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.
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.
The work described in this thesis is related to various projects that I worked on towards the production of ultra-cold ensembles of ⁸⁵Rb, ⁸⁷Rb and fermionic ⁶Li. In the past few years, ultra-cold atomic gases have evolved into a mature field of research, driving various theoretical and experimental groups towards new possibilities. This thesis starts with an overview of the research direction of the field and the lab in particular, to use ultra-cold fermionic atoms as quantum simulators for several condensed matter problems. It discusses the experimental route to quantum degeneracy in a sample of ultra-cold atoms and techniques to get there. The rest of the thesis primarily discusses the first step to degeneracy- production of ultra-cold ensembles of rubidium and lithium. It starts with the theoretical concepts that enable laser cooling and trapping. The interaction between light and atoms and how it leads to a decrease in temperature of the ensemble is discussed. The limits of different cooling mechanism with relevance of the atoms of interest are described. The starting point for all laser cooling experiments is an atomic source, the details of the requirements and efficiency of different atomic sources is discussed, emphasizing our choice of sources for the two atoms. Other technical details such as the vacuum system and the control system for the experiment are briefly discussed. Preliminary data from our first ensembles of ultra-cold lithium and rubidium is shown. At the end, the planning and progress of the first experiments that we aim to achieve with these ultra-cold atoms namely looking for Feshbach resonances and studying the effect of DC electric fields on them, and studies with ultra-cold lithium atoms in optical lattices, is discussed.
Ultracold mixture experiments hold the promise of providing new insights into many-body quantum systems as well as ultracold chemistry and few-body phenomena. The work presented in this thesis dealt with the construction of a new apparatus for the production and study of ultracold gases of fermionic lithium-6 and bosonic caesium-133. These isotopes offer a wide tunability in their interaction strength, both in inter-species and intra-species collisions, through magnetic Feshbach resonances. Additionally, the widely different resonance frequencies of lithium and caesium enables independent control of each of the species. With this apparatus, Bose-Einstein condensates (BEC) containing 10^4 lithium Feshbach molecules are routinely produced. The cooling system for caesium has been developed in parallel and important steps towards producing ultracold caesium gases have been made. An optical dipole trap has been loaded with 2x10^6 caesium atoms and evaporative cooling towards quantum degeneracy can now be pursued. Laser, vacuum, magnetic and control systems have been developed for the implementation of this experiment. Light produced with this laser system was used to laser cool atoms, create conservative dipole traps as well as to provide means of imaging atomic clouds. Additionally, a system to produce strong magnetic fields of up to 1400 G has been established in order to exploit the wide tunability in the atomic interactions. Software that was developed for the computerised control system facilitated the coordination of all the components involved in the experimental sequence. Measurements and calculations that showcase the functionality of relevant parts of the setup are presented in this thesis. In this experiment, lithium and caesium atoms are obtained from a novel type of Zeeman slower and are loaded into a magneto-optical trap (MOT). The system is capable of doing this independently for each of the atomic species as well as sequentially. After the MOT has been loaded with atoms, they are transferred into a conservative far-off-resonance optical dipole trap. By adjusting the interactions between atoms and lowering the depth of the dipole trap, efficient evaporative cooling of lithium was carried out from which a molecular BEC was obtained. Time-of-flight measurements were used to characterise the condensate and study its expansion dynamics.
The work described in this thesis can be divided into two parts. The first part is concerned with the production of degenerate Fermi gases and Bose-Fermi mixtures. The second part of the thesis describes studies of strongly interacting spin-mixtures of ultracold fermions. We have cooled a magnetically trapped spin-polarized 6Li Fermi gas into quantum degeneracy by sympathetic cooling with bosonic 23Na. In order to do this, we have converted our previously developed apparatus for Bose-Einstein condensation of 23Na into a two-species cooling facility. We have produced 6Li samples with up to 7 × 107 atoms at temperatures below 0.5TF , and up to 3× 107 atoms at temperatures as low as 0.05TF . Further, we have also produced stable quantum degenerate mixtures of 23Na and 6Li, with several million atoms of each species. In a second set of experiments, we have studied strongly interacting spin-mixtures of 6Li. The strength of interactions was resonantly controlled by applying a magnetic field and tuning to “Feshbach resonances”, which occur when the total energy of the colliding particles coincides with the energy of a bound molecular state. These studies are relevant for the continuing quest for a superfluid transition in a Fermi gas. By studying the inelastic decay of the cloud, we have experimentally identified two Feshbach resonances for the inter-state interactions of the two lowest ground states of 6Li. Most importantly, we found that the lifetime of the strongly interacting system is long enough to observe a superfluid transition in the future. The effects of the coherent collisions in 6Li spin-mixtures were studied using radiofrequency (RF) spectroscopy. We demonstrated the absence of mean field “clock shifts” in a two-state mixture of fermions, and have introduced a three-level method to observe the interaction energy shifts. In the strongly interacting regime, near a Feshbach resonance, we have observed universal behavior of the interaction energy, independent of the value of the scattering length. Finally, we have theoretically studied the effects of Pauli blocking during a free expansion of a degenerate Fermi gas. We have concluded that a strongly interacting normal gas will undergo a hydrodynamic expansion even at zero temperature, due to inefficiency of the Pauli suppression of collisions. Therefore, the already observed hydrodynamic expansion cannot be conclusively interpreted as a signature of superfluidity. Thesis Supervisor: Wolfgang Ketterle Title: John D. MacArthur Professor of Physics
This thesis describes a new apparatus designed to study cold, ultracold, and quantum degenerate mixtures of rubidium and caesium atoms. The Rb- Cs mixture is prepared using a double magneto-optical trap (MOT) system in which a two-species pyramid MOT acts as a source of cold atoms for a 'science' MOT. The first results of experiments on the magneto-optically trapped mixture are presented, including measurements of trap loss rates due to single-species and interspecies inelastic collisions. A technique for reducing interspecies loss by spatially separating the MOTs during loading is described. This technique allows 50-50 mixtures of Rb and Cs atoms to be loaded into a magnetic trap at close to their respective maximum single- species atom numbers. Alternatively, one species can be loaded with arbitrarily small amounts of the other. The displaced MOT technique is thus аn excellent starting point for investigations of interspecies Feshbach resonances and sympathetic cooling of Rb-Cs mixtures in magnetic and optical traps. In addition, a model of polarisation spectroscopy based on numerical integration of population rate equations is described. Theoretical polarisation spectra generated by the model are shown to agree with experimental spectra for the F = I + 1/2 → F' transitions in Rb and Cs. An investigation of the sub-Doppler dichroic atomic vapour laser locking (DAVLL) technique demonstrates how locking signals can be optimised for the Rb D2 transitions. The role of polarisation purity in generating the spectra is discussed, and impurities are modeled using a Jones matrix approach. Comparisons with polarisation spectroscopy and DAVLL are used to enhance understanding of atom-light interactions in spectroscopic systems, and indicate methods for optimising locking signals for use in cold atom experiments.
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.
A cold atomic gas formed by two different species represents an intriguing system for a deeper understanding of atom-atom interactions at ultralow temperatures. We present experiments on a mixture of atomic lithium and cesium which are of particular interest regarding the formation of heteronuclear molecules on the one hand, and the prospects for sympathetic cooling of atomic gases through mutual thermalization on the other hand. A first series of experiments on interaction in presence of a near-resonant light field is performed in a two-species magneto-optical trap. The collisional properties of the lithium-cesium mixture are investigated through detailed analysis of trap-loss processes induced by the trap light. Photoassociation in an additional near-resonant laser field yields high-resolution spectra of the excited Cs_2 dimers, but shows no unambiguous indication of LiCs molecule formation. A second series of experiments on pure ground-state collisional properties utilizes an optical dipole trap formed by light that is detuned extremely far below atomic resonance (quasi-electrostatic trap). Storage times of many minutes are achieved in a particularly simple and versatile setup for both atomic species. Cooling of cesium through evaporation and thermalization by elastic collisions is observed. The evolution of temperature and particle number is compared with model simulations of evaporative cooling. Direct laser cooling of trapped cesium in the absolute energetic ground state is demonstrated. Homonuclear spin-changing collisions of ground-state cesium and lithium atoms are analyzed, and first evidence for pure ground-state collisions between atoms of different species is found. Based on the current achievements, prospects for future experiments are discussed. (orig.)