Ultracold atomic gas experiments have proven to be a versatile ground for studying quantum mechanics, quantum many-body physics, quantum simulation and computation. A precise model for two-body collisions in those systems is essential. Coupled-channels models can accurately describe the two-atom system at ultracold temperatures by detailed interaction potentials that are finetuned by just a few parameters, determined from experiment. We extend such a coupled-channels model to include the situation in a Mott insulator phase of ultracold bosonic atoms, where two atoms are confined to one lattice site. Of particular importance is the specific conversion between the on-site interaction energy, which remains finite in the lattice, and the scattering length around a Feshbach resonance that diverges. Recently spectroscopic techniques allowed for a precise experimental determination of the on-site interaction energy in a system of 7Li atoms, we analyze this data with our model to improve the precision of current lithium interaction potentials.
Ultracold atomic gas experiments have proven to be a versatile ground for studying quantum mechanics, quantum many-body physics, quantum simulation and computation. A precise model for two-body collisions in those systems is essential. Coupled-channels models can accurately describe the two-atom system at ultracold temperatures by detailed interaction potentials that are finetuned by just a few parameters, determined from experiment. We extend such a coupled-channels model to include the situation in a Mott insulator phase of ultracold bosonic atoms, where two atoms are confined to one lattice site. Of particular importance is the specific conversion between the on-site interaction energy, which remains finite in the lattice, and the scattering length around a Feshbach resonance that diverges. Recently spectroscopic techniques allowed for a precise experimental determination of the on-site interaction energy in a system of 7Li atoms, we analyze this data with our model to improve the precision of current lithium interaction potentials.
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.
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.
An important new development in the field of ultracold atomic gases is the study of the properties of these gases in a so-called optical lattice. An optical lattice is a periodic trapping potential for the atoms that is formed by the interference pattern of a few laser beams. A reason for the interest in these systems is that the effects of the interatomic interactions can be strongly enhanced. More specifically, it has been shown in a beautiful experiment by Greiner et al. in 2002 that by loading a Bose-Einstein condensate into an optical lattice it is possible for the system to undergo a quantum phase transition to a new quantum phase of matter, the so-called Mott insulator phase. Within this Mott insulator phase each lattice site is occupied by exactly one atom. This makes the Mott insulator phase especially well suited for applications in the field of quantum computation and quantum information processing. We have theoretically investigated the above mentioned quantum phase transition and our formalism allows for a description of the Mott insulator phase at nonzero temperatures. Another important experimental development in the field of ultracold atomic gases is the use of Feshbach resonances to control the interatomic interactions. Such a resonance occurs whenever two colliding atoms form a long-lived molecule for some time. The crucial point of a Feshbach resonance is that the above mentioned molecule has a magnetic moment that is not equal to twice the magnetic moment of the atom. As a consequence the energy difference between the two atoms and the molecule and hence the interactions between the atoms can be controlled by using an external magnetic field. By combining these two techniques, i.e, by trapping ultracold atomic gases in an optical lattice and by tuning a magnetic field near a Feshbach resonance there can be a new quantum phase transition between two superfluid phases. We gave derived the the theory for the description of these Feshbach resonances in optical lattices and applied it to various systems. To be a bit more precise, if we tune the external magnetic field such that the energy difference between a molecule and two atoms is sufficiently negative, then the gas consists of a Bose-Einstein condensate of molecules. In contrast, if the energy difference is large enough and positive we have a gas that consists primarily of a Bose-Einstein condensate of atoms. It turns out that these two limits are separated by an Ising-like quantum phase transition. By using atomic Bose gases near a Feshbach resonance detailed experimental studies which test the theoretical predictions of the statistical and dynamical properties of these quantum phase transitions can be made.
This work investigates how the closed channel of a Feshbach resonance is characterised by experimental observables. Surprisingly, it is found that the two-body observables associated with the Feshbach resonance can be insensitive to the properties of the closed channel. In particular, it is impossible in this situation to determine the energy of the bound state causing the resonance from the usual experimental data. This is the case for all magnetic Feshbach resonances in ultracold atoms, due to their deep two-body interaction potentials. This insensitivity highlights a major difference with Feshbach resonances that involve shallow interaction potentials, such as hadron resonances. It appears however that short-range two-body correlations and three-body observables are affected by a parameter of the closed channel called the “closed-channel scattering length”. A photoassociation experiment is proposed to measure this parameter in ultracold atom systems.
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.