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Measuring the Electron Electric Dipole Moment with Trapped Molecular Ions

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Measuring the Electron Electric Dipole Moment with Trapped Molecular Ions Measuring the Electron Electric Dipole Moment with Trapped Molecular Ions by Matt Grau B.S., California Institute of Technology, 2009 M.S., University of Colorado Boulder, 2011 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Physics 2016 This thesis entitled: Measuring the Electron Electric Dipole Moment with Trapped Molecular Ions written by Matt Grau has been approved for the Department of Physics Prof. Eric Cornell Prof. Jun Ye Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Grau, Matt (Ph.D., Physics) Measuring the Electron Electric Dipole Moment with Trapped Molecular Ions Thesis directed by Prof. Eric Cornell An electron electric dipole moment (eEDM) directly violates time-reversal symmetry, a fact which has far reaching implications for physics beyond the Standard Model. An experiment us- ing trapped molecular ions offers high sensitivity because of the large effective electric fields and long coherence times that are possible. We demonstrate precision spectroscopy on many trapped HfF+ ions in a radiofrequency quadrupole trap with rotating electric and magnetic fields. The 3 spectroscopy performed is a Ramsey type experiment between spin states of the metastable ∆1 electronic state and has a coherence time exceeding 1 second. We have collected and analyzed over 200 hours of Ramsey spectroscopy data taken under a variety of experimental conditions. We identify several systematic errors that could potentially affect an eEDM measurement and estimate the size of these interloping effects. By collecting data under pairs of conditions where the eEDM has opposing signs (e.g. performing Ramsey spectroscopy on the two Λ-doublets) we are able to take frequency differences that can suppress some of these systematic effects. Although our data set includes runs where we have intentionally varied experimental parameters to study systematic effects, we achieve a 1σ statistical sensitivity of 2:76 × 10−28 e·cm and place a 1σ upper bound on the size of systematic effects of 2:82 × 10−28 e·cm. Finally we present a preliminary upper bound −28 on the eEDM of jdej < 4:6 × 10 e·cm with 90% confidence. Dedication To Mom & Dad { Thanks. Also BJ is great. v Acknowledgements This thesis is only possible thanks to the help of a great many people. In particular my fellow graduate students Dan Gresh and Will Cairncross, who not only make working in lab productive but enjoyable as well. Proper tribute must be paid to Dan for his stoic relentlessness. Like a boulder tumbling down a hill, he will surely crush all opposition in between us and the EDM. Will is as enthusiastic as he is talented, and his zeal for simulation causes me to worry that we might all be inside of one. Additionally, Yan Zhou, amazes me by his embodiment of the principle of superposition - he seems to be everywhere and working on everything at once. Kia is new to the group, but I am sure that he will have the experiment control completely rewritten in Python in no time flat. Finally I must thank Yiqi Ni, our brilliant undergraduate, who did all the real work on the experiment while only complaining a little. I've been very fortunate to work with exceptionally great colleagues in the past as well. Huanqian Loh was a fantastic labmate for many years on the experiment, and a great role model for me. I learned a great deal from her. I've also benefited greatly from working closely with Kevin Cossel, ever since he lent me a drill almost a decade ago. Additionally I'd like to thank Kang-Kuen Ni, Laura Sinclair, Russel Stutz, Tyler Yahn, and Tyler Coffey for all of their past contributions to the experiment. My advisers Eric Cornell and Jun Ye have been influential in more ways than I have space to write about here. Eric taught me to question everything, and to never even think about collecting data without a plan to analyze and interpret it first. His intuition for physics never ceases to astonish me. Jun is a constant source of energy and enthusiasm, and is never afraid to jump right vi into any problem that needs solving. I'd also like to thank Deborah Jin and her group for great feedback during the Jin/Cornell meetings, and also Pam Leland and Krista Beck, who are the only reason anything ever gets done. I've had great technical support from the JILA instrument shop and electronics shop. Todd Asnicar machined and delicately hand polished the ion trap that made all of the experiments in this thesis possible. He did a great job, and the trap has never disappointed me. David Alchenberger was critical in cleaning the trap electrodes for ultrahigh vacuum and gold coating them for high optical reflectivity. Terry Brown, James Fung-A-Fat, Carl Sauer, and Chris Ho all provided expert guidance for electronics projects large and small. My fellow classmates at CU, Dan Weflen, Maya Fabrikant, Dan Lobser, Adam Kaufman, and Brandon Ruzic, have provided me the occasional useful idea as well as the more occasional entertaining diversion. In particular Josh Weiner has been a great friend for the past decade, ever since he explained to me how a rotisserie functioned in undergrad. Jon Malmaud aided me with tons of useful insight into statistics and general strategic thought. Todd Gingrich has always been a source of motivation for me. I'd also like to thank John Leichty for more than a little help with microcontrollers, and Dan Lo and Gabe Cohn for answering countless questions about FPGAs and digital electronics. I've had many great teachers along the way, but I'd like to especially thank Michael Cross and Gil Refael for always having time to answer my questions. Mondania Gallagher was my wonderful middle school science teacher who was always engaged and ever patient. She was always delighted to share in her students' discoveries. Karen Young was a great teacher and an awesome scoutmaster. Without them I would be nowhere. I'd also like to thanks my parents, my siblings Dan, Christina, and Maria for their support, as well as all my family in Virginia, Maryland, and especially Colorado for their unwavering encour- agement and cheer-leading. Finally, I want to thank my wonderful wife BJ for her love and care while I've been writing this. She also painstakingly revised the inchoate neighing and braying of barnyard animals into something that resembles prose. She pushes me to be all I can be. Contents Chapter 1 Introduction 1 1.1 The electron EDM.....................................1 1.1.1 EDM searches...................................6 1.2 Overview for thesis.....................................8 2 Experimental apparatus 10 2.1 Summary of techniques.................................. 10 2.1.1 Choice of molecular species............................ 10 2.1.2 Neutral HfF production.............................. 11 2.1.3 Photoionization................................... 11 2.1.4 State transfer.................................... 12 2.1.5 State detection................................... 14 2.2 Ion Trap........................................... 16 2.2.1 Refinements unique to the eEDM experiment.................. 16 2.2.2 Rotating electric field............................... 19 2.2.3 Erot amplitude pulses................................ 20 2.2.4 Experiment sequence................................ 24 2.2.5 Future trap directions............................... 26 2.3 Computer control...................................... 26 viii 2.3.1 uBinary file format................................. 26 2.3.2 Experiment control state machine........................ 32 3 Statistical sensitivity 37 3.1 Theory of measurement.................................. 37 3.1.1 Measurement principles.............................. 37 3 3.1.2 ∆1 state Hamiltonian............................... 38 3.1.3 Effect of the rotating frame............................ 42 3.2 Measurement........................................ 42 3.2.1 Ramsey spectroscopy................................ 42 3.2.2 Experimental Ramsey sequence.......................... 45 3.2.3 Applying π=2 pulses................................ 46 3.2.4 Optimizing statistical sensitivity......................... 47 4 Systematic uncertainty 57 4.1 Overview.......................................... 57 4.1.1 Strategy....................................... 62 4.2 Understood systematic effects............................... 63 4.2.1 Differential g-factor................................ 63 4.2.2 Effective differential g-factor........................... 65 4.2.3 Non reversing magnetic field........................... 67 4.2.4 Axial magnetic fields................................ 77 4.2.5 Fields inhomogeneities............................... 84 4.2.6 Unintentional gradients.............................. 88 4.3 Measured systematics................................... 90 4.3.1 f B ∼ B·~ ~r ...................................... 93 4.3.2 f BR ∼ (B~ × ~r) · ~! .................................. 98 4.3.3 f BR ∼ zr2 ...................................... 99 ix 4.4 Potential other systematics................................ 102 5 Conclusion 105 5.1 A precision measurement of the electron EDM..................... 105 5.1.1 Measurement overview............................... 105 5.1.2 Data blinding.................................... 110 5.1.3 Blinded EDM measurement............................ 114 5.1.4 Systematic corrections..............................
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