassociation spectroscopy to be performed with very high spectral resolution. Of particular interest is the investigation of molecular states whose properties can be related, with high precision, to the properties of their constituent atoms with the ``complications'' of chemical binding accounted for by a few parameters. These include bound long-range or purely long-range vibrational states in which two atoms spend most or all of their time at large internuclear separations. Low-energy atomic scattering states also share this characteristic. Photoassociation techniques have made important contributions to the study of all of these. This review describes what is special about photoassociation spectroscopy at ultracold temperatures, how it is performed, and a sampling of results including the determination of scattering lengths, their control via optical Feshbach resonances, precision determinations of atomic lifetimes from molecular spectra, limits on photoassociation rates in a Bose-Einstein condensate, and briefly, production of cold molecules. Discussions are illustrated with examples on alkali-metal atoms as well as other species. Progress in the field is already past the point where this review can be exhaustive, but an introduction is provided on the capabilities of photoassociation spectroscopy and the techniques presently in use.