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Diploar Quantum Gases of Erbium

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Diploar Quantum Gases of Erbium Dipolar Quantum Gases of Erbium DISSERTATION by Albert Frisch, Mag. submitted to the Faculty of Mathematics, Computer Science, and Physics of the University of Innsbruck in partial fulfillment of the requirements for the degree of Doctor of Philosophy (PhD) advisors: Univ.-Prof. Dr. Francesca Ferlaino, Institute for Experimental Physics, University of Innsbruck Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences Univ.-Prof. Dr. Rudolf Grimm, Institute for Experimental Physics, University of Innsbruck Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences Innsbruck, October 2014 Attention: This is not the original version of the thesis! Changes have been made to the original version to correct a number of spelling mistakes. The contents, however, has remained entirely untouched. The original version can be obtained directly from the author, or through the University of Innsbruck. The publications presented in Chapter 10 and in Chapter 11 are replaced by their respective preprint versions for online access of this thesis. Summary Since the preparation of the first Bose-Einstein condensate about two decades ago andthe first degenerate Fermi gas following four years later a plethora of fascinating quantum phe- nomena have been explored. The vast majority of experiments focused on quantum degen- erate atomic gases with short-range contact interaction between particles. Atomic species with large magnetic dipole moments, such as chromium, dysprosium, and erbium, offer unique possibilities to investigate phenomena arising from dipolar interaction. This kind of interaction is not only long-range but also anisotropic in character and imprints qualitatively novel features on the system. Prominent examples are the d-wave collapse of a dipolar Bose-Einstein condensate of chromium atoms realized by the group in Stuttgart, the spin magnetization and demagnetization dynamics observed by groups in Stuttgart, Paris, and Stanford, and the deformation of the Fermi surface observed by our group in Innsbruck. This thesis reports on the creation and study of the first Bose-Einstein condensate and degenerate Fermi gas of erbium atoms. Erbium belongs to the lanthanide group of elements and has a large magnetic moment of seven Bohr magneton. In particular, this thesis describes the experimental apparatus and the sequence for producing a dipolar quantum gas. There is an emphasis on the production of the narrow-line magneto-optical trap of erbium since this represents a very efficient and robust laser-cooling scheme that greatly simplifies the experimental procedure. After describing the experimental setup this thesis focuses on several fundamental questions related to the dipolar character of erbium and to its lanthanide nature. A first set of studies centers on the scattering properties of ultracold erbium atoms, including the elastic and the inelastic cross section and the spectrum of Feshbach resonances. Specifically, we observe that identical dipolar fermions do collide and rethermalize even at low temperatures. The corresponding elastic cross section predicted by the theory of universal dipolar scattering scales only with the particle's mass and its magnetic moment and is temperature indepen- dent. This represents a dramatic difference compared to non-dipolar fermions, which exhibit a rapidly vanishing elastic cross section at lower temperatures. Another distinctive feature of erbium is its spectrum of Feshbach resonances. Using bosonic erbium we observed an enormous density of resonances exceeding that of alkali metals by at least a factor of ten. We statistically analyzed the spectrum in terms of the random matrix theory and demonstrated that the resonances bare a strong correlation to each other. We identify the origin of this correlation in the highly anisotropic van der Waals interaction potential of erbium. This is a phenomenon not previously encountered in ultracold quantum gases. At the many-body level we observed the d-wave collapse of the Bose-Einstein condensate as previously observed in the chromium experiment in Stuttgart. With the dipolar Fermi gas we demonstrated that the Fermi surface deforms into an ellipsoid induced by the action of the dipole-dipole interaction in momentum space. i Zusammenfassung Die Erzeugung des ersten Bose-Einstein-Kondensats vor ungef¨ahrzwei Jahrzehnten sowie des ersten entarteten Fermigases vier Jahre sp¨ater,¨offnetedie T¨urzur Erkundung einer Vielzahl faszinierender Quantenph¨anomene.Der Großteil dieser Experimente konzentrierte sich dabei auf quantenentartete atomare Gase mit kurzreichweitiger Kontaktwechselwirkung zwischen den Teilchen. Atome mit großem magnetischen Dipolmoment, wie zum Beispiel Chrom, Dysprosium und Erbium, bieten einmalige M¨oglichkeiten, durch die Dipolwechselwirkung hervorgerufene Ph¨a- nomene zu erforschen. Der Charakter dieser Wechselwirkung ist nicht nur langreichweitig sondern auch richtungsabh¨angigund pr¨agtdem System qualitativ neue Eigenschaften auf. Herausragende Beispiele hierf¨ursind der d-Wellen-Kollaps eines dipolaren Bose-Einstein- Kondensats aus Chromatomen, realisiert von der Gruppe in Stuttgart, die Spin-Magneti- sierungs- und Demagnetisierungsdynamik, beobachtet von Gruppen in Stuttgart, Paris und Stanford sowie eine Deformation der Fermifl¨ache, welche von unserer Gruppe beobachtet werden konnte. Die vorliegende Dissertation behandelt die Erzeugung und Untersuchung des ersten Bose- Einstein-Kondensats und des ersten entarteten Fermigases von Erbiumatomen. Erbium geh¨ortzur Gruppe der Lanthanoide und besitzt ein großes magnetisches Moment von sieben Bohr Magnetonen. Diese Arbeit beschreibt im Besonderen die experimentelle Apparatur und den Ablauf, welcher zur Erzeugung eines dipolaren Quantengases notwendig ist. Das Haupt- augenmerk liegt dabei auf der Produktion der schmalbandigen magneto-optischen Falle f¨ur Erbium, die eine sehr effiziente und robuste Art der Laserk¨uhlung darstellt und das experi- mentelle Herstellungsverfahren maßgeblich vereinfacht. Nach der Beschreibung des experimentellen Aufbaus werden in der Arbeit einige funda- mentale Fragen bez¨uglich des dipolaren Charakters von Erbium und seiner Natur als Ele- ment der Lanthanoiden behandelt. Erste Untersuchungen konzentrieren sich dabei auf die Streueigenschaften bei ultrakalten Temperaturen, welche den elastischen und inelastischen Streuquerschnitt sowie das Spektrum von Feshbach-Resonanzen einschließen. Im Speziellen beobachten wir, dass identische dipolare Fermionen kollidieren und rethermalisieren k¨onnen, und dies sogar im tiefen Temperaturbereich. Der damit verbundene elastische Streuquer- schnitt, welcher im Rahmen der Theorie der universellen dipolaren Streuung berechnet wer- den kann, h¨angtnur von der Masse des Teilchens und seinem magnetischen Moment ab und ist temperaturunabh¨angig. Dies stellt einen entscheidenden Unterschied im Vergleich zu nicht dipolaren Fermionen dar, welche einen mit der Temperatur schnell abklingenden elastischen Streuquerschnitt aufweisen. Eine weitere markante Eigenschaft von Erbium ist dessen Spektrum von Feshbach-Resonan- zen. Unter der Verwendung von bosonischem Erbium beobachteten wir eine enorme Dichte von Resonanzen, welche die bei Alkalimetallen vorhandene Resonanzdichte um mehr als das Zehnfache ¨ubersteigt. Wir f¨uhrten eine statistische Analyse der Verteilung von Feshbach- Resonanzen im Sinne der Theorie der Zufallsmatrizen durch und zeigten, dass die Resonanzen eine starke Korrelation aufweisen. Wir identifizierten den Urprung dieser Korrelation indem ii hochgradig richtungsabh¨angigenvan der Waals Potential von Erbium, wie es erstmals in ultrakalten Quantengasen beobachtet werden konnte. In Bezug auf Mehrk¨orperwechselwirkungen konnten wir den d-Wellen-Kollaps des Bose- Einstein-Kondensates beobachten, ¨ahnlich wie im Chrom-Experiment in Stuttgart. Mithilfe des dipolaren Fermigases demonstrierten wir dar¨uberhinaus die Deformation der Fermifl¨ache in ein Ellipsoid, welche durch Auswirkungen der Dipolwechselwirkung im Impulsraum zu erkl¨arenist. iii Contents Summary i Zusammenfassung ii 1. Introduction1 1.1. Motivation ..................................... 1 1.2. Thesis overview ................................... 5 2. Erbium properties 8 2.1. The discovery of erbium .............................. 8 2.2. Basic properties ................................... 9 2.2.1. Electron configuration ........................... 9 2.3. Atomic energy spectrum .............................. 12 2.3.1. Laser-cooling transitions .......................... 13 2.3.2. Hyperfine structure ............................. 16 2.3.3. Isotope shift ................................. 16 2.4. Magnetic properties ................................ 17 2.4.1. Magnetic moment ............................. 17 2.4.2. Land´eg-factor ............................... 19 2.4.3. Zeeman splitting .............................. 20 2.4.4. Hyperfine Zeeman splitting ........................ 21 3. Experimental setup 23 3.1. Experimental requirements ............................ 23 3.2. Vacuum chamber design .............................. 24 3.2.1. High vacuum section ............................ 25 3.2.2. Ultra-high vacuum section ......................... 29 3.3. Slow atom beam with high flux .......................... 32 3.3.1. Transversal cooling ............................. 32 3.3.2. Zeeman slower ............................... 32 3.3.3. Velocity distribution ............................ 37 3.4. Coil setup at main chamber
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