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arXiv:1604.00234 · Physical Review A

Feshbach resonances and weakly bound molecular states of boson-boson and boson-fermion NaK pairs

Alexandra Viel, Andrea Simoni

Published Apr 5, 2016• 24 citations
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Abstract

We conduct a theoretical study of magnetically induced Feshbach resonances and near-threshold bound states in isotopic NaK pairs. Our calculations accurately reproduce Feshbach spectroscopy data on $\mathrm{Na}^{40}\mathrm{K}$ and explain the origin of the observed multiplets in the $p$ wave [Phys. Rev. A 85, 051602(R) (2012)]. We apply the model to predict scattering and bound state threshold properties of the boson-boson $\mathrm{Na}^{39}\mathrm{K}$ and $\mathrm{Na}^{41}\mathrm{K}$ systems. We find that the $\mathrm{Na}^{39}\mathrm{K}$ isotopic pair presents broad magnetic Feshbach resonances and favorable ground-state features for producing nonreactive polar molecules by two-photon association. Broad $s$-wave resonances are also predicted for $\mathrm{Na}^{41}\mathrm{K}$ collisions.

DOI
10.1103/physreva.93.042701

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We conduct a theoretical study of magnetically induced Feshbach resonances and near-threshold bound states in isotopic NaK pairs. Our calculations accurately reproduce Feshbach spectroscopy data on Na40K\mathrm{Na}^{40}\mathrm{K}Na40K and explain the origin of the observed multiplets in the ppp wave [Phys. Rev. A 85, 051602(R) (2012)]. We apply the model to predict scattering and bound state threshold properties of the boson-boson Na39K\mathrm{Na}^{39}\mathrm{K}Na39K and Na41K\mathrm{Na}^{41}\mathrm{K}Na41K systems. We find that the Na39K\mathrm{Na}^{39}\mathrm{K}Na39K isotopic pair presents broad magnetic Feshbach resonances and favorable ground-state features for producing nonreactive polar molecules by two-photon association. Broad sss-wave resonances are also predicted for Na41K\mathrm{Na}^{41}\mathrm{K}Na41K collisions.
We perform extensive magnetic Feshbach spectroscopy of an ultracold mixture of fermionic 40K^{40}\mathrm{K}40K and bosonic 87Rb^{87}\mathrm{Rb}87Rb atoms. The magnetic-field locations of 13 interspecies resonances are used to construct a quantum collision model able to predict accurate collisional parameters for all $\mathrm{K}\text{\ensuremath{-}}\mathrm{Rb}$ isotopic pairs. In particular, we determine the interspecies sss-wave singlet and triplet scattering lengths for the $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ mixture as $(\ensuremath{-}108\ifmmode\pm\else\textpm\fi{}3){a}_{0}$ and $(\ensuremath{-}205\ifmmode\pm\else\textpm\fi{}5){a}_{0}$, respectively. We also predict accurate scattering lengths and the position of Feshbach resonances for the other $\mathrm{K}\text{\ensuremath{-}}\mathrm{Rb}$ isotopic pairs. We discuss the consequences of our results for current and future experiments with ultracold $\mathrm{K}\text{\ensuremath{-}}\mathrm{Rb}$ mixtures.
We present a detailed study of interspecies Feshbach resonances of the bosonic 23Na+39K^{23}\mathrm{Na}+^{39}\mathrm{K}23Na+39K mixture for magnetic fields up to 750G750\phantom{\rule{0.16em}{0ex}}\mathrm{G}750G in various collision channels. A total of 14 Feshbach resonances are reported, as well as four zero crossings of the scattering length and three inelastic two-body loss features. We use the observed magnetic-field locations of the resonant features together with the known data on 23Na+40K^{23}\mathrm{Na}+^{40}\mathrm{K}23Na+40K to refine the singlet and triplet ground-state potentials of NaK and achieve a consistent description of Feshbach resonances for both the Bose-Bose mixture of 23Na+39K^{23}\mathrm{Na}+^{39}\mathrm{K}23Na+39K and the Bose-Fermi mixture of 23Na+40K^{23}\mathrm{Na}+^{40}\mathrm{K}23Na+40K. We also discuss the influence of the interplay between inelastic two-body and three-body processes on the observation of a Feshbach resonance.
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 present a detailed study of the scattering properties of ultracold mixtures of bosonic potassium atoms. We locate 20 previously unobserved Feshbach resonances in isotopic $^{39}\mathrm{K}\text{\ensuremath{-}}^{41}\mathrm{K}$ mixtures. These are assigned to sss-wave molecular channels by comparison to an asymptotic bound state model and coupled-channel calculations. Additional Feshbach resonances are studied in spin mixtures of a single potassium isotope, both in 39K^{39}\mathrm{K}39K and 41K^{41}\mathrm{K}41K. In particular, we characterize the parameters of a selected 39K^{39}\mathrm{K}39K Feshbach resonance by radio-frequency association of Feshbach molecules. Our results could be exploited to refine the model potentials for potassium scattering. Furthermore, these new Feshbach resonances enlarge the range of experiments possible with degenerate Bose-Bose mixtures.
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.