Summary form only given. For non-resonant atomic interactions the properties of ultra-cold scattering can be accurately represented by the scattering length. When the interactions are resonant, for instance when the atoms are colliding via a Feshbach resonance, the scattering properties become strongly dependent on energy, and the scattering length approximation is no longer valid. We show that there is a limited set of parameters that fully characterizes the scattering in the ultra-cold regime, and that this description can be easily incorporated into a theory of many-body physics. In effect, it can be shown that with a Hamiltonian where the resonant bound-state is explicitly treated, the resulting many-body mean-field equations have built in the microscopic two-body coupled-channels scattering equations. We have used this many-body theory to derive a theory of resonance superfluidity, and applied it to both fermionic /sup 40/K and /sup 6/Li. Since the scattering length a does not appear as an expansion parameter of the theory it can be shown that this field theory does not break down as a goes to infinity. In fact, the theory describes the high-T/sub c/ behavior of the system and predicts a critical temperature which can be as high as half the Fermi temperature.
Summary form only given. For non-resonant atomic interactions the properties of ultra-cold scattering can be accurately represented by the scattering length. When the interactions are resonant, for instance when the atoms are colliding via a Feshbach resonance, the scattering properties become strongly dependent on energy, and the scattering length approximation is no longer valid. We show that there is a limited set of parameters that fully characterizes the scattering in the ultra-cold regime, and that this description can be easily incorporated into a theory of many-body physics. In effect, it can be shown that with a Hamiltonian where the resonant bound-state is explicitly treated, the resulting many-body mean-field equations have built in the microscopic two-body coupled-channels scattering equations. We have used this many-body theory to derive a theory of resonance superfluidity, and applied it to both fermionic /sup 40/K and /sup 6/Li. Since the scattering length a does not appear as an expansion parameter of the theory it can be shown that this field theory does not break down as a goes to infinity. In fact, the theory describes the high-T/sub c/ behavior of the system and predicts a critical temperature which can be as high as half the Fermi temperature.
We derive a theory of superfluidity for a dilute Fermi gas that is valid when scattering resonances are present. The treatment of a resonance in many-body atomic physics requires a novel mean-field approach starting from an unconventional microscopic Hamiltonian. The mean-field equations incorporate the microscopic scattering physics, and the solutions to these equations reproduce the energy-dependent scattering properties. This theory describes the high-Tc behavior of the system, and predicts a value of Tc that is a significant fraction of the Fermi temperature. It is shown that this mean-field approach does not break down for typical experimental circumstances, even at detunings close to resonance. As an example of the application of our theory, we investigate the feasibility for achieving superfluidity in an ultracold gas of fermionic 6Li.
We derive a resonance field-theory for ultra-cold Bose or Fermi gases that is valid when scattering resonances are present. Experiments with a ^85Rb condensate have shown new interesting physics close to resonance(N.R. Claussen, E.A. Donley, S.T. Thompson, C.E. Wieman, e-print cond-mat/0201400.). It is also expected that utilizing a Feshbach resonance can greatly enhance the critical temperature for superfluidity in a Fermi gas(M. Holland, S.J.J.M.F. Kokkelmans, M.L. Chiofalo, and R. Walser, Phys. Rev. Lett. 87), 120406 (2001).. Therefore it is important to treat the rich scattering physics properly inside a many-body theory. We show that the scattering length only is insufficient to describe a system close to resonance. Our many-body equations have build-in the two-body scattering equations, and we include the full scattering solution over the relevant energy range by means of a renormalized resonance scattering theory(S.J.J.M.F. Kokkelmans, J.N. Milstein, M.L. Chiofalo, R. Walser, and M.J. Holland, e-print cond-mat/0112283.).
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 Feshbach resonance in the s-wave scattering length occurs if the energy of the two atoms in the incoming open channel is close to the energy of a bound state in a coupled closed channel. Starting from the microscopic Hamiltonian that describes this situation, we derive the effective atom–molecule theory for a Bose gas near a Feshbach resonance. In order to take into account all two-body processes, we have to dress the bare couplings of the atom–molecule model with ladder diagrams. This results in a quantum field theory that exactly reproduces the scattering amplitude of the atoms and the bound-state energy of the molecules. Since these properties are incorporated at the quantum level, the theory can be applied both above and below the critical temperature of the gas. Moreover, making use of the true interatomic potentials ensures that no divergences are encountered at any stage of the calculation. We also present the mean-field theory for the Bose–Einstein condensed phase of the gas.
With help of a Feshbach scattering resonance it is possible to change the effective two-body interaction of ultra-cold atoms from repulsive to attractive, from weak to strong. Regular field theory for the description of Bose-Einstein condensates is based on a single interaction parameter only, the scattering length. Such a description, however, is not valid anymore for the resonance regime. We formulated a field-theory that incorporated the microscopic energy-dependent two-body interactions, that also takes pair correlations into account. This theory allowed us to explain an experiment at JILA where Ramsey fringes were observed in a ^85Rb Bose-Einstein condensate by making use of a Feshbach resonance. The theory and experiment show that coherent molecules are created, a first step in the direction of molecular BEC. For non-resonant interactions, the self-energy corresponding to the atom-atom interactions is proportional to the scattering length. Close to resonance, however, this relationship no longer applies, and the energy will level off to a finite value on resonance. We investigate this resonance self-energy, and compare it with experimental results from strongly interacting Fermi systems.
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.