This thesis presents the investigation of the two-body scattering properties of cold atoms in \nsodium and lithium-sodium mixtures and their effects on the many body dynamics. Since both \nspecies are alkali atoms, the combined spin of both unpaired electrons can be either zero or one, \nproviding two different scattering channels. \nThe coupling of bound molecular states in these channels with the free atoms asymptote \ngives rise to the rich field of Feshbach resonance physics, where the interaction between the \nparticles can be controlled as an easily accessible experimental parameter. We have investigated \nthe Feshbach spectrum in the bosonic 7LiNa mixture and could confirm predictions based on \n6LiNa measurements, with a shift of the predicted spectrum by about 50 G. Also, the prospects \nof interaction tuning via Feshbach resonances were examined. \nThe difference of the scattering lengths of the electronic potentials also causes a coupling \nof atomic collisional channels, which can enable a spin exchange between the atoms. In this \nthesis, spin exchange processes have been studied in coherent oscillations in a thermal gas and \na Bose-Einstein condensate of sodium, as well as the evolution of this spinor gas into its ground \nstate. Preliminary studies of the heteronuclear spin exchange process in both the bosonic 7LiNa \nand in the fermionic-bosonic mixture 6LiNa are presented as well.
This thesis presents the investigation of the two-body scattering properties of cold atoms in \nsodium and lithium-sodium mixtures and their effects on the many body dynamics. Since both \nspecies are alkali atoms, the combined spin of both unpaired electrons can be either zero or one, \nproviding two different scattering channels. \nThe coupling of bound molecular states in these channels with the free atoms asymptote \ngives rise to the rich field of Feshbach resonance physics, where the interaction between the \nparticles can be controlled as an easily accessible experimental parameter. We have investigated \nthe Feshbach spectrum in the bosonic 7LiNa mixture and could confirm predictions based on \n6LiNa measurements, with a shift of the predicted spectrum by about 50 G. Also, the prospects \nof interaction tuning via Feshbach resonances were examined. \nThe difference of the scattering lengths of the electronic potentials also causes a coupling \nof atomic collisional channels, which can enable a spin exchange between the atoms. In this \nthesis, spin exchange processes have been studied in coherent oscillations in a thermal gas and \na Bose-Einstein condensate of sodium, as well as the evolution of this spinor gas into its ground \nstate. Preliminary studies of the heteronuclear spin exchange process in both the bosonic 7LiNa \nand in the fermionic-bosonic mixture 6LiNa are presented as well.
We study ultracold gases of alkali-metal atoms in the quantum degenerate regime. The interatomic interactions in these type of systems can be tuned using resonances induced by magnetic or electric fields. The tunability of the interactions, together with the possibility of confining the atoms with several kinds of external potentials, allows for a completely novel approach to study basic problems in many-body physics, and moreover, allows to enter regimes which have never been accessible in condensed matter or nuclear physics. For example, this has led to the experimental demonstration of an intimate relation between two types of superfluidity: the crossover from Bose-Einstein condensation of tightly bound molecules to the superfluid behavior related to weakly bound BCS-like pairs. Another experimental landmark was reached when the existence of universal Efimov three-body bound states was proven in experiments with ultracold bosonic cesium atoms. In this thesis, we study several aspects of these strongly interacting and ultracold atomic gases. We develop an analytical model that encapsulates all of the relevant scattering physics in atomic systems where open-channel shape resonances and closedchannel Feshbach resonances give rise to complicated and non-trivial scattering properties. This model provides lots of physical insight and is shown to describe important quantities, such as the molecular energies and scattering phase shifts, with a high level of accuracy. The model is compared to full numerical coupled-channel calculations in two atomic systems: rubidium and lithium. We study the BCS-BEC crossover using a many-body description of the ultracold gas that includes the non-trivial energy dependence of the scattering model. We show that it gives rise to superfluid behavior associated with the formation of BCS-like pairs while the low-energy interactions are repulsive in character. The energy dependence of the interactions is crucial, as it gives rise to attractive interactions at the Fermi energy, necessary for the formation of Cooper pairs. We demonstrate new ways of controlling the interatomic interactions using a combination of magnetic and electric fields. This leads to experimental control of, for instance, the three-body parameter in the context of Efimov physics and of non-universal behavior in the BCS-BEC crossover in fermionic gases. Using a four-body method based on first principles, we solve the molecule-molecule scattering problem to calculate several important properties of bosonic and fermionic Summary 145 molecules that consist of light and heavy atoms. These type of molecules are of current experimental interest, and we predict several exciting relations between three- and four-body observables in these type of systems.
This thesis reports on scattering experiments performed with an ultracold mixture of fermionic 6Li and bosonic 133Cs atoms, studying two-, few-, and many-body effects in a highly mass-imbalanced system. To this end, the existing apparatus for the creation of ultracold gases is extended and improved by gray molasses cooling of 6Li and high-resolution absorption imaging. s-, p-, and d-wave Feshbach resonances in the two energetically lowest hyperfine channels are detected via atom-loss and binding energy spectroscopy. These measurements in combination with the coupled channels modeling provide a ten-fold improved parametrization of the interspecies s-wave scattering length and precise determination of the LiCs molecular potential curves. For the first time effects of spin-rotation coupling in Feshbach resonances are observed, reflected in a triplet splitting of the p-wave components. The influence of the intraspecies scattering length on the heteronuclear Efimov scenario is studied by means of threebody loss rate measurements in the vicinity of two Feshbach resonances, characterized either by a positive or negative intraspecies scattering length. The measurements are quantitatively compared to the hyperspherical adiabatic formalism. The positive intraspecies scattering length can be interpreted as three-body parameter. The impact of few-body physics in the many-body impurity problem is discussed and prospects for realization of quantum degenerate Bose-Fermi mixtures with large mass imbalance are provided.
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.
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.
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
We have observed 26 interspecies Feshbach resonances at fields up to 2050 G in ultracold 6Li+23Na mixtures for different spin-state combinations. Applying the asymptotic bound-state model to assign the resonances, we found that most resonances have d-wave character. This analysis serves as guidance for a coupled-channel calculation, which uses modified interaction potentials to describe the positions of the Feshbach resonances well within the experimental uncertainty and to calculate their widths. The scattering length derived from the improved interaction potentials is experimentally confirmed and deviates from previously reported values in sign and magnitude. We give prospects for 7Li+23Na and predict broad Feshbach resonances suitable for tuning.