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.
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.
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 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.
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.
During my PhD, I participated in the full setup from scratch of an experiment that aims at cooling down and manipulating two fermionic alkaline atomic species, 6Li and 40K. Our goal is to study ultracold Fermi mixtures with mass imbalance, and to realize a flexible quantum analog simulator. In fact, for certain quantum many-body problems, such as high critical temperature superconductivity and frustrated anti-ferromagnetism, there is neither complete analytical nor numerical solution. Therefore, cold atoms systems, due to their purity and their high degree of tunability, even on their interaction itself, offer an interesting complementary point of view in the study of those phenomena. As far as the experimental setup is concerned, we built an ultra-high vacuum system, a complete and stable laser source for each species, as well as two performing atomic sources, a 6Li Zeeman slower and a 40K bidimensionnal magneto-optical trap; most of the optical and electrical quantities, as well as the imaging diagnostics, being computer controlled. Once those preliminary steps have been performed and optimized, we could obtain an efficient double magneto-optical trap, containing typically 5x10^9 atoms of 6Li and 8x10^9 atoms of 40K. In this configuration, we produced the first 6Li40K* heteronuclear molecules by photoassociation, for which we identified 70 rovibrational lines. In a second part, I describe in detail the magnetic transport of the atomic mixture, between the magneto-optical trap chamber and a science cell, located in an ultra-high vacuum region with large optical access. The complete setup, from its design to its experimental implementation and optimization, as well as the development of the program and the useful numerical diagnostics, are the heart of my work. The transport efficiency could be tested and optimized, allowing for an efficient transfer of the mixture in the science cell. Thus, after this thesis, all the experimental tools are operational in order to allow for evaporative cooling of the mixture in an optically plugged magnetic trap. Therefore, the field is open for quantum simulation and understanding of many-body problems in ultracold Fermi mixtures.
Research interest in designing sources of cold atoms has significantly increased during the past ten years with the development of suitable laser sources for magneto-optical trapping and the further mastering of evaporative cooling in order to achieve Bose-Einstein condensation. The magneto-optical trap is now viewed as a standard research facility worldwide and has opened up many new exciting research directions in atomic physics. One area of interest is that of combining spherical microcavities with cold atomic sources in order to achieve efficient photon exchange between the cavity and atom for further understandings of cavity quantum electrodynamics. This could eventually lead to atom entanglement via photon exchange which would have implications for quantum logic design. However, initial attempts to achieve such interactions have been hindered by inadequate control and manipulation of the cold atom source. Here, we present work on designing and building an ultra-stable source of magneto-optically cooled rubidium atoms with a temperature in the tens of microKelvin range. We discuss the different cooling mechanisms involved in the process and present a suitable experimental arrangement including details on the ultra-high vacuum chamber, the laser systems being used and the source of rubidium vapour. Finally, we discuss some future direction for the research including the diffraction of atoms from gratings and micron-sized objects and the parameter control of the cloud of atoms.
This thesis presents an experimental apparatus capable of producing and studying ultra-cold mixtures of ⁶Li and Rb, and progress towards the creation of ultra-cold ground state ⁶Li₂ and LiRb molecules. Ultra-cold experiments with molecules have applications in many quantum computation and simulation experiments. We discuss elements of the apparatus which are important to these experiments, including electric field plates in air capable of producing fields up to 18 kV/cm, and a laser system for photoassociation spectroscopy based on two Ti:Sapphire lasers phase locked to the same optical frequency comb. With respect to ⁶Li and ⁸⁵Rb mixtures, we report on the observation of six Feshbach resonances, which represent an important step towards molecule production and future experiments in this heteronuclear mixture. In addition, we demonstrate the production of a BEC of ⁶Li₂ Feshbach molecules, a degenerate Fermi gas of ⁶Li and the formation of BCS pairs. In the ⁶Li system, we report on the high resolution spectroscopy of the v'=20-26 vibrational levels of the c(1³∑⁺g) potential and the v'=29-35 vibrational levels of the A(1¹∑⁺u) potential. In the A(1¹∑⁺u) potential, we find that the v'=31 and v'=35 levels have the largest transition strength and are therefore good candidates to use as intermediate states in molecule formation. We demonstrate atom-molecule dark states in the BEC-BCS crossover regime and additionally use dark-state spectroscopy to make extremely high resolution measurements of the least bound N''=0 ro-vibrational levels in the X(1¹∑⁺g) and a(1³∑⁺u) potential. In addition, we present spectroscopy of all ten N''=0 and N''=2 ro-vibrational levels in the a(1³∑⁺u) potential and furnish a preliminary interpretation of the observed energy structure. Finally, we report on the observation of anomalous Autler-Townes and dark-state spectrum. Using an extension to the standard three level model, we show that these anomalous profiles are due to degeneracies that exist in the bound molecular states, and to the choice of polarization of the coupling fields. These results have a direct impact on molecule formation, and provide a clear guide to future experiments.