<p>A trapped Fermi gas near a collisional resonance provides a unique laboratory for testing many-body theories in a variety of fields. The ultracold Fermi gas produced in our lab is comprised of the lowest two spin states of $^6$Li. At 834 G there is a collisional or Feshbach resonance between the two spin states. The scattering length between trapped atoms of opposing spins far exceeds the interparticle spacing of the gas. On resonance, a strongly interacting, unitary, Fermi gas is created which exhibits universal behavior. The unitary Fermi gas is a prototype for other exotic systems in nature from nuclear matter to neutron stars and high temperature superconductors.</p> <p>For magnetic fields less than 834 G the scattering length is positive, and pairs Fermi atoms can form molecular dimers. These dimers, comprised of two fermions, are bosons. At ultracold temperatures the molecular bosons populate the lowest energy level and form a Bose Einstein Condensate (BEC). For magnetic fields greater than 834G the scattering length between fermions in opposing spin states is negative, like Cooper pairs formed between electrons in a superconductor. The Bardeen, Cooper, and Shriefer (BCS) theory was developed to describe the pairing effect in the context of superconductors. In our experiment we produce an ultracold unitary gas. By tuning the magnetic field to either side of the Feshbach resonance we can transform the gas into a weakly interacting BEC or BCS superfluid. Therefore, the region near a Feshbach resonance is called the BEC-BCS crossover.</p> <p>This dissertation presents a precision measurement of the hydrodynamic sound velocity in an ultracold Fermi gas near a Feshbach resonance. The sound velocity is measured at various magnetic fields both above and below resonance. Moreover, we are able compare our measurements to theoretical descriptions of hydrodynamic sound propagation. Further, our measurement of sound velocity exactly reproduces the non-perturbative case, eliminating the need to consider nonlinear effects. At resonance the sound velocity exhibits universal scaling with the Fermi velocity to within 1.8\% over a factor of 30 in density. In a near zero temperature unitary gas the average sound velocity at the axial center was measured, $c(0)/v_F$ = 0.364(0.005), as well as the universal constant, $\beta$ = -0.565(0.015). The measurement of sound velocity in an ultracold gas throughout the BEC-BCS crossover provides further evidence of the continuous connection between the physics of the BEC, unitary, and BCS systems.</p> / Dissertation

The problem of the evolution from BCS theory with cooperative Cooper pairing to the formation and condensation of composite bosons has attracted considerable attention for the past several decades. It has gained renewed impetus in the mid-eighties with the discovery of the high-Tc superconductors, which have a coherence length comparable to the interparticle spacing. More recently, this subject has spurred a great deal of research activity in connection with experiments involving dilute atomic gases of fermionic atoms. The initial objective of this work will be to use functional integral techniques to analyze the low-temperature BCS-to-BEC evolution of d-wave superconductors within the saddle point (mean field) approximation for a continuum model. Then, the same mathematical formalism will be applied to the problem of the BCS-to-BEC evolution of fully spin-polarized p-wave Fermi gases in two dimensions. We find that a quantum phase transition occurs for both systems as they are driven from the BCS-like regime of weakly interacting fermionic pairs to the opposite BEC-like regime of strongly interacting bosonic molecules. This is in contrast to the smooth crossover predicted and observed in systems that exhibit s-wave pairing symmetry. We calculate several spectroscopic and thermodynamic properties that signal the occurrence of this phase transition, and suggest some possible experimental realizations. Finally, fluctuations about the saddle point solution are included in the calculations, and the effects of such correction are analyzed in the low (T~0) and high (T~Tc) temperature limits. We conclude that, at high temperatures, the bosonic degrees of freedom that arise from two-particle bound states become essential to describe the strong coupling limit, as the saddle point approximation alone becomes unreliable.

As the hydrodynamic theory breaks down with the local density ap- proximation in the fermionic superfluid with spin-polarization, we develop a general formalism of the adiabatic dynamics for the low-lying collective modes in the BEC-BCS crossover, which is exact in the adiabatic limit. This adi- abatic dynamic theory is based on a static density functional theory of the spin-polarized superfluid system, which we derive as a generalization of the conventional density functional theory of superfluid for current experimental interests. A special case where the system is uniform and analytically solv- able is studied in detail. We show that our adiabatic equations of motion are reduced to the hydrodynamic equations of motion within local density approx- imation, which provides a solid microscopic foundation for the well-publicized phenomenological hydrodynamic theory. / text

Turbulence in classical fluids has been the subject of scientific study for centuries, yet there is still no complete general theory of classical turbulence connecting microscopic physics to macroscopic fluid flows, and this remains one of the open problems in physics. In contrast, the phenomenon of quantum turbulence in superfluids has well-defined theoretical descriptions, based on first principles and microscopic physics, and represents a realm of physics that can connect the classical and quantum worlds. Studies of quantum turbulence may thus be viewed as a path for progress on the long-standing problem of turbulence.A dilute-gas Bose-Einstein condensate (BEC) is, in most cases, a superfluid that supports quantized vortices, the primary structural elements of quantum turbulence. BECs are particularly convenient systems for the study of vortices, as standard techniques allow the microscopic structure and dynamics of the vortices to be investigated. Vortices in BECs can be created and manipulated using a variety of techniques, hence BECs are potentially powerful systems for the microscopic study of quantum turbulence.This dissertation focuses on quantized vortices in BECs, specifically experimental and numerical studies of their formation, dynamics, and decay, in an effort to understand the microscopic nature of vortices as elements of quantum turbulence. Four main experiments were performed, and are described in the main chapters of this dissertation, after introductions to vortices, experimental methods, and turbulence are presented. These experiments were aimed at understanding various aspects of how vortices are created and behave in a superfluid system. They involved vortex dipole nucleation in the breakdown of superfluidity, persistent current generation from a turbulent state in the presence of energy dissipation, decay of angular momentum of a BEC due to trapping potential impurities, and exploration of the spontaneous formation of vortices during the BEC phase transition. These experiments represent progress towards enhanced understanding of the formation, dynamics, and decay of vortices in BECs and thus may be foundational to more general studies of quantum turbulence in superfluids.

An apparatus for producing atomic-gas Bose-Einstein condensates (BECs) of 87-Rb atoms is described. The apparatus produces 87-Rb BECs in a dual-chamber vacuumsystem that incorporates magnetic transport of trapped atoms from the magneto-optical trapping cell to the BEC production cell via the operation of a series of overlapping magnet coils. The design, construction, and operation of the apparatus are described in detail.The apparatus is used to study the creation of quantized vortices in BECs by the merging and interference of multiple trapped condensates. In this experiment, a single harmonic potential well is partitioned into three sections by an optical barrier,enabling the simultaneous formation of three independent, uncorrelated BECs. The BECs may either merge together during their growth, or, for high-energy barriers, the BECs can be merged together by barrier removal after their formation. Either process may instigate vortex formation in the resulting BEC, depending on the initially indeterminate relative phases of the condensates and the merging rate.

R??sum?? : De par le monde, des populations tentent d???organiser leurs atouts afin de parer ?? l?????ventualit?? d???une v??ritable crise globale d???accessibilit?? ?? l???eau douce au XXIe si??cle. Alors que certains territoires sont aux prises avec un ??tat de p??nurie qui menace la sant?? et la s??curit?? ?? court terme des humains et des ??cosyst??mes qui y vivent, d???autres disposent des ressources requises pour accommoder les multiples usages qui sont faits de l???eau au sein de soci??t??s d??velopp??es. C???est le cas notamment du Qu??bec, qui est en voie de mettre en ??uvre ses propres m??canismes de gouvernance de l???eau, ancr??s dans la gestion int??gr??e par bassin versant. Le pr??sent m??moire vise ?? observer les fondements du syst??me qu??b??cois de gouvernance de l???eau, de mani??re ?? ??valuer dans quelle mesure la province serait apte ?? tenir compte du contexte global de l???eau douce lors de l?????laboration et la mise en place de ses politiques de l???eau. Pour ce faire, une revue sommaire de la litt??rature r??cente est effectu??e, dans les domaines de la gouvernance d??mocratique et environnementale, ainsi que sur les pratiques en gestion des ressources en eau par bassin versant et sur le plan international. Sont aussi ?? l?????tude les lois et politiques qui donnent le cadre pratique de la gouvernance de l???eau au Qu??bec et au Canada. Les r??sultats de cet effort de recherche laissent croire qu???il soit bel et bien possible de mener une discussion voulant que le Qu??bec dispose des outils n??cessaires afin de s?????tablir en tant qu???intendant territorial de la ressource eau sur la sc??ne globale. Cependant, d???une disposition capacitaire d???agir ainsi ne d??coule pas directement le devoir moral de le faire. Cette responsabilisation de l?????tat qu??b??cois face ?? la crise de l???eau doit ??tre v??hicul??e par une volont?? populaire soutenue, d??sireuse de prendre en charge des projets de soci??t?? dont les b??n??fices ?? long terme s?????tendent au-del?? des fronti??res g??opolitiques traditionnellement admises. // Abstract : Over the world, populations are trying to organize their assets in order to face the eventuality of a 21st century global crisis pertaining to the accessibility of freshwater resources. While some territories are hit by water shortages that threaten the health and security of the humans and ecosystems living there, others offer sufficient resources to accommodate the various usages of water that are distinctive of current developed societies. That is notably the case in Quebec, where the province is moving towards implementing its own water governance mechanisms, anchored in integrated watershed resources management. This research report aims to observe the foundations of Quebec???s water governance system, in order to assess to what extent the province might be able to account for the global water context during the development and implementation of its water policies. This is to be done through a cursory review of recent literature, in the fields of democratic and environmental governance as well as those of watershed and international water management practices. Also of interest are the laws and policies that provide the practical framework for water governance in Quebec and in Canada. The results of this exercise tend to show that it is in fact possible to hold a discourse to the effect that the province of Quebec has the necessary tools to establish itself as a territorial steward of water resources on the global scale. However, Quebec???s potential capacity to act in such a way does not directly imply the moral duty to do so. The acknowledgement of moral responsibility towards the water crisis by the Quebec government must be driven by a sustained popular movement that is willing to undertake society-wide projects, the long-term benefits of which carry over traditionally accepted geopolitical boundaries.

Thèse (Ph. D.)--Université Laval, 1997. / Bibliogr.: f. [224]-232. Publié aussi en version électronique.

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京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21546号 / 理博第4453号 / 新制||理||1639(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 池田 隆介, 教授 前野 悦輝, 教授 川上 則雄 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM