This thesis reports on experimental studies of few-body physics in ultracold Fermi gases. The main part is devoted to the first realisation of an ultracold three-component Fermi gas in thermal equilibrium that consists of atoms in the three lowest spin states of 6Li. In first experiments the collisional stability of the gas was investigated in dependence of the interparticle interaction. The interaction strength was tuned by an external magnetic field employing Feshbach resonances in all three two-body scattering channels. At two magnetic field values a resonant enhancement of three-body loss was observed that can be explained by an Efimov-like trimer consisting of one atom in each of the three states which crosses the continuum twice in the studied magnetic field region. The behaviour of three-body loss rates could be understood by taking into account a variation of the lifetime of the trimer with the magnetic field. These experiments were performed with large ensembles of atoms. A finite deeply degenerate Fermi gas consisting of a controlled number of atoms may serve as a clean model for finite Fermi systems as for example atomic nuclei. An approach for the preparation of such a gas is discussed and first experimental steps are presented.
This thesis reports on experimental studies of few-body physics in ultracold Fermi gases. The main part is devoted to the first realisation of an ultracold three-component Fermi gas in thermal equilibrium that consists of atoms in the three lowest spin states of 6Li. In first experiments the collisional stability of the gas was investigated in dependence of the interparticle interaction. The interaction strength was tuned by an external magnetic field employing Feshbach resonances in all three two-body scattering channels. At two magnetic field values a resonant enhancement of three-body loss was observed that can be explained by an Efimov-like trimer consisting of one atom in each of the three states which crosses the continuum twice in the studied magnetic field region. The behaviour of three-body loss rates could be understood by taking into account a variation of the lifetime of the trimer with the magnetic field. These experiments were performed with large ensembles of atoms. A finite deeply degenerate Fermi gas consisting of a controlled number of atoms may serve as a clean model for finite Fermi systems as for example atomic nuclei. An approach for the preparation of such a gas is discussed and first experimental steps are presented.
This thesis reports on experiments studying the few-body physics of three distinguishable fermionic atoms with large scattering lengths. The experiments were performed with ultracold gases of fermionic 6Li atoms in three different hyperfine states. By tuning the strength of the interactions between the atoms with Feshbach resonances and measuring the rate constants for inelastic three-atom and atom-dimer collisions the intersections of two universal trimer states with the three-atom and atom-dimer continuum could be located. Subsequently, one of these Efimov states was directly observed with RF-association spectroscopy. Using this technique the binding energy of this Efimov state was measured as a function of the strength of the interparticle interactions. The experiments presented in this thesis provide a nearly complete understanding of the universal few-body physics of three-component Fermi gases of 6Li atoms. This understanding will be the foundation for future studies of the many-body physics of three-component Fermi gases.
This thesis concerns quasi-two-dimensional (quasi-2D) ultracold Fermi systems with short range interactions. Here, quasi-2D geometries are those that lie between two- and three-dimensions. We study few- and many-body systems composed of two or three distinguishable species of fermions. Of principle interest are the bound states that form in these systems and how these bound states are affected by the quasi-2D geometries. In the first research chapter, we focus on the two-dimensional (2D) regime of quasi- 2D. We begin by developing an effective 2D model of this 2D-like geometry. We use this model to analyse a Fermi system consisting of three fermionic species with equal interactions between all distinguishable pairs. Starting with the few-body problem, we show that there is always a three-body bound state (trimer) in the effective 2D model and that these 2D trimers are stable. This is notably different from the extremely unstable ‘Efimov’ trimers found in three-dimensional (3D) systems. Using a low-density expansion and a variational approach, we investigate the fate of the 2D trimers as the system’s density is increased from the three-body limit to the many-body limit. We find that remnants of trimers can persist in the form of strong three-body correlations in the many-body system. In the second research chapter, we analyse a realistic experimental system of three distinguishable fermions confined to quasi-2D. We develop a model that goes beyond the previous chapter in two regards. Firstly, we allow for unequal interactions between the pairs of fermions. Secondly, we use a full quasi-2D model that is not specific to the 2D-like regime. With this general model, we use the scattering and confinement parameters from experiments on ultracold 6Li atoms to calculate the trimer spectrum across the dimensional crossover from 2D to 3D. We show that one state smoothly evolves from an unstable 3D-like trimer to a 2D-like trimer as the attractive interactions are decreased. We furthermore compute the trimer wave function and quantify the stability of the trimer with respect to three-body recombination by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry. This opens the door to realising long-lifetime trimers in ultracold gas experiments and furthermore, the many-body state of trimers predicted in the preceding chapter. vii In the final research chapter, we examine an alternative approach to accessing quasi-2D geometries by using a system of coupled 2D planes. We study the two-component Fermi gas in this geometry, as a preliminary to studying the three-component gas. We find that the interplanar coupling can be tuned to drive a dimensional crossover from 2D to 3D. We study the effect of this dimensional crossover on the two- and many-body systems. In general, we find that two-body correlations are strengthened by weakening the coupling between 2D planes. In the many-body system, we use mean-field theory to find that the critical temperature of pairing is increased by weakening the coupling between 2D planes. This represents a first step towards a more general representation of quasi-2D geometries, namely: A system of coupled quasi-2D planes.
This thesis presents experiments exploring Feshbach molecules and Efimov trimers in an ultracold Bose-Fermi atomic gas mixture of 40K and 87Rb. These bound states are accessed via scattering resonances, called Fano-Feshbach resonances, which arise as a consequence of a bound state being tuned through degeneracy with the threshold energy of colliding atoms. In addition to allowing the tunability of interactions, the Fano-Feshbach resonance allows for a weakly bound molecule state, called the Feshbach molecule state, to be populated. The efficiency of conversion to the Feshbach molecule state depends upon the rate with which the bound state energy is swept through degeneracy with atomic threshold energy. In regions of large scattering lengths, three-body bound states, called Efimov states, also influence inelastic Bose-Bose-Fermi collisions and boson+molecule collisions in our system. The work presented in this thesis utilizes a magnetically tunable Fano-Feshbach resonance to study Feshbach molecule creation in the perturbative limit (the limit of fast magnetic-field sweeps) and the saturated limit (the limit of slow sweeps), where a phenomenological model is applied to understand the conversion efficiency as well as the quantum degeneracy of the molecules. In addition, I present a study of boson+molecule collision rates and Bose-Bose-Fermi collision rates in order to observe signatures of Efimov states and compare against results in the gas mixture 41K-87Rb to address the question of universality of the three-body parameter in heteronuclear gas mixtures.
Ultracold atomic gases with tunable interactions offer an ideal platform for studying interacting quantum matter. While the few- and many-body physics are generally complex and intractable, the problem can be greatly simplified in an atomic gas by a controlled separation of relevant length and energy scales. Precise control of experimental parameters, via Feshbach resonances, optical potentials and radio-frequency radiation, enables deterministic measurements of few-body physics, including universal physics and the Efimov effect. In this thesis, I present our recent studies on precisely measuring two- and three-body physics in an ultracold Bose gas. I begin by describing our new apparatus used for generating and studying ultracold 39K gas samples. Then, I focus on our precision spectroscopy of Feshbach dimer binding energies, spanning three orders of magnitude and with sub-kilohertz resolution. These measurements enable us to locate a Feshbach resonance and determine scattering length values with unprecedented accuracy. Finally, I present our precise measurements locating an exotic three-body state, specifically the Efimov ground state. We find that the trimer state location significantly deviates from the value predicted by van der Waals universality. Due to small experimental and systematic uncertainties, our measurement is the strongest evidence of departure from the universal value and is the first observed deviation near a Feshbach resonance of intermediate strength.
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 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.