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High-Precision Spectroscopy of Forbidden Transitions in Ultracold 4He and 3He

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High-Precision Spectroscopy of Forbidden Transitions in Ultracold 4He and 3He VRIJE UNIVERSITEIT High-Precision Spectroscopy of Forbidden Transitions in Ultracold 4He and 3He ACADEMISCH PROEFSCHRIFT ter verkrijging van de graad Doctor aan de Vrije Universiteit Amsterdam, op gezag van de rector magnificus prof.dr. V. Subramaniam in het openbaar te verdedigen ten overstaan van de promotiecommissie van de Faculteit der Exacte Wetenschappen op woensdag 15 maart 2017 om 15.45 uur in de aula van de universiteit, De Boelelaan 1105 door Remy Paulus Margaretha Joseph Willem Notermans geboren te Venray promotor: prof.dr. W.M.G. Ubachs copromotor: dr. W. Vassen voor mijn familie en vrienden Science is an ongoing process. It never ends. There is no single ul- timate truth to be achieved, after which all the scientists can retire. Carl Sagan, Cosmos This thesis was approved by the members of the reviewing committee: Prof. Dr. K.S.E. Eikema (Vrije Universiteit Amsterdam) Prof. Dr. K.H.K.J. Jungmann (University of Groningen) Prof. Dr. C. Salomon (Ecole Normale Sup´erieure, Paris) Dr. R.J.C.Spreeuw (UniversityofAmsterdam) Dr. Ir. E.J.D. Vredenbregt (Eindhoven University of Technology) This work is part of the research programme of the Foundation for Fun- damental Research on Matter (FOM), which is part of the Netherlands Organisation for Scientific Research (NWO), and was carried out at the LaserLaB of the Vrije Universiteit Amsterdam. The cover shows the observed absorption line shapes of a narrow optical transition in a degenerate Fermi gas (top) and a Bose-Einstein conden- sate (bottom) of metastable helium. The large difference is caused by the fundamental difference in quantum statistics between fermions and bosons. Printed by Ipskamp Drukkers B.V., Enschede ISBN: 978-94-028-0502-4 Contents 1 Introduction 1 1.1 Prologue 1 1.2 A revolution in physics 2 1.3 PushingQEDtothelimit 4 1.4 Determiningfundamentalconstants 8 1.5 Physics with ultracold He∗ 14 1.6 Outline of this thesis 17 2 Experimental setup 21 2.1 Slowing, trapping, and cooling He∗ 23 2.2 Detecting atoms 38 2.3 Optical setup 51 2.4 Digitalcontroloftheexperiment 56 2.5 Anewspectroscopylasersystem 58 3 1 3 High-precision spectroscopy of the 2 S1 2 P1 transition → 77 3.1 Introduction 77 3.2 Experimental setup 80 3.3 Transition line shape 82 3.4 Systematic effects 90 3.5 Results 98 3.6 Conclusion 102 4 Line shapes of the 2 3S 2 1S transition for quantum degenerate bosons and fermions→ 105 4.1 Introduction 106 4.2 Experimental setup 107 4.3 Comparing the line shape of a BEC to a degenerate Fermi gas 108 v Contents 4.4 Bragg-likescatteringinanopticallattice 111 4.5 Determining the 2 3S 2 1S s-wave scattering length 115 − 4.6 Conclusion 116 4.A Appendix:BEClineshapemodel 117 4.B Appendix: EstimatingtheRabifrequency 125 4.C Appendix:Anopticallattice 139 4.D Appendix: Extracting the s-wave scattering length 148 5 Towards a new measurement of the 2 3S 2 1S transition159 → 5.1 Introduction 159 5.2 Magic wavelengths for the 2 3S 2 1S transition in helium160 → 5.3 Ramsey-type Zeeman spectroscopy in He∗ 178 4 5.4 Spectroscopy in the He∗ mJ = 0 state 190 3 5.5 Prospects for He∗ 197 4 5.A Appendix: Collisions between two He∗ mJ = 0 atoms 199 5.B Appendix:Traplosscalculations 202 Bibliography 205 List of Publications 235 Summary 237 Samenvatting 241 Dankwoord 245 vi CHAPTER 1 Introduction 1.1 Prologue Science is in perpetual motion, and changes in our fundamental under- standing of the workings of the physical universe are inevitable as we are presented with new evidence through observations. Of all the methods an experimental physicist has in his toolbox, spectroscopy is the most accurate tool available to observe the universe. Applied to a suitable test object, whose measurable quantities can be calculated to high precision, physical theories can be tested to extreme limits within the confines of a (relatively small-scale) laboratory setup. The test object in this thesis is the helium atom, which is a three- body system consisting of a nucleus and two electrons. This makes it simple enough that high precision calculations can be performed for this system, yet it contains sufficient complexity to be challenging on both the theoretical and experimental front. My work in this thesis focuses on high-precision spectroscopy in the helium atom, and in this introduction I provide an overview of the many different facets of fundamental physics where the helium atom plays an important role. But first I will discuss the essential role that spectroscopy played in the ‘quantum-revolution’ of the 20th century, and how it still does to this date. 1 1. Introduction 1.2 A revolution in physics A little over a century ago there was general consensus that mankind’s understanding of physics was nearly complete. With the grand suc- cesses of Maxwell’s laws of electromagnetism, Newton’s laws of gravity and motion, and the framework of thermodynamics, there were few gaps to be filled to complete our view of the workings of the universe. This is immortalized by Lord Kelvin’s - the worlds’ foremost natural philoso- pher at the time - speech in 1900 in which he states that physics is understood apart from two ‘clouds’ [1]. The first cloud was caused by the famous experiment by Michelson and Morley which seemed to dis- prove the ‘luminiferous ether’ theory as no translational variation in the speed of light could be observed. The second cloud was related to the Maxwell-Boltzmann theory of equipartition of energy, which could not explain the specific heat properties of matter based on a continuum distribution of energy states. Within five years, four papers were published by Albert Einstein to address these clouds and they sparked a revolution [2–5]. In the next decades our understanding of the physical world would transform from a deterministic view to the exciting yet astonishing world of quantum and relativistic mechanics, and even relativistic quantum mechanics. This revolution is now associated with names like Bethe, Bohr, Born, de Broglie, Dirac, Ehrenfest, Fermi, Feynman, Heisenberg, Lamb, Pauli, Planck, Schr¨odinger, and Sommerfeld, and I am definitely doing many other physicists wrong by reducing the contributions to this single list. Some of these names will reappear multiple times in this thesis. The initial test model for the theoretical developments was the hydrogen atom. This is understandable from a theoretical point of view, as the two-body system (one electron and one proton) allowed exact analyt- ical solutions of the electronic level energies. As the energy difference between energy levels could be measured using spectroscopy, the early success of quantum mechanics was the explanation of the hydrogen spec- trum using the model proposed by Bohr and the resulting derivation of the empirical Rydberg constant in terms of fundamental constants [6]. This paved the road for spectroscopy as the main experimental force be- hind further refinement and development of the theory. Although very successful, there already were some problems with the theory proposed 2 1.2. A revolution in physics by Bohr as it could not explain the presence of so-called ‘doublet’ lines that had been observed in hydrogen spectra already in 1887 [7]. There soon appeared an explanation by Sommerfeld by introducing elliptical Keplerian orbitals for the electrons [8], but the real breakthrough was made by Dirac, who proposed a relativistic quantum mechanical de- scription of the electron [9]. In this model the observed fine structure in the hydrogen energy levels could be explained by spin-orbit coupling, and the degenerate 2S and 2P levels in hydrogen would actually be split 2 2 2 2 into the 2 S1/2, 2 P1/2, and 2 P3/2 levels where only the 2 S1/2 and 2 2 P1/2 levels would remain degenerate. Within 30 years since the speech by Lord Kelvin, our understanding of physics was completely revolutionized both in the realm of the ex- tremely small and the extremely fast. And yet even the model proposed by Dirac would soon appear incomplete due to advances in the spectro- scopic techniques. In 1947 Lamb and Retherford finished an experiment 2 2 from which they concluded that the hydrogen 2 S1/2 and 2 P1/2 lev- els were not degenerate but actually split by 0.033 cm 1 ( 1 GHz) − ∼ [10, 11]. The explanation of this so-called ‘Lamb shift’, given by Bethe [12], required a new mathematical framework where quantum mechanics and electrodynamics were incorporated into a single operating model: quantum electrodynamics (QED). As if quantum mechanics was not weird enough, QED tells us that the vacuum is not empty. Given sufficiently short time, particles can ‘pop up’ in a vacuum and disappear a short time later without violating any conservation laws. However, these so-called ‘virtual’ particles can still interact with other particles, and lead to shifts in the electronic level energies of atoms. The observation of the Lamb shift accelerated the development of QED as laid out by Tomonaga, Schwinger, and Feyn- mann. One of the earliest overviews of the theory - authored by Dyson - would be published a mere two years after the observation of the Lamb shift [13]. By this time the expected value for any observable parameter could be calculated in QED theory as a series expansion of contributing processes as function of powers of the fine structure constant α, where each higher order involves more complex processes. As there is no a priori reason to accept that the series expansion converges [14], higher- order terms can still significantly contribute and require evaluation and continuous comparison with increasingly accurate measurements. 3 1.
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