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.
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.
We report on experiments investigating the collisional properties of atoms at ultralow collision energies using an all-optical atom collider. By using a pair of optical tweezers, we can manipulate two ultracold atom clouds and collide them together at energies up to three orders of magnitude larger than their thermal energy. Our experiments measure the scattering of 87 Rb, 40 K, and 40 K- 87 Rb collisions. The versatility of our collider allows us to probe both shape resonances and Feshbach resonances in any partial wave. As examples, we present experiments demonstrating p-wave scattering with indistinguishable fermions, inelastic scattering at non-zero energies near a homonuclear Feshbach resonance, and partial wave interference in heteronuclear collisions.
The work described in this thesis is related to two projects I worked on towards the ultracold collisions experiment between fermionic lithium and bosonic rubidium atoms in our lab. The first part is about the simulation of sympathetic cooling of Bose-Fermi mixture inside the magnetic trap. An original single species code, which was specially designed for simulating the forced radio-frequency evaporation of ¹³³Cs atoms in the magnetic trap (within harmonic approximation), is developed so that it can simulate the dynamics of a multi-species trap including iriter-atomic collisions and honharmonic trapping potentials, and thus aid in the design of our future degenerate gas experiments. To validate the consistence between our multi-species code and the original single-species code, a comparison was tried using the parameters from Clauz Zimmermann's sympathetic cooling of fermionic Lithium using Rubidium atoms. The result shows a very good consistence between the multi-species and single species codes. Based on the same parameters from Zimmermann's experiment, another comparison is performed to check the influence of different macro-atom distributions on the simulation results when the total number of real atoms is constant, since the number of macro-atoms determines how fast the simulation can run. The result shows that using less number of macro-atoms (2¹¹ vs 2¹³) won't effect the simulation too much and we can use less number of macro-atoms to speed up the simulation. The second part of this thesis is concerned with the design of the experimental apparatus to study hetero-nuclear Feshbach resonances between Lithium and Rubidium. The strategy for this study was discussed in the experimental setup section, in which the required experimental subsystems for the Feshbach resonance studies were discussed, such as the vacuum system, the atomic sources for both species. This work also involved some experiments to calibrate the alkali metal dispensers to be used in this apparatus. A model was created to describe the Rubidium partial pressure in room temperature, parameters required by this model was calibrated by an absorption experiment, in which the Rubidium resonant laser was sent through a vapor cell.
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 reports on calculations of the scattering properties of a variety of ultracold alkali-metal mixtures. In particular, we have calculated the scattering properties of homonuclear mixtures of 85Rb, in a variety of incoming channels, and we have calculated the properties of heteronuclear mixtures of the isotopologues of Rb and Cs, and K and Cs. In general, we are interested in the location and character of Feshbach resonances in these mixtures with a view towards ultracold molecule formation. In 85Rb there is a rich Feshbach structure and potential uses for the resonances that we find, in the scattering lengths of the various incoming channels, are discussed. In 85RbCs there is a rich Feshbach structure and the prospects for ultracold molecule formation using this system are detailed. Similarly, we detail the Feshbach resonances of 87RbCs and discuss our results in the context of the successful formation of ultracold ground-state molecules. In the isotopologues of KCs each system has a rich Feshbach structure and we detail the location and width of the resonances, as well as the potential for ultracold molecule formation using each of the isotopes of potassium. In addition to scattering calculations, we have also calculated the location and character of the highest-lying bound states of each system. We have investigated the energy dependence of the scattering length using accurate coupled-channel calculations on 6Li, 39K and 133Cs to explore the behaviour of the effective range in the vicinity of both broad and narrow Feshbach resonances. We present an alternative parametrization of the effective range and further demonstrate that an analytical form of an energy and magnetic field-dependent phase shift, based on multichannel quantum defect theory, gives accurate results for the energy-dependent scattering length. Lastly, we examine the effect of additional external fields on alkali-metal collisions and discuss how external fields can be used to manipulate the interaction properties of a system.
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.
In this dissertation, I present ab initio theoretical results on cold and ultra-cold collision of atomic and molecular systems with magnetic and electric dipole moments. The collisions of different isotopes of maximally spin-polarized chromium atoms (52Cr and 53Cr), alkali-metal atom (Rb) - chromium atom, and magnetically trapped hydroxide (OH) with cold supersonic helium beam are considered in this thesis. Spin-changing cross sections and rate constants in Cr-Cr isotopic collision in the presence of a magnetic field are calculated by propagating a set of multichannel equations in the field. The coupling between dipole-dipole allowed and hyperfine channels are included. The short range electrostatic interactions between atoms and atom-molecule are represented with highly-accurate Born-Oppenheimer (BO) potential energy curves. Due to the large spin multiplicity in Cr-Cr and Rb-Cr interactions, more than the usual singlet and triplet channels are obtained. The long-range van der Waals (vdW) interactions between atoms are calculated, for Cr, by including accurate transition frequencies, discrete dipole matrix elements, and photoionization continuum oscillator strengths, and for Rb, using published dynamic polarizabilities. The vdW coefficients for Cr-Cr and Rb-Cr are obtained. In the cold collision regime, I investigate the influence of angular momentum shape resonances on the elastic and inelastic (loss channel) rate coefficients, and when the Zeeman relaxation, resulting in the loss of atoms from the trap, dominates elastic collision. Dipolar collisions are crucial to achieving quantum degeneracy. Magnetically tuned Fano-Feshbach closed-channel resonances are used to obtain zero-energy scattering lengths in comparison with observation of trap loss. In bosonic chromium collisions, resonances appear due only to dipolar interaction. The interplay between hyperfine and dipolar resonances in mixed-species Cr-Cr and Rb-Cr collisions is studied. In Rb-Cr, it is found that the molecule has broken symmetry and therefore contains a large permanent electric dipole moment in the ground state. A recent collisional experiment at JILA of a supersonic helium beam with a magnetically trapped OH radical found the onset of a quantum threshold in the total OH loss rate. Using ab initio BO energy surfaces, I calculated the spin-changing collisions which removed OH from the trap. Only after including the effect of the trapping potential on the collision dynamics, some agreement with observation was found. ^