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Beyond Born-Oppenheimer approximation in ultracold atomic collisions

E. Tiemann, Philipp Gersema, Kai K. Voges, Torsten Hartmann, Alessandro Zenesini, Silke Ospelkaus

Published Jan 1, 2020• 14 citations
Publisher

Abstract

We report on deviations beyond the Born-Oppenheimer approximation in potassium interatomic potentials. Identifying three previously unknown d-wave Feshbach resonances, we significantly improve the understanding of the K39 interatomic potentials. Combining these observations with the most recent data on known inter- and intraisotope Feshbach resonances, we show that Born-Oppenheimer corrections can be determined from atomic collisional properties alone and that significant differences between the homo- and heteronuclear cases appear.

DOI
10.15488/16306

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Physical Review A•Apr 29, 2009•54 citations
We report on deviations beyond the Born-Oppenheimer approximation in potassium interatomic potentials. Identifying three previously unknown d-wave Feshbach resonances, we significantly improve the understanding of the K39 interatomic potentials. Combining these observations with the most recent data on known inter- and intraisotope Feshbach resonances, we show that Born-Oppenheimer corrections can be determined from atomic collisional properties alone and that significant differences between the homo- and heteronuclear cases appear.
This work observes deviations from the Born-Oppenheimer approximation already from ultracold diatomic collisions of K. To improve the potential energy curves, the most recent available data from all inter- and intra-isotope combinations of K as well as three newly measured d\mathit{\text{d}}d-wave Feshbach resonances in 39K{}^{39}\text{K}39K are used.
We report results from close-coupling calculations for homonuclear ultracold collisions between potassium atoms, using the most up-to-date Born-Oppenheimer potential curves. The present study includes both of the bosonic isotopes 39K^{39}\mathrm{K}39K and 41K^{41}\mathrm{K}41K. The sss-wave scattering lengths as functions of the magnetic field strength for collisions between atoms in identical and different hyperfine states are obtained. Several Feshbach resonances are located and characterized for both isotopes. Comparison with experiments, where such data are available, show excellent agreement. We also study weakly bound molecular states of the K2{\mathrm{K}}_{2}K2​ molecule in close relation to the calculated Feshbach resonances. Another objective of the present work is to study inelastic collisions in which the hyperfine states of the colliding atoms are changed. From this type of calculation we obtain transition rates as functions of the magnetic field strength. Finally, we discuss how such transition rates might be of importance for experimental work.
We investigate magnetic Feshbach resonances in two different ultracold K-Rb mixtures. Information on the $^{39}\text{K}\text{\ensuremath{-}}^{87}\text{R}\text{b}$ isotopic pair is combined with preexisting observations of resonance patterns for $^{40}\text{K}\text{\ensuremath{-}}^{87}\text{R}\text{b}$. Interisotope resonance spectroscopy improves significantly our near-threshold model for scattering and bound-state calculations. Our analysis determines the number of bound states in singlet and triplet potentials and establishes precisely near-threshold parameters for all K-Rb pairs of interest for experiments with both atoms and molecules. In addition, the model verifies the validity of the Born-Oppenheimer approximation at the present level of accuracy.
We perform Feshbach spectroscopy in an ultracold mixture of 23Na^{23}\mathrm{Na}23Na and 40K^{40}\mathrm{K}40K with different spin-state combinations. We observed 24 new interspecies Feshbach resonances at magnetic fields up to 350 G. A full coupled-channel calculation is performed to assign these resonances. Among them, 12 resonances are identified as ddd-wave Feshbach resonances. These ddd-wave Feshbach resonances are about 5 G systematically smaller than the predictions based on the previous model potential. Taking into account these experimental results, we improve the Born-Oppenheimer potentials between Na and K and achieve good agreement between the theory and experiment for all the observed Feshbach resonances.
The susceptibility of ultracold gases to precise manipulation via external fields makes them ideal systems to study fundamental quantum mechanical phenomena. Various regimes, which are not possible to reach in condensed matter or nuclear physics, can be probed with these quantum gases. Especially the tunability of the interactions and confining potentials make that these ultracold gases offer unique possibilities to explore and study universal behavior. The tunability of the dominant two-body interactions in dilute ultracold atomic gases stems from the presence of Feshbach resonances. Via these resonances pairs of ultracold atoms can be associated to form ultracold molecules. In fact, measurements of Feshbach resonance positions can be used to reveal part of the underlying molecular structure. Vica versa, accurate molecular Born-Oppenheimer potentials can be used as input for full numerical coupled-channels calculations to reliably predict Feshbach resonances. For most of the heteronuclear mixtures currently studied however, the relevant molecular potentials are not accurate enough. As the coupled-channels method is often too elaborate and too time consuming to be used to fit the measured data to enable the construction of more accurate potentials, a need for accurate models which complement this established method is created. In this thesis we have developed a simplified model for resonant scattering of two ultracold atoms which fulfills this need. The asymptotic bound-state model (ABM) is a hierarchical model which can be systematically increased in complexity and accuracy. In its most simple form, the ABM only needs two parameters to predict the position and strength of Feshbach resonances: Two binding energies corresponding to the least bound state of the two molecular potentials involved. We demonstrate that this model, although it is solely based on bound states, can incorporate threshold effects. Additionally, the model can be extended to include: Multiple vibrational levels, overlapping resonances, and magnetic dipole-dipole interactions. This versatile model allows for a description of Feshbach resonances in a large variety of systems without accurate knowledge of the relevant molecular Born-Oppenheimer potentials. Being computationally light, the ABM can be used to analyze measurements of Feshbach resonances and hereby expose the basic underlying molecular structure. Additionally, the ABM is well suited to map out all available Feshbach resonances in a system. This ability is particularly useful when an optimal resonance is required for a certain experiment. For the 6Li-40K mixture we have utilized this ability to experimentally observe a strong Feshbach resonance which offers promising perspectives to reach the strongly interacting universal regime in a mass-imbalanced Fermi gas. By analyzing the various inelastic decay processes and the accuracy of the ab initio Born-Oppenheimer potentials, we predict a strong resonance in a mixture of metastable bosonic and fermionic helium atoms. For the homonuclear (bosonic as well as fermionic) helium gas we do not find strong resonances. For an ultracold gas of 40K atoms, an elaborate combined theoretical and experimental effort is presented to map out the Feshbach resonance structure. On the experimental side we observed 36 Feshbach resonances, 31 of which where observed for the first time. These observations are in excellent agreement with coupled-channels calculations which use unmodified Born-Oppenheimer potentials as input. On the theoretical side, we present a comparison between different simplified models of resonance scattering and the full numerical coupled-channels calculations. We have developed the resonant state model (RSM) to describe the resonant scattering of two ultracold atoms. This model is founded on resonant states, the natural (eigen) frequencies of the two-body system, and their non-trivial properties. Threshold effects are implicitly build into the RSM. The RSM can describe the effect of the continuum of scattering states, states which are neglected in the ABM, on the position and strength of a Feshbach resonance by only a few resonant states. Especially when a low-energy resonance is embedded in the continuum of scattering states, the effect of these states on the Feshbach resonance cannot be neglected. The RSM can be viewed as the natural generalization of the ABM. As the RSM can be based on just a few resonant states, it retains the computational simplicity of the ABM. Using the tunability of two-body interactions induced by a Feshbach resonance, we describe a crossover for a rotating Fermi gas between two strongly-correlated many-body states. We demonstrate that the correlation induced long-range interaction will shift the crossover with respect to the non-rotating case.
High-resolution Fourier transform spectroscopy was used to record fluorescence progressions of KLi formed in a heat pipe. Lithium isotope effects were used to derive the adiabatic correction to the Born-Oppenheimer potential for the electronic ground state over a wide range of internuclear separations. With a short extrapolation from the experimentally determined potential functions of the coupled states $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ and $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ toward their common atomic asymptote, we have improved the modeling of recently observed Feshbach resonances for the fermionic atom pair 6Li^{6}\text{L}\text{i}6Li and 40K^{40}\text{K}40K. Predictions for cold collisions between different isotopologues are presented using mass scaling with or without Born-Oppenheimer corrections. Predictions for Feshbach resonance positions differ by up to 0.5 G within reach of current experimental verification.