Combining the measured binding energies of four of the most weakly bound rovibrational levels of the 87Rb2 molecule with results of two other recent high-precision experiments, we obtain exceptionally strong constraints on the atomic interaction parameters in a highly model independent analysis. The comparison of (85)Rb and (87)Rb data, where the two isotopes are related by a mass scaling procedure, plays a crucial role. We predict scattering lengths, clock shifts, and Feshbach resonances with an unprecedented level of accuracy. Two of the Feshbach resonances occur at easily accessible magnetic fields in mixed-spin channels. One is related to a d-wave shape 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.
The research described in this thesis is part of an international effort with the aim of studying ultracold quantum degenerate gas samples like Bose-Einstein condensates and Fermi degenerate systems, consisting of atoms confined in magnetic or optical traps. The behavior of such samples is governed by the inter-atomic interactions and the resulting properties of the atom-atom scattering. At the relevant temperatures of 1nK to 10µK a key property is the atom-atom scattering length a. In chapter 2 a theoretical method is presented which enables one to describe the interaction and scattering of (ultra)cold atoms to unprecedented precision. It is also unparalleled in comprehensiveness: it allows the prediction of a large and varied set of experimental data for all isotopes of the same element. The method relies on the extraction from experiments of a few (phase) parameters which completely summarize the behavior of the atoms in the (ultra)cold regime. In chapter 3 the method is applied to the "workhorses" of cold-atom physics: the atomic species 85Rb and 87Rb. We extract the foregoing parameters to a very high precision from several recent high precision experiments, allowing us to predict e.g. the 87Rb spinor condensate to be ferromagnetic: a prediction for which the scattering length has to be calculated with a precision better than 1%. We also predict Feshbach resonances at experimentally accessible magnetic field strengths; resonances searched for and found by the experimental group of Rempe. In close collaboration with his group we "fine-tune" the interaction parameters found previously, by making use of only one of the observed resonances. We then obtain agreement with 42 out of the observed 43 resonance field strengths and are able to identify bound states inducing the Feshbach resonances at these locations. Chapter 4 describes the results of this research. With a thorough understanding of the rubidium interactions, we then switch to lithium which has a fermionic (6Li) and a bosonic (7Li) isotope. Both are being used in cold-atom experiments. In chapter 5 we evaluate the interaction parameters for lithium allowing us to predict magnetic field strengths for which a sample of fermionic 6Li atoms can be regarded as strongly interacting. Furthermore, a three-level method for measuring mean-field shifts, based on radio-frequency techniques, is introduced. For weak interactions we find proportionality of resonance shifts to interaction strengths. In the strongly interacting regime, however, these shifts become very small reflecting the quantum unitarity limit and many-body effects. Most interesting is the fact that in this regime the shifts are small both for large positive a and for large negative a, likely reflecting the universality of the interaction energy. In chapters 6 and 7 the interactions between lithium atoms are reinvestigated, making use of newly available experimental data and with the updated interaction parameters special attention is paid to locating field strengths at which magnetically tunable Feshbach resonances occur in the scattering of lithium atoms. In chapter 6 scattering events in a gas of (fermionic) 6Li atoms are studied. In chapter 7 we show that a consistent description of the 6Li+6Li system can be given. We discuss theoretical uncertainties for the position of the wide 6Li Feshbach resonance and present an analytic scattering model for this resonance, based on the inclusion of a field-dependent virtual open-channel state. We predict new Feshbach resonances for the 6Li-7Li system, and their importance for different types of crossover superfluidity models is discussed. Molecules created by magnetically sweeping over these resonances will have a fermionic character. One magnetic field strength is predicted at which two different fermionic molecules can be created simultaneously.
The ultracold mixture of
23Na and
87Rb atoms has become an important system for investigating physics in Bose-Bose atomic mixtures and for forming ultracold ground-state polar molecules. In this work, we provide an improved characterization of the most commonly used Feshbach resonance near 347.64 G between
23Na and
87Rb in their absolute ground states. We form Feshbach molecules using this resonance and measure their binding energies by dissociating them via magnetic-field modulation. We use the binding energies to refine the singlet and triplet potential-energy curves, using coupled-channel bound-state calculations. We then use coupled-channel scattering calculations on the resulting potentials to produce a high-precision mapping between magnetic field and scattering length. We also observe ten additional
s-wave Feshbach resonances for
23Na and
87Rb in different combinations of Zeeman sublevels of the
F=1 hyperfine states. Some of the resonances show two-body inelastic decay due to spin exchange. We compare the resonance properties with coupled-channel scattering calculations that full take account of inelastic properties.
We present an analysis of experimentally accessible magnetic Feshbach resonances in ultracold heteronuclear $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{6}\mathrm{Li}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ mixtures. Using recent experimental measurements of the triplet scattering lengths for $^{6}\mathrm{Li}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{7}\mathrm{Li}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ mixtures and Feshbach resonances for one combination of atomic states, we create model potential curves and fine-tune them to reproduce the measured resonances and to predict the location of several experimentally relevant resonances in Li-Rb collisions. To model $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ collisions, we use accurate
Rb2 potentials obtained previously from the analysis of experiments on $^{87}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ collisions. We find resonances that occur at very low magnetic fields, below
10G, which may be useful for entanglement generation in optical lattices or atom chip magnetic traps.
We model the binding energies of rovibrational levels of the RbYb molecule using experimental data from two-color photoassociation spectroscopy in mixtures of ultracold
87Rb with various Yb isotopes. The model uses a theoretical potential based on state-of-the-art ab initio potentials, further improved by least-squares fitting to the experimental data. We have fixed the number of bound states supported by the potential curve, so that the model is mass scaled, that is, it accurately describes the bound-state energies for all measured isotopic combinations. Such a model enables an accurate prediction of the
s-wave scattering lengths of all isotopic combinations of the RbYb system. The reduced mass range is broad enough to cover the full scattering lengths range from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}$. For example, the
87Rb
174Yb system is characterized by a large positive scattering length of
+880(120) a.u., while
87Rb
173Yb has $a=\ensuremath{-}626(88)$ a.u. On the other hand
87Rb
170Yb has a very small scattering length of $\ensuremath{-}11.5(2.5)$ a.u. confirmed by the pair's extremely low thermalization rate. For isotopic combinations including
85Rb the variation of the interspecies scattering lengths is much smoother ranging from
+39.0(1.6) a.u. for
85Rb
176Yb to
+230(12) a.u. in the case of
85Rb
168Yb. Hyperfine corrections to these scattering lengths are also given. We further complement the fitted potential with interaction parameters calculated from alternative methods. The recommended value of the van der Waals coefficient is
C6=2837(13) a.u. agrees with but is more precise than the current state-of-the-art theoretical predictions [M. S. Safronova, S. G. Porsev, and C. W. Clark, Phys. Rev. Lett. 109, 230802 (2012)].
We measure the binding energies of weakly bound Feshbach molecules formed between \Na and \Rb atoms in their lowest hyperfine Zeeman levels. We form molecules at the Feshbach resonance near 347.64 G and dissociate them by magnetic field modulation. We use the binding energies to refine the singlet and triplet potential energy curves, using coupled-channel bound-state calculations. We then use coupled-channel scattering calculations on the resulting potentials to produce a high-precision mapping between magnetic field and scattering length. We also observe 10 additional
s-wave Feshbach resonances for \Na and \Rb in different combinations of Zeeman sublevels of the
F=1 hyperfine states. Some of the resonances show 2-body inelastic decay due to spin exchange. We compare the resonance properties with coupled-channel scattering calculations that full take account of inelastic properties.