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Amar C. Vutha, “A Search for the Electric Dipole Moment of The Abstract A search for the electric dipole moment of the electron using thorium monoxide Amar Chandra Vutha 2011 This thesis is concerned with the conception, design and construction of an exper­ iment to search for the permanent electric dipole moment of the electron (de) with improved sensitivity. This dipole moment, de, is a hypothesized quantity whose de­ tection, or (in the absence of detection) an improved constraint on its size, would shed some light on the part played by discrete symmetries of space-time in the evo­ lution of our universe. A non-zero de is evidence of parity and time-reversal violation in fundamental physical processes, and provides an experimental test of many pro­ posed extensions to the Standard Model of particle physics. The experiment takes advantage of the enhanced sensitivity of the H state in the thorium monoxide (ThO) molecule to de. The precession of the spins of the valence electrons in the internal electric field of the molecule is measured using a molecular beam apparatus. This ex­ 30 periment has the potential to improve the experimental limit on de to ~ 10~ e cm, an improvement by a factor of 103 over the current experimental limit. I will describe the analysis that led to the identification of ThO as a favorable system for such an experiment, details of the design and construction of the experimental apparatus, and measurements of various properties of ThO which guide estimates of the sta­ tistical sensitivity and the size of potential systematic errors in the experiment. A method of analysis of geometric phase effects in terms of off-resonant energy level shifts, which was developed in order to understand potential systematic errors in this experiment, is also described. A search for the electric dipole moment of the electron using thorium monoxide A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy by Amar Chandra Vutha Dissertation Director: David DeMille December 2011 UMI Number: 3496993 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMT UMI 3496993 Copyright 2012 by ProQuest LLC. All rights reserved. This edition of the work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 Copyright © 2011 by Amar Chandra Vutha All rights reserved. Contents 1 Introduction T-violation, electric dipole moments and ThO 1 1.1 eEDM experiments with atoms and molecules 3 1.1.1 Measuring the eEDM-induced energy shift in a molecule ... 8 1.1.2 The choice of ThO for an eEDM experiment 9 2 Overview of the experiment 18 2.1 Overview of the apparatus 18 2.2 Measurement scheme 23 2.2.1 Effect of £ and B fields on the molecule 23 2.2.2 State preparation and detection 27 2.3 Phase noise 36 2.3.1 Projection noise 36 2.3.2 Effect of finite detection efficiency 37 2.3.3 Magnetic noise 39 2.4 eEDM sensitivity of the experiment 41 3 Potential systematics 45 3.1 Harmless components 46 3.1.1 Electric quadrupole shifts 46 iii 3.1.2 Leakage currents 51 3.1.3 Stress-induced birefringence 52 3.1.4 g-factor difference between fi-doublets 53 3.1.5 Motional fields 53 3.2 Dangerous combinations 54 3.2.1 Polarization rotations and light shifts 54 3.2.2 Non-reversing £-fields & g-factor difference 58 4 Measurements 62 4.1 Production of ThO beams 62 4.2 Lifetime of the H state 67 4.3 Magnetic and electric dipole moments of the H state 69 4.3.1 Magnetic dipole moment 71 4.3.2 Molecule-fixed electric dipole moment 79 5 Apparatus 83 5.1 Mini-beam sources 83 5.2 Electric field plate assembly 86 5.3 Vacuum system 92 5.4 Magnetic shielding 95 5.5 Dead ends, and other lessons 101 6 Summary 106 A Miscellany 110 A.l P, T-violation and EDMs 110 A.2 State mixing in an electric field 113 A.3 Matrix elements between molecular states 114 A.4 Simple picture of fi-doublets 116 iv A.5 Magnetic Johnson noise 120 A.6 Cross-polarization in Gaussian beams 122 B Geometric phases from energy shifts 128 B.l Spin-1/2 system in a magnetic field 132 B.2 Spin-1/2 system with multiple evolution frequencies 136 B.3 Hyperfine states of hydrogen 140 B.4 An anisotropic system 142 B.5 Spin-1 system in an electric field 143 B.6 Combined effect of electric and magnetic fields 147 B.7 Energy shifts in the non-perturbative regime 152 B.8 H state fi-doublets 156 v List of Figures 1.1 Level structure of ThO 15 2.1 Overview of the experiment 19 2.2 ^-doublet in £,B fields 28 2.3 Projective measurement by laser-induced fluorescence 31 2.4 Preparing the state and detecting its precession 32 4.1 Production of ThO molecules in a buffer gas cell 65 4.2 Lifetime of the H state in a buffer gas cell 68 4.3 H state electric & magnetic moments: transitions 71 4.4 Permanent magnet assembly and S-field profiles 72 4.5 ,8-field profiles, zoomed 73 4.6 Permanent magnet assembly for [iu measurement, photo 73 4.7 Zeeman splitting of the H,J=l state in B = 1.9 kG 75 4.8 Stark shift of the H,J = 1 state 80 5.1 Mini-beam apparatus 85 5.2 Electric field plate assembly 90 5.3 Kinematic linkage diagram 91 5.4 Vacuum chamber 94 5.5 Magnetic circuit model of nested shields 98 vi 5.6 Magnetic shields 99 A.l Simple picture of ^-doublets 118 B.l B-field tracing out a loop 131 B.2 S = 1/2 system in a B-field 134 B.3 £-field geometric phase 145 B.4 Geometric phase from combined £- & £>-fields 149 B.5 Breakdown of geometric approximation at high perturbation frequencies 154 B.6 Energy shift and geometric approaches in the non-perturbative regime 155 B.7 eEDM shifts compared to off-resonant energy shifts 158 vn List of Tables 2.1 Estimated eEDM sensitivity 44 B.l Geometric phase: static #-field + rotating £-field 150 B.2 Geometric phase: static 5-field + rotating £>-field 152 vm Acknowledgments I have been fortunate to work with, and learn from, many colleagues and collabo­ rators over the years. I thank them for all the good times. In the end, physics is a human endeavor, whatever it is. I would like to express my deep gratitude to the people who made it fun: Dave DeMille, mentor, friend and more, who opened my eyes to a world full of wonders. Jessie Petricka, David Glenn and Paul Hamilton, who tolerated my bumbling startup transients, endured many stupid questions and shared their wisdom freely. Atomz & Edmz. You all made it interesting. Jan Ragusa and Daphne Klemme, for making the transitions between New Haven and Cambridge easy. Dave Johnson, Stan Cotreau, Steve Sansone and Jim MacArthur, who taught me much and built many things to drive the rods that turned the knobs that worked the thingummyb obs. The Goons and other goons, for all the occasions of insanity that stopped me from going mad. Various Kanpuriyas, ADN, DH and CS, freonds who made the journey meaningful. "For the best that we find in our travels is an honest friend, and he is a fortunate voyager who finds many." This is for you. ix Abstract A search for the electric dipole moment of the electron using thorium monoxide Amar Chandra Vutha 2011 This thesis is concerned with the conception, design and construction of an exper­ iment to search for the permanent electric dipole moment of the electron (de) with improved sensitivity. This dipole moment, de, is a hypothesized quantity whose de­ tection, or (in the absence of detection) an improved constraint on its size, would shed some light on the part played by discrete symmetries of space-time in the evo­ lution of our universe. A non-zero de is evidence of parity and time-reversal violation in fundamental physical processes, and provides an experimental test of many pro­ posed extensions to the Standard Model of particle physics. The experiment takes advantage of the enhanced sensitivity of the H state in the thorium monoxide (ThO) molecule to de. The precession of the spins of the valence electrons in the internal electric field of the molecule is measured using a molecular beam apparatus. This ex­ 30 periment has the potential to improve the experimental limit on de to ~ 10~" e cm, an improvement by a factor of 103 over the current experimental limit. I will describe the analysis that led to the identification of ThO as a favorable system for such an experiment, details of the design and construction of the experimental apparatus, and measurements of various properties of ThO which guide estimates of the sta­ tistical sensitivity and the size of potential systematic errors in the experiment. A method of analysis of geometric phase effects in terms of off-resonant energy level shifts, which was developed in order to understand potential systematic errors in this experiment, is also described.
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