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
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
Two sets of studies are described in this thesis. In the first set, an atom interferometry technique was developed for the measurement of the fine structure constant using a BoseEinstein Condensate. In the second set, degenerate Fermi gases were prepared and their properties explored in a regime of strong interactions. We have developed an atom interferometer which is capable of measuring with high precision the “photon recoil frequency” (ωrec). ωrec corresponds to the kinetic energy of an atom recoiling due to absorption of a photon. ωrec can be used to determine the quantity h/matom and the fine structure constant, α. A preliminary measurement using a 23Na BoseEinstein Condensate yielded ωrec with a precision of 7 × 10−6 which deviated by 2 × 10−4 from the currently accepted value. Plausible upgrades to the apparatus should produce a precision of 10−9 which would bring within reach a measurement of h/matom and α in the 10−9 range. Such accuracy would be of considerable scientific and metrological import. A quantum degenerate gas of 6Li fermions was produced by sympathetic cooling with 23Na bosons in a two-species atom trapping apparatus. The cooling strategy was optimized to enable production of fermions with atom numbers up to 7 × 107 at half the Fermi temperature (TF ), or temperatures down to 0.05TF ∼ 100 nK with 3× 107 atoms. We can also produce degenerate Bose-Fermi mixtures with several million atoms in each species. We studied the behavior of mixtures of fermi gases in regimes of strong interactions near “Feshbach” resonances. A study of system stability enabled the experimental observation of two such Feshbach resonances. We carried out a theoretical study to interpret the observation (by many experimental groups) of hydrodynamic behavior of fermi gases during expansion out of an atom trap in a strongly-interacting regime. The study concluded that this behavior was not a qualitative signature of fermionic superfluidity and could arise from classical collisions. Finally, radio-frequency (RF) spectroscopy was used to probe interaction in 6Li. We demonstrated the absence of mean field “clock” shifts of RF transitions in a two-(spin)state fermion system. Using a three-state system, we measured the interaction strength between different spin states. The measurements near Feshbach resonances indicate a saturation of the interaction strength at a large negative value. This result is of relevance in the continuing quest for fermionic superfluidity in atomic gases. Thesis Supervisor: David E. Pritchard Title: Cecil and Ida Green Professor of Physics Thesis Supervisor: Wolfgang Ketterle Title: John D. MacArthur Professor of Physics
This thesis presents studies of quantum degenerate atomic gases of fermionic 6Li and bosonic 7Li. Degeneracy is reached by evaporative cooling of 7Li in a strongly confining magnetic trap. Since at low temperatures direct evaporative cooling is not possible for a polarized fermionic gas, 6Li is sympathetically cooled by thermal contact with 7Li. In a first series of experiments both isotopes are trapped in their low-field seeking higher hyperfine states. A Fermi degeneracy of is achieved for 105 fermions. For more than ~300 atoms, the 7Li condensate collapses, due to the attractive interatomic interaction in this state. This limits the degeneracy reached for both species. To overcome this limit, in a second series of experiments 7Li and 6Li atoms are transferred to their low field seeking lower hyperfine states, where the boson-boson interaction is repulsive but weak. The inter-isotope collisions are used to thermalize the mixture. A 7Li Bose-Einstein condensate (BEC) of 104 atoms immersed in a Fermi sea is produced. The BEC is quasi-one-dimensional and the thermal fraction can be negligible. The measured degeneracies are . The temperature is measured using the bosonic thermal fraction, which vanishes at the lowest temperatures, limiting our measurement sensitivity. In a third series of experiments, the bosons are transferred into an optical trap and their internal state is changed to , the lowest energy state. A Feshbach resonance is detected and used to produce a BEC with tunable atomic interactions. When the effective interaction between atoms is tuned to be small and attractive, we observe the formation of a matter-wave bright soliton. Propagation of the soliton without spreading over a macroscopic distance of 1.1~mm is observed.
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.
Laser cooling and atom trapping techniques have enabled atomic physicists to attain temperatures on the order of 100 nK. In this regime, a trapped gas must be described within the framework of quantum statistical mechanics. In 1995, Bose-Einstein condensation (BEC) was achieved for the first time in such a system by three independent groups. The success of attaining BEC has encouraged research in quantum degenerate Fermi gases (DFG). One of the most exciting opportunities for a DFG is the prospect for Cooper pairing in a two-component gas. The experimental techniques for obtaining degenerate gases, as well as the mechanism for Cooper pairing, hinges on understanding and characterizing ultracold collisional interactions.\nThis thesis is a twofold study in this exciting field. The first section is an in-depth treatment of collisions in atomic lithium. Lithium has two isotopes, 6Li which is a fermion and 7Li which is a boson. This makes it an ideal candidate for studying quantum degenerate gases. In a series of experiments using a magneto-optical trap, we have spectroscopically measured the ground and excited state molecular potentials for both isotopes. From this work we have been able to obtain the most accurate potentials for lithium to date. These precise measurements have enabled us to extract the most accurate value to date for the 2P atomic radiative lifetime of lithium. Furthermore, we have developed a coupled-channel treatment of two-body collisions which has enabled us to calculate the scattering amplitude, elastic cross section, and rate of spin-exchange decay for any ground state collision in lithium as a function of temperature and magnetic field.\nArmed with this knowledge, we have made progress on the design and construction of an electromagnetic trap for lithium. This trap will enable the study of a degenerate Fermi gas of 6Li as well as the possibility of observing a Cooper pairing transition. The trap performance has been characterized for each isotope and current work is focussed on cooling lithium down to degeneracy. Measurements of spin-exchange decay have been made and compare well with the collisional theory that has been developed.
This doctoral dissertation is concerned with the physics of strongly interacting cold alkali atoms at low temperatures near a Feshbach resonance. In Chapter 1, we establish a connection between superfluid 4He and the BCS theory of superconductivity, and cold alkali atoms. We give the history of cold atoms, describing the significant achievements, pitfalls and challenges. In Chapter 2, we explore the thermodynamics of strongly interacting Bosonic atoms. We explore the stability of atomic Bosonic condensates near a Feshbach resonance. We show that the experimentally attained atomic condensate is a saddle point of the free energy, but the kinetics of its decay is slow. We also show that there is a second, higher density condensate branch which has an Ising-like phase transition to a molecular (paired) condensate when ramped across the Feshbach resonance. We argue that due to the high density, inelastic 3-body processes possibly render this transition unobservable. In Chapter 3, we explore the thermodynamics of Fermionic atoms near a Feshbach resonance. We determine the zero-temperature (T less than/less than T sub(F) ) pair propagator for a spinimbalanced mixture of up and down spin Fermions, and use it to show that such a mixture becomes completely polarized at mu sub(down arrow)= -0.9 mu sub(up arrow) . We also determine the Thouless criterion for superfluidity in a spin-imbalanced Fermi mixture, and construct a phase diagram of such a system at zero temperature. We then compare our results with experiments performed by two different groups. We find that interaction modifications to the minority spin self-energy inferred from our analysis is roughly double those observed in experiments. This discrepancy is consistent with the expected accuracy of the theory. In Chapter 4, we extend our analysis of the preceding chapter to calculate the surface tension of an interface between spin-polarized Fermions in the normal and superfluid phases. We show that, as expected, this surface tension decreases with increasing temperature and vanishes at a tricritical temperature, above which the transition becomes continuous. We also calculate the thickness of the interface; at T = 0, this is a few interparticle spacings, but diverges at the tricritical temperature. To compare with a set of relevant experiments, we also develop a phenomenological model for surface tension, and conclude that experimental surface tensions are an order of magnitude higher than what our microscopic calculation yields. We hypothesize possible mechanisms. In Chapter 5, we calculate the finite temperature phase diagram of a Bose-Fermi mixture produced from a spin-imbalanced two-component Fermi gas deep in the BEC phase. We show that there is a discontinuous transition between the superfluid and normal phase, with an entropy of mixing sufficient to cool the system down. We detail the construction of such a cooling scheme to cool a Fermi system below what is possible evaporatively, and find that the cooling efficiency is comparable to typical evaporative schemes. In Chapter 6, we shift our focus from thermodynamics to dynamics. We calculate shifts in the energy spectrum of a spin-balanced Fermionic superfluid of Cooper pairs due to the presence of energetically close states coupled by a Feshbach resonance. These shifts manifest themselves as clock-shifts in the radio-frequency spectrum of the superfluid. In addition to a broad asymmetric peak coming from the break-up of Cooper pairs, we find (for certain parameter ranges) a sharp, symmetric "bound-bound" spectral line coming from the conversion of Cooper pairs in one channel to pairs or molecules in another channel. Our theory shows remarkable quantitative agreement with experiments performed by an experimental group.
This thesis describes the construction of a versatile apparatus to study ultracold quan-tum mixtures capable of simultaneously cooling fermionic 6Li and 40K, as well as the bosonic 41K. The main features of the experimental setup are presented, in particular the addition of a new species 23Na, which has enabled the study of the Bose-Fermi mixture 23Na-40K. Three main experimental benchmarks are outlined: first, the production of a Bose-Einstein Condensate of 41K is discussed and an evaluation of its properties as a coolant are analysed. Secondly, the creation of triply degenerate Bose-Fermi-Fermi of 41K-40K-6Li gas is presented. Simultaneous observation of Pauli Pressure and Bose Condensation in the triply degenerate gas is reported. In addition, interspecies Fes-hbach resonances between 41K-40K and 6Li-41K are observed, opening the way to the study of a strongly interacting isotopic Bose-Fermi mixture of 41K-40K, which have similar mass. Thirdly, the creation of a quantum degenerate Bose-Fermi mixture of 23Na-40K is discussed and over thirty Feshbach resonances are identified.