This thesis presents a simple theoretical model of a Feshbach resonance between two colliding ultracold atoms and experimental progress towards the observation of such a resonance in Rb85. On the theoretical side, the inter-atomic scattering potential is approximated by a spherical square well potential. The potential supports a number of bounds states whose energy depends on the width and depth of the well. In the low energy limit, only s-wave scattering is present, and the associated scattering length for the process diverges if there is a bound state at the dissociation limit: this is the hallmark of a Feshbach resonance. The model also shows that the Feshbach resonance can be shifted to higher scattering energies by adjusting the well depth, indicating the presence of a quasi-bound state above the dissociation limit. On the the experimental side, a crossed dipole trap has been developed and used to trap ultracold rubidium atoms. The performance of the trap is characterized, and the thesis describes work towards upgrading it for an experiment to observe a Feshbach resonance in the F=2, m_F=-2 hyperfine ground state of Rb85.
This thesis presents a simple theoretical model of a Feshbach resonance between two colliding ultracold atoms and experimental progress towards the observation of such a resonance in Rb85. On the theoretical side, the inter-atomic scattering potential is approximated by a spherical square well potential. The potential supports a number of bounds states whose energy depends on the width and depth of the well. In the low energy limit, only s-wave scattering is present, and the associated scattering length for the process diverges if there is a bound state at the dissociation limit: this is the hallmark of a Feshbach resonance. The model also shows that the Feshbach resonance can be shifted to higher scattering energies by adjusting the well depth, indicating the presence of a quasi-bound state above the dissociation limit. On the the experimental side, a crossed dipole trap has been developed and used to trap ultracold rubidium atoms. The performance of the trap is characterized, and the thesis describes work towards upgrading it for an experiment to observe a Feshbach resonance in the F=2, m_F=-2 hyperfine ground state of Rb85.
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.
In this thesis we explore ultracold atomic collisions in the vicinity of a magnetic Feshbach resonance located at 9.1 G, between 87Rb atoms in the |F = 2, mF = 1> and the |F =1, mF = 1> hyperfine states. We experimentally investigate the energy dependence of the enhancement of inelastic interaction in the neighborhood of this Feshbach resonance by analyzing the temperature dependence of a loss spectroscopy feature. An asymmetric widening of the resonance feature with respect to temperature is observed. We develop a simple model which captures these asymmetric line shapes through thermal averaging over the collision energy dependence of the Feshbach resonance. The energy dependence of the Feshbach interactions is further explored by colliding ultracold atomic samples at a fixed energy significantly above threshold using an optical trapping system; the elastic scattering enhancement analyzed by colliding the samples in free space, while for the inelastic measurements the collisions were carried out in trap. No conclusive resonant behavior could obtained for the elastic component of the 9.1 G resonance, however the inelastic scattering enhancement exhibited an anticipated shift.
This thesis describes experiments investigating the collisions of alkali metal atoms at energies between 10 - 2000 uK, measured in units of the Boltzmann constant. The atoms are accelerated towards each other using a purpose-built collider comprised of a crossed-beam optical dipole trap, which enables us to collide dense ensembles of ultracold atoms in any internal state at relatively high energies. I present the results of two experiments centered around resonant enhancement of the collisions. The first is between homonuclear 40K atoms near a shape resonance where the fermionic nature of the atoms determines the character of multiple scattering effects. The second experiment involves heteronuclear 40K87Rb collisions near a magnetically-tunable Feshbach resonance where we measure parameters describing the resonance as a function of collision energy. Theoretical models are developed that let us describe the collisions using published empirical interaction potentials, and we find good agreement between these models and the experiment.
In this undergraduate thesis, we discuss the two-body quantum mechanical problem of two ultra- cold bosonic atoms at low energy limit, interacting through a square potential with and without an external confinement. The two-body s-wave scattering length is introduced in terms of the radial wavefunction. In free space with no confinement, the interaction-scattering length relation is calculated and compared in 3- and 1-dimensions; we show the recurring resonance regions where the scattering length diverges and the existence of dimer bound state with positively large scattering length. Lastly, in the case of a 3-dimensional isotropic harmonic confinement, again under the ultracold limit, we obtain the universal (s-state) energy spectrum of the two atoms in terms of the scattering length.
This thesis reports the observation of interspecies Feshbach resonances in an ultracold mixture of Rb and Cs atoms. A versatile combined magnetic and optical potential has been designed and constructed which is capable of bringing both 87Rb and 133Cs to degeneracy, and reaching high phase-space density in 85Rb. High phase-space density mixtures are the first step required in the production of ultracold polar molecules, the topic of much current research. The apparatus capitalises on the efficient capture of atoms by a magnetic trap from a magneto-optical trap, and the efficient sympathetic cooling of Cs by Rb therein. Upon transfer to the crossed optical dipole trap condensates in excess of 1×10687Rb atoms and approximately 1×105133Cs atoms are produced after direct evaporation and gravito-magnetic tilting of the potential. The observation of six interspecies 87Rb-133Cs Feshbach resonances are reported, three of which had only been predicted theoretically, allowing testing and development of the theoretical model. Furthermore, the extrapolation of this model has predicted numerous Feshbach resonances between 85Rb and 133Cs, none of which have been experimentally observed prior to this work. The versatile nature of this apparatus is discussed, including the application of the current system to cooling of 85Rb. Initial experiments observed seven interspecies resonances, including a broad s-wave resonance at a magnetic field of (644±2) G which is in excellent agreement with the theoretical prediction. Further work has revealed that fourteen Feshbach resonances exist in the 0-700 G magnetic field range between 85Rb and 133Cs atoms in the ∣2,+2⟩ and ∣3,+3⟩ states, respectively. Several of these resonances would be ideal for magneto-association of RbCs molecules, prior to transfer to the rovibrational ground-state.
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.