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Progress Towards a Measurement of the Electric Dipole Moment of the Electron Using Pbo∗

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Abstract Progress Towards a Measurement of the Electric Dipole Moment of the Electron using PbO¤ Sarah Rachel Bickman 2007 We have proposed and begun implementing an experiment to look for an electric dipole 3 + moment (EDM) of the electron, de, using the metastable a(1) § state of the PbO molecule. A non-zero measurement of de within the next few orders of magnitude beyond the current limit ¡27 of jdej < 1:6£10 e-cm [1] would be clear evidence for physics beyond the standard model. We ¤ have designed and built a stable apparatus for the measurement of de using PbO in a heated vapor cell. Using this apparatus, the ­ doublet splitting in the a(1) J=1 state was measured to be 11.214(5) MHz. Without an applied electric ¯eld, the di®erence in g-factors between the ­ doublet states was found to be ±g=-31(9)£10¡4. Measurements of the Stark shift were found to be consistent with previous measurements [2]. The counting rate has been optimized and agrees with models. Three di®erent types of detectors with associated low-noise preampli¯ers were built and tested. To improve the sensitivity, an alternate detection scheme using reexcitation to the C0 state was explored and ultimately rejected in the form proposed here. In the ¯rst generation experiment, with the current fluorescence detection along the a(1)!X transition, the ¡25 p expected sensitivity to an electron EDM is ±de ¼10 e cm/ day. Two proposals for second generation experiments are considered. Progress Towards a Measurement of the Electric Dipole Moment of the Electron using PbO¤ A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy by Sarah Rachel Bickman Dissertation Director: David Paul DeMille December 2007 Copyright °c 2007 by Sarah Rachel Bickman All rights reserved. ii Acknowledgements This work never could have been accomplished without constant support, advice, and kindness from many people. Most important, I would like to thank my advisor, David DeMille, who has been the best advisor I could have imagined. Despite the decade that we have worked together, his exceptional patience, skillful teaching, and brilliant ideas continue to amaze me. Without his guidance I would have left physics countless times, and I am exceptionally grateful for his continual encouragement. Working with him has been a privilege. When it came time to form my thesis committee, it was obvious to me whom I wanted on it. I am grateful to these people not only for their time and advice on this committee, but also their time over the years. Steve Lamoreaux has helped us solve di±cult problems, even before he came to Yale. I have learned much in discussions with Daniel McKinsey about how to design an experiment and make a better measurement. Thomas Appelquist's excellent explanations has made him an invaluable resource. Bonnie Fleming has been a mentor and opened up new kinds of physics to me. I would also like to thank Larry Hunter who made some initial measurements on PbO, and since then has continued to provide advice on our more di±cult problems. In addition, I would like to thank him for his years of patience and skill in teaching me as an undergraduate. I have been fortunate to work with many talented, and supportive colleagues. I am grateful for our long friendships, and have learned much from all of them. David Kawall is the most persistent and careful person I have ever met. Paul Hamilton has consistently challenged me to think harder and work better. Yong Jiang can solve any computer or physics problem. This work never could have been accomplished without the help of many others: Frederik Bay, Valmiki Prasad, Yulia Gurevich, Amar Vutha, Richard Paolino, and Jordan Weil, and Hunter Smith. There are many others who contributed to this work. Vincent Bernardo and the entire Gibbs iii Machine Shop did much of the metal machining and advised on many of my designs. Sidney Cahn o®ered advice on electrical designs and many other issues. The entire DeMille group has cheerfully lifted shields on countless occasions and provided advice. I am very lucky to have found a loving husband who is my equal in all respects, and who treats me as one. Daniel Farkas has become so much a part of my life that I cannot imagine being without him. I am looking forward to sharing our next adventure. It is an understatement to say that I am grateful to my parents. They have been my biggest source of encouragement and support and have shared every triumph and failure with me. They spent many years teaching me that \Education is not ¯lling a bucket, but lighting a ¯re"{William Butler Yeats. I never could have dreamed of being here today without them. My brother, Jed, has made me laugh when all else has failed, and has been one of the most enthusiastic members of my fan club. My friends Benjamin Turek, Alexandra Gueydan, Stephen Maxwell, Iva Maxwell, and Dale Li have added much needed humor and have provided wise advice. iv Contents Acknowledgements iii 1 Introduction 1 1.1 Introduction . 1 1.2 EDMs Violate Parity and Time Reversal Symmetries . 2 1.3 Direction of de ..................................... 3 1.4 Overview of Relevant Particle Theory . 4 1.5 General Method to Measure de ............................ 6 1.6 Enhancement Factors . 8 1.7 Enhancement Factor of PbO . 10 1.8 Relating a Measurement of the EDM of PbO to the EDM of Fundamental Particles 11 1.9 Other Current Experimental Approaches . 12 1.9.1 Atoms . 12 1.9.2 Molecules . 14 1.9.3 Solid State Materials . 17 1.10 Prospects for PbO as a System for Measuring de .................. 18 2 Experimental Methods 19 2.1 Level structure of PbO . 20 2.2 Excitation Sequence . 23 2.2.1 Horizontally Polarized Light, and No Electric Field . 23 2.2.2 Horizontally Polarized Light, With an Applied Electric Field . 25 2.2.3 Vertically Polarized Light and Microwave Excitation . 26 2.3 Quantum Beat Spectroscopy . 30 v 2.3.1 Contrast of Quantum Beats in Molecules . 34 2.4 Lifetime of the a(1) State and Density of Available Molecules . 38 2.5 Noise Sources . 40 2.5.1 Stray Magnetic Fields . 40 2.5.2 Magnetic Johnson Noise . 41 2.5.3 Ferromagnetic Materials . 42 2.6 Common Systematic E®ects . 43 2.6.1 Leakage Currents . 43 2.6.2 v £ E E®ects . 44 2.6.3 Berry's phases . 46 3 Apparatus 48 3.1 Vapor Cell . 49 3.1.1 Material Selection . 52 3.1.2 Gold Bonding Technique . 53 3.1.3 Birefringence of Sapphire Windows . 54 3.1.4 Stem . 55 3.1.5 Plunger . 55 3.1.6 Electric Field Homogeneity . 56 3.1.7 Leakage Currents . 57 3.1.8 Monitoring of Leakage Currents . 57 3.1.9 Material Selection . 57 3.2 Oven . 62 3.2.1 Eddy Current Suppression . 68 3.3 Vacuum System . 71 3.4 Magnetic Shielding . 75 3.5 Laser Excitation . 78 3.6 Microwave State Population . 80 3.7 Detection . 81 3.7.1 Filters . 83 3.7.2 Absorbing Filters . 88 vi 3.7.3 Winston Cones . 90 3.7.4 Monte Carlo Model of Detection . 93 3.7.5 Detectors . 101 3.7.6 PMTs . 102 3.7.7 Transimpedance Ampli¯ers . 106 3.7.8 Noise in Transimpedance Ampli¯ers . 107 3.7.9 PIN Photodiode . 116 3.7.10 APDs . 118 3.7.11 Recovery Time . 120 3.7.12 Final Choice of Detectors . 127 3.8 Data Acquisition and Analysis . 129 3.9 Data Acquisition Hardware . 129 3.10 Measurement Sequence . 130 3.11 Data Analysis . 130 3.11.1 Fitting Function . 130 3.11.2 Optimization of Computation . 133 4 Measurements of PbO Structure 134 4.1 Measurement of g-factor Di®erence and the ­-doublet Splitting . 135 4.2 g-factors with Applied Electric Fields . 141 4.3 DC Stark Shifts . 146 4.4 Summary of Measurements of a(1) State . 149 5 Measurements of Signal Magnitudes 150 5.1 Calculated Signal Sizes . 150 5.2 Attempted Improvements to SNR . 156 5.3 Optimal Conditions . 163 5.4 Conclusions on Signal Sizes . 164 6 Development Towards Future Generations 166 6.1 Laser Reexcitation to the C0 state . 166 6.1.1 Introduction . 166 vii 6.1.2 Determination of C0 Energy Level Structure . 168 6.1.3 Franck-Condon Factors . 174 6.1.4 ­-Doublet Splitting in the C0 state . 176 6.1.5 a(1)! C0 Excitation Cross Sections . 178 6.1.6 Determination of Expected Contrast With No Electric Field . 180 6.1.7 Determination of Expected Contrast With an Applied Electric Field . 182 6.1.8 Reexcitation Measurement Scheme . 186 6.1.9 a(1)! C Excitation Cross Sections . 193 6.2 Summary of C' Measurements . 194 6.3 Microwave Detection . ..
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