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.
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.
eshbach resonances play a central role in the manipulation of the interparticle interaction in ultracold atomic gases. The Asymptotic Bound-state Model (ABM) [1,2] is a powerful and easy-to-use tool to predict properties of these Feshbach resonances. This model exploits the fact that only the least bound states in the interaction potential determine the low energy interaction properties. These bound states are coupled by hyperfine and Zeeman interactions, and the intersection of these coupled bound states with the scattering threshold determine the position of these Feshbach resonances. The high accuracy of this model was clearly demonstrated when assigning 13 resonances in the 6Li-40K mixture by using only two bound state parameters [1]. Here we discuss the extension of the ABM by the including threshold effects, which allow for the prediction of the resonance width as well.
We present an Asymptotic Bound state Model (ABM), which is useful to predict Feshbach resonances. The model utilizes asymptotic properties of the interaction potentials to represent coupled molecular wavefunctions. The bound states of this system give rise to Feshbach resonances, localized at the magnetic fields of intersection of these bound states with the scattering threshold. This model was very successful to assign measured Feshbach resonances in an ultra cold mixture of ^6Li and ^40K atomsootnotetextE. Wille, F.M. Spiegelhalder, G. Kerner, D. Naik, A. Trenkwalder, G. Hendl, F. Schreck, R. Grimm, T.G. Tiecke, J.T.M. Walraven, S.J.J.M.F. Kokkelmans, E. Tiesinga, P.S. Julienne, arXiv:0711.2916. For this system, the accuracy of the determined scattering lengths is comparable to full coupled channels results. However, it was not possible to predict the width of the resonances. We discuss how an incorporation of threshold effects will improve the model, and we apply it to a mixture of ^87Rb and ^133Cs atoms, where recently Feshbach resonances have been measured.
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.
By applying a magnetic field across a trapped ultracold gas of alkali metal atoms, it is possible to alter the binding energies of near threshold molecular states. The proximity of molecular states to the scattering threshold has a strong effect on the threshold scattering characteristics. Because of this the magnetic field strength can be used to control low energy scattering within the gas. This resonant phenomena is referred to as a magnetically tuneable Feshbach resonance. This thesis looks at these and related phenomena in the context of trapped potassium atoms. First, we perform coupled-channels calculations in order to characterise a group of previously unreported Feshbach resonances, occurring in a host of different collision channels. Next, we compare these characterisations to empirical data, and more simplified models. Second, a detailed investigation into the photodissociation of weakly bound Feshbach molecules is carried out. This allows us to gain new insights into the structure of the exit channel interaction. We make semi-classical arguments which enable experimentalists to directly measure the height of potential barriers. We also perform detailed numerical calculations which, in conjunction with experimental data, allow us to develop a fine-tuned potential model for the exit state. Third, we model weakly bound triatomic states and their impact on near threshold scattering. Then, we discuss the use of three body recombination as a tool for observing Efimov states. Furthermore, we model the three body recombination rate using a simplified two channel model. Finally we suggest a method intended to provide the basis for numerical calculations using realistic Born-Oppenheimer potentials. It could also be used to analytically study near threshold three body physics.
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.
Ultracold 39K gases provide an ideal platform to study quantum few- and many-body systems, due to the high degree of control present in these systems. In particular, Feshbach resonances facilitate a magnetically tunable interaction strength between the atoms in the gas, and allow the formation of two- and three-body bound states, called Feshbach molecules and Efimov trimers respectively. Radio-frequency dissociation spectroscopy of weakly bound Feshbach molecules is one of the most precise ways to characterize the properties of a Feshbach resonance. We apply a numerical method to our Feshbach molecule binding energy data to compute the shift in the molecule’s binding energy due to the presence of a confining potential. These simulations are first used to replicate the confinement shift found for 6Li Feshbach molecules by another group, and then to correct our measurement results for the binding energy of 39K Feshbach molecules. The correction of these measurements is necessary for our determination of the Feshbach resonance location with unprecedented accuracy.