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A New Limit on the Electron Electric Dipole Moment: Beam Production, Data Interpretation, and Systematics

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A New Limit on the Electron Electric Dipole Moment: Beam Production, Data Interpretation, and Systematics A New Limit on the Electron Electric Dipole Moment: Beam Production, Data Interpretation, and Systematics The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Hutzler, Nicholas Richard. 2014. A New Limit on the Electron Electric Dipole Moment: Beam Production, Data Interpretation, and Systematics. Doctoral dissertation, Harvard University. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:12274509 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA A New Limit on the Electron Electric Dipole Moment: Beam Production, Data Interpretation, and Systematics A dissertation presented by Nicholas Richard Hutzler to The Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Physics Harvard University Cambridge, Massachusetts February 2014 c 2014 - Nicholas Richard Hutzler All rights reserved. Thesis advisor Author John M. Doyle Nicholas Richard Hutzler A New Limit on the Electron Electric Dipole Moment: Beam Production, Data Interpretation, and Systematics Abstract The charge distribution associated with an electron has surprising implications for a number of outstanding mysteries in physics. Why is the universe made out of matter versus anti-matter, instead of both equally? What new particles and interactions lie beyond the current reach of accelerators like the LHC? Models which propose answers to these questions, such as Supersymmetry, tend to predict a small, yet potentially measurable, asymmetric interaction between an electron and an electric field, characterized by an electric dipole moment (EDM). Despite over six decades of experimental searching, no EDM of any fundamental particle has ever been measured; however, these experiments continue to provide some of the most stringent limits on new physics. Here, we present the results of a new search for the electron EDM, −29 de = (−2:1 ± 3:7stat ± 2:5syst) × 10 e cm, which represents an order of magnitude improvement in sensitivity from the previous best limit. Since our measurement is −29 consistent with zero, we present the upper limit of jdej < 8:7 × 10 e cm with 90 percent confidence. iii Contents Title Page . i Abstract . iii Table of Contents . iv Citations to Previously Published Work . ix Acknowledgments . x Dedication . xi 1 Electric Dipole Moments 1 1.1 Introduction . 1 1.1.1 EDMs in the Standard Model, and Beyond . 2 1.1.2 EDMs in Atoms and Molecules . 8 1.2 Thorium monoxide electron EDM . 12 2 Molecules 16 3 2.1 Summary: Structure of the ∆1 EDM State . 16 2.1.1 Stark Shift . 18 2.1.2 Zeeman Shift . 20 2.1.3 E-field dependence of g-factors . 21 2.1.4 EDM Shift . 21 2.2 Molecular Structure . 22 2.2.1 Electronic states . 22 2.2.2 Rotation and vibration . 24 2.2.3 Hunds' Cases . 26 2.3 Matrix Elements for Spherical Tensor Operators . 27 2.3.1 Transforming Between Lab and Molecule Frames . 29 2.3.2 Matrix elements using multiple frames . 31 2.4 Stark Shift . 33 2.4.1 Molecule Orientation and the Quantum Number N . 35 2.4.2 Molecular polarization: linear vs. quadratic Stark regime . 36 2.5 Zeeman Shift . 37 2.6 Rotational Perturbations: Spin-Orbit, Uncoupling, Ω-doubling . 40 iv Contents 2.6.1 Spin-Orbit, L · S ......................... 41 2.6.2 Spin Uncoupling, J · S ...................... 42 2.6.3 Ω-doubling, J · Je ......................... 44 2.7 Optical Absorption Cross Sections and Branching Ratios . 45 2.7.1 Electronic Branching . 46 2.7.2 Vibrational Branching - Franck-Condon Principle . 47 2.7.3 Rotational Branching - H¨onl-LondonFactors . 48 2.7.4 Molecular transition notation - P; Q; and R branches . 50 3 Buffer Gas Cooled Beams 51 3.1 Introduction . 51 3.1.1 Cold atoms and molecules . 53 3.1.2 Buffer gas cooling and beam production . 58 3.2 Effusive and Supersonic Beam Properties . 60 3.2.1 Characterization of gas flow regimes . 60 3.2.2 Effusive beams . 63 3.2.3 Fully hydrodynamic, or \supersonic" beams . 66 3.3 Buffer Gas Cooled Beams . 69 3.3.1 Species production, thermalization, diffusion, and extraction . 71 3.3.2 Forward velocity . 81 3.3.3 Forward (longitudinal) velocity spread . 89 3.3.4 Transverse velocity spread . 91 3.3.5 Angular spread and divergence . 92 3.3.6 Rotational Temperature . 95 3.3.7 Measured Cell Extraction and Molecule Production . 97 3.3.8 Effect of buffer gas species on beam properties . 98 3.4 Details of the ThO Beam Study . 101 3.4.1 Apparatus . 101 3.4.2 Measured Beam Properties . 103 3.5 Applications to Precision Measurements . 108 4 Measurement and Data Analysis 114 4.1 Apparatus overview . 114 4.1.1 Beam Source . 115 4.1.2 Stem Region . 116 4.1.3 Interaction Region . 117 4.2 Measurement scheme . 118 4.2.1 Magnetic Field, Fringe Number, and B-corrected Asymmetry . 124 4.3 Data analysis . 125 4.3.1 Extracting Counts . 128 4.3.2 Extracting Asymmetry and Asymmetry Uncertainty . 129 4.3.3 Computation of Contrast, τ, and Angular Frequencies . 132 v Contents 4.3.4 Data cuts: count rate, asymmetry, and χ2 . 135 4.3.5 Computation of Parity Sums, and the EDM . 138 4.3.6 Blinded analysis . 141 4.3.7 Superblock Switches . 143 4.3.8 Analysis Checks . 146 4.4 Notes about statistics . 149 4.4.1 The shot noise limit . 150 4.4.2 Bias of sample standard deviation . 152 4.4.3 Asymmetries . 154 4.4.4 Chi-square Tests with Unknown Variance . 157 4.4.5 Weighted means . 169 4.4.6 Monte Carlo Simulation of Statistics . 172 5 Interpretation of Measured Phases 175 5.1 Ideal system: applied fields, and an EDM . 175 5.1.1 Zeeman Shift . 176 5.1.2 g-factor Difference (η) . 177 5.1.3 Stark Shift . 177 5.1.4 Electron EDM . 178 5.2 Non-Ideal Effects Appearing in the Hamiltonian: \Systematics" . 178 5.2.1 Non-reversing Fields . 180 5.2.2 Light Shifts . 181 5.2.3 Correlated detunings . 187 5.2.4 Correlated Rabi frequencies . 189 5.2.5 Correlated magnetic fields: leakage current and switch ordering 190 5.2.6 Contrast correlations . 192 5.2.7 Summary of terms in the Hamiltonian, including known sys- tematics . 192 5.3 Measurement and Suppression of Systematic Effects . 194 5.3.1 False EDM from light shifts and non-reversing E-field . 194 5.3.2 False EDM from light shifts and correlated Rabi frequency . 198 5.3.3 False EDM from contrast correlations and phase offsets . 199 5.3.4 NEB-correlated precession from light shifts and correlated Rabi frequency . 200 5.3.5 N -correlated Laser Pointing . 201 5.4 Determination of Systematic Shift and Uncertainty . 202 5.4.1 Criteria for inclusion . 204 5.4.2 Non-reversing E-field . 205 5.4.3 Correlated Rabi frequency . 206 5.4.4 E-odd phases . 207 5.4.5 Drifting !N ............................ 207 5.4.6 Magnetic field offsets and gradients . 208 vi Contents 5.4.7 Laser detunings . 209 5.4.8 Rejected Methods . 212 5.5 Final Error Budget and Result . 214 5.5.1 A new limit on the electron-nucleon pseudoscalar coupling, CS 214 3 6 Effective Zeeman Hamiltonian in ThO H ∆1 216 6.1 Summary of perturbations . 217 6.2 g−factor . 219 3 6.2.1 Parallel g-factor in a ∆1 state . 219 6.2.2 Spin-Orbit mixing with B and C states . 220 6.2.3 Zeeman/Spin-uncoupling Perturbation . 221 6.3 Electric field-dependent g−factor Difference between N states . 223 6.3.1 Second Order Stark/Zeeman Perturbation . 225 6.3.2 Stark/Spin-uncoupling/Zeeman Perturbation . 227 6.3.3 Combined effect of perturbations . 230 6.3.4 Smaller Effects . 231 6.4 Measurement of g and η . 234 6.4.1 Measurement of η . 235 6.4.2 Measurement of the g-factor . 237 6.4.3 Checking the sign . 238 6.4.4 Fast N switching . 240 A Thermal Stress Birefringence 241 A.1 Size of Effect . 242 A.1.1 Relationship to Linear Gradient . 243 A.2 Thermal Stress Induced Birefringence . 243 A.2.1 Different substrates . 249 A.2.2 Optical Properties of ITO . 250 A.3 Other Effects . 252 A.3.1 Vacuum Stress Induced Birefringence . 252 A.3.2 Optically Induced Birefringence ..
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