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Quantum Degeneracy and Interactions in the 87Rb -40K Bose-Fermi Mixture

J. Goldwin, Written Jonathan Michael Goldwin, Deborah S. Jin

Published Jan 1, 2005• 5 citations
OpenAlex

Abstract

The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Goldwin, Jonathan Michael (Ph.D., Physics) Quantum Degeneracy and Interactions in the 87Rb-40K Bose-Fermi Mixture Thesis directed by Associate Professor Deborah S. Jin An apparatus for producing dilute-gas quantum degenerate Bose-Fermi mix-tures is presented. The experiment uses forced evaporative cooling to obtain a nearly pure 87Rb Bose-Einstein condensate immersed in a gas of sympathetically cooled 40K atoms at 0.2 times the Fermi temperature. The design, construction, and operation of the apparatus are described in detail. The onset of quantum degeneracy is characterized and contrasted between species, revealing the effects of quantum statistics on the bulk properties of the gases. The apparatus is then used to study the interactions between species in ultracold non-degenerate mixtures. Measurements of rethermalization rates are used to determine the elastic scattering cross-section between species. From these measurements the magnitude of the inter-species s-wave scattering length is de-termined. The scattering length is central to characterizing a variety of static and dynamic properties of the mixture. The apparatus is additionally used to study for the first time Feshbach resonances in the collisions between 87Rb and 40K atoms. These resonances present a means for experimentally tuning the scattering length between species to any desired value. Prospects for future experiments exploiting this real-time control over the interactions are discussed. iv

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The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Goldwin, Jonathan Michael (Ph.D., Physics) Quantum Degeneracy and Interactions in the 87Rb-40K Bose-Fermi Mixture Thesis directed by Associate Professor Deborah S. Jin An apparatus for producing dilute-gas quantum degenerate Bose-Fermi mix-tures is presented. The experiment uses forced evaporative cooling to obtain a nearly pure 87Rb Bose-Einstein condensate immersed in a gas of sympathetically cooled 40K atoms at 0.2 times the Fermi temperature. The design, construction, and operation of the apparatus are described in detail. The onset of quantum degeneracy is characterized and contrasted between species, revealing the effects of quantum statistics on the bulk properties of the gases. The apparatus is then used to study the interactions between species in ultracold non-degenerate mixtures. Measurements of rethermalization rates are used to determine the elastic scattering cross-section between species. From these measurements the magnitude of the inter-species s-wave scattering length is de-termined. The scattering length is central to characterizing a variety of static and dynamic properties of the mixture. The apparatus is additionally used to study for the first time Feshbach resonances in the collisions between 87Rb and 40K atoms. These resonances present a means for experimentally tuning the scattering length between species to any desired value. Prospects for future experiments exploiting this real-time control over the interactions are discussed. iv
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
This thesis describes trapping and evaporative cooling of ultracold 87Sr and 88Sr mixtures in an optical dipole trap to produce the first Bose-Einstein condensate (BEC) of 88Sr. Furthermore, this work presents thermalization studies that characterize the scattering properties of these ultracold strontium samples. Such ultracold atomic gases have become an important area of research because of their potential for improving optical frequency standards and for realizing quantum computation using neutral atoms. A BEC of 88Sr is particularly interesting because the small value of its background s-wave scattering length may enable the use of optical Feshbach resonances to create two-dimensional solitons. However, the small scattering length for 88Sr also hinders efficient evaporative cooling in the optical dipole trap, a necessary step to producing a BEC. Experiments with other ultracold gases have successfully overcome this hurdle by mixing in a second atomic species which, by introducing stronger interactions with the weakly interacting species, enables evaporation to colder temperatures via sympathetic cooling. For this work, we use 87Sr to sympathetically cool 88Sr during forced evaporation to quantum degeneracy.\nPrevious experiments in the Killian Lab characterized 88Sr in detail. Here, I emphasize the new or improved aspects that have allowed trapping and cooling of the mixtures of 87Sr and 88 Sr: trapping of 87Sr by itself, spectroscopic measurements of all the stable strontium isotopes to guide the trapping of isotopic mixtures, imaging of both 87Sr and 88Sr, and the various trade-offs necessary to simultaneously trap 87Sr and 88Sr. Finally, I discuss how the thermalization studies of the scattering properties of the isotopes guide the forced evaporation of mixed isotope samples. These efforts result in the production of the BEC of 88Sr, but they also point the way to future studies of fermionic quantum degeneracy in 87Sr and to the rich physics of mixed species ultracold atomic systems.
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.
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.
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
Ultracold atoms are powerful platforms through which to study many-body physics. In recent years there has been a marked increase in the number and variety of species (lanthanides, transition metals, dipolar molecules, etc.) brought to ultracold temperatures, providing new ingredients from which to build interesting systems. In this thesis I report on the design and construction of an erbium-lithium mixture apparatus with broad applicability for quantum simulation. The combination of large mass imbalance, competition of interaction length scales, and variable quantum statistics points toward this mixture hosting a rich variety of Bose-Bose and Bose-Fermi phases with applications ranging from condensed matter to astrophysics. Leveraging these desirable properties, however, necessitated the development of a new quantum gas platform. The first section of this thesis is dedicated to describing that process in detail. The second section of this thesis describes the development of experimental sequences through which we synthesize quantum gases. In our experiments we successively laser cool each species before combining them in a suite of optical dipole traps for evaporative cooling to degeneracy. I finally present our creation of the first degenerate Bose-Bose mixture of erbium-166 and lithium-7, as well as a measurement of the interspecies s-wave scattering length.