Cavity Control In A Single-Electron Quantum Cyclotron: An .
Cavity Control in a Single-Electron QuantumCyclotron: An Improved Measurement of theElectron Magnetic MomentA thesis presentedbyDavid Andrew HanneketoThe Department of Physicsin partial fulfillment of the requirementsfor the degree ofDoctor of Philosophyin the subject ofPhysicsHarvard UniversityCambridge, MassachusettsDecember 2007
c 2007 - David Andrew HannekeAll rights reserved.
Thesis advisorAuthorGerald GabrielseDavid Andrew HannekeCavity Control in a Single-Electron Quantum Cyclotron: AnImproved Measurement of the Electron Magnetic MomentAbstractA single electron in a quantum cyclotron yields new measurements of the electronmagnetic moment, given by g/2 1.001 159 652 180 73 (28) [0.28 ppt], and the finestructure constant, α 1 137.035 999 084 (51) [0.37 ppb], both significantly improvedfrom prior results. The static magnetic and electric fields of a Penning trap confinethe electron, and a 100 mK dilution refrigerator cools its cyclotron motion to thequantum-mechanical ground state. A quantum nondemolition measurement allowsresolution of single cyclotron jumps and spin flips by coupling the cyclotron and spinenergies to the frequency of the axial motion, which is self-excited and detected witha cryogenic amplifier.The trap electrodes form a high-Q microwave resonator near the cyclotron frequency; coupling between the cyclotron motion and cavity modes can inhibit spontaneous emission by over 100 times the free-space rate and shift the cyclotron frequency,a systematic effect that dominated the uncertainties of previous g-value measurements. A cylindrical trap geometry creates cavity modes with analytically calculablecouplings to cyclotron motion. Two independent methods use the cyclotron dampingrate of an electron plasma or of the single electron itself as probes of the cavity modestructure and allow the identification of the modes by their geometries and couplings,
ivthe quantification of an offset between the mode and electrostatic centers, and thereduction of the cavity shift uncertainty to sub-dominant levels. Measuring g at fourmagnetic fields with cavity shifts spanning thirty times the final g-value uncertaintyprovides a check on the calculated cavity shifts.Magnetic field fluctuations limit the measurement of g by adding a noise-modeldependence to the extraction of the cyclotron and anomaly frequencies from theirresonance lines; the relative agreement of two line-splitting methods quantifies a lineshape model uncertainty.New techniques promise to increase field stability, narrow the resonance lines, andaccelerate the measurement cycle.The measured g allows tests for physics beyond the Standard Model throughsearches for its temporal variation and comparisons with a “theoretical” g-value calculated from quantum electrodynamics and an independently measured fine structureconstant.
ContentsTitle Page . . . .Abstract . . . . .Table of ContentsList of Figures . .List of Tables . .Acknowledgments.iiiivixxixii1 Introduction1.1 The Electron Magnetic Moment . . . . . . . . . . . . .1.1.1 The fine structure constant . . . . . . . . . . .1.1.2 QED and the relation between g and α . . . . .1.1.3 Comparing various measurements of α . . . . .1.1.4 Comparing precise tests of QED . . . . . . . . .1.1.5 Limits on extensions to the Standard Model . .1.1.6 Magnetic moments of the other charged leptons1.1.7 The role of α in a redefined SI . . . . . . . . . .1.2 Measuring the g-Value . . . . . . . . . . . . . . . . . .1.2.1 g-value history . . . . . . . . . . . . . . . . . .1.2.2 An artificial atom . . . . . . . . . . . . . . . . .1.2.3 The Quantum Cyclotron . . . . . . . . . . . . .123591116242629293032.363639424345455051562 The Quantum Cyclotron2.1 The Penning Trap . . . . . . . . . . . . . . . . . . .2.1.1 Trap frequencies and damping rates . . . . .2.1.2 The Brown–Gabrielse invariance theorem . .2.2 Cooling to the Cyclotron Ground State . . . . . . .2.3 Interacting with the Electron . . . . . . . . . . . .2.3.1 Biasing the electrodes . . . . . . . . . . . .2.3.2 Driving the axial motion . . . . . . . . . . .2.3.3 Detecting the axial motion . . . . . . . . . .2.3.4 QND detection of cyclotron and spin statesv.
Contents2.42.52.3.5 Making cyclotron jumps . . . . . .2.3.6 Flipping the spin . . . . . . . . . .2.3.7 “Cooling” the magnetron motion .The Single-Particle Self-Excited OscillatorSummary . . . . . . . . . . . . . . . . . .vi.3 Stability3.1 Shielding External Fluctuations . . . . . . .3.2 High-Stability Solenoid Design . . . . . . . .3.3 Reducing Motion in an Inhomogeneous Field3.3.1 Stabilizing room temperature . . . .3.3.2 Reducing vibration . . . . . . . . . .3.4 Care with Magnetic Susceptibilities . . . . .3.5 Future Stability Improvements . . . . . . . .4 Measuring g4.1 An Experimenter’s g . . . . . . . . . . . . . . . . . . . . . . .4.2 Expected Cyclotron and Anomaly Lineshape . . . . . . . . . .4.2.1 The lineshape in the low and high axial damping limits4.2.2 The lineshape for arbitrary axial damping . . . . . . .4.2.3 The cyclotron lineshape for driven axial motion . . . .4.2.4 The saturated lineshape . . . . . . . . . . . . . . . . .4.2.5 The lineshape with magnetic field noise . . . . . . . . .4.3 A Typical Nightly Run . . . . . . . . . . . . . . . . . . . . . .4.3.1 Cyclotron quantum jump spectroscopy . . . . . . . . .4.3.2 Anomaly quantum jump spectroscopy . . . . . . . . . .4.3.3 Combining the data . . . . . . . . . . . . . . . . . . . .4.4 Splitting the Lines . . . . . . . . . . . . . . . . . . . . . . . .4.4.1 Calculating the weighted mean frequencies . . . . . . .4.4.2 Fitting the lines . . . . . . . . . . . . . . . . . . . . . .4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 Cavity Control of Lifetimes and Line-Shifts5.1 Electromagnetic Modes of an Ideal Cylindrical Cavity . . . .5.2 Mode Detection with Synchronized Electrons . . . . . . . . .5.2.1 The parametric resonance . . . . . . . . . . . . . . .5.2.2 Spontaneous symmetry breaking in an electron cloud5.2.3 Parametric mode maps . . . . . . . . . . . . . . . . .5.2.4 Mode map features . . . . . . . . . . . . . . . . . . .5.3 Coupling to a Single Electron . . . . . . . . . . . . . . . . .5.3.1 Single-mode approximation . . . . . . . . . . . . . .5.3.2 Renormalized calculation . . . . . . . . . . . . . . . 9101106107109113.115117122123124126130136137139
Contents5.45.55.6vii5.3.3 Single-mode coupling with axial oscillations . . . . . .Single-Electron Mode Detection . . . . . . . . . . . . . . . . .5.4.1 Measuring the cyclotron damping rate . . . . . . . . .5.4.2 Fitting the cyclotron lifetime data . . . . . . . . . . . .5.4.3 Axial and radial (mis)alignment of the electron positionCavity-shift Results . . . . . . . . . . . . . . . . . . . . . . . .5.5.1 2006 cavity shift analysis . . . . . . . . . . . . . . . . .5.5.2 Current cavity shift analysis . . . . . . . . . . . . . . .Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 Uncertainties and a New Measurement of g6.1 Lineshape Model Uncertainty and Statistics .6.1.1 Cyclotron and anomaly lineshapes with6.1.2 The line-splitting procedure . . . . . .6.1.3 2006 lineshape model analysis . . . . .6.1.4 Current lineshape model analysis . . .6.1.5 Axial temperature changes . . . . . . .6.2 Power Shifts . . . . . . . . . . . . . . . . . . .6.2.1 Anomaly power shifts . . . . . . . . . .6.2.2 Cyclotron power shifts . . . . . . . . .6.2.3 Experimental searches for power shifts6.3 Axial Frequency Shifts . . . . . . . . . . . . .6.3.1 Anharmonicity . . . . . . . . . . . . .6.3.2 Interaction with the amplifier . . . . .6.3.3 Anomaly-drive-induced shifts . . . . .6.4 Applied Corrections . . . . . . . . . . . . . . .6.4.1 Relativistic shift . . . . . . . . . . . .6.4.2 Magnetron shift . . . . . . . . . . . . .6.4.3 Cavity shift . . . . . . . . . . . . . . .6.5 Results . . . . . . . . . . . . . . . . . . . . . .6.5.1 2006 measurement . . . . . . . . . . .6.5.2 New measurement . . . . . . . . . . .7 Future Improvements7.1 Narrower Lines . . . . . . . . . . . . . .7.1.1 Smaller magnetic bottle . . . . .7.1.2 Cooling directly or with feedback7.1.3 Cavity-enhanced sideband cooling7.2 Better Statistics . . . . . . . . . . . . . .7.2.1 π–pulse . . . . . . . . . . . . . .7.2.2 Adiabatic fast passage . . . . . .7.3 Remaining questions . . . . . . . . . . .146147149150153159159161162. . . . . . . . . . . .magnetic field noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88189190191191193.196197197199200210210212214.
Contents7.4viiiSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2158 Limits on Lorentz Violation8.1 The Electron with Lorentz Violation . . . . . . .8.1.1 Energy levels and frequency shifts . . . . .8.1.2 Experimental signatures . . . . . . . . . .8.1.3 The celestial equatorial coordinate system8.2 Data Analysis . . . . . . . . . . . . . . . . . . . .8.2.1 Local Mean Sidereal Time . . . . . . . . .8.2.2 Fitting the data . . . . . . . . . . . . . . .8.2.3 Comparisons with other experiments . . .8.3 Summary and outlook . . . . . . . . . . . . . . .9 Conclusion9.1 A New Measurement of g . . . . . . . . . . . . . . . .9.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . .9.2.1 The e g-value and testing CPT . . . . . . . .9.2.2 The proton-to-electron mass ratio . . . . . . .9.2.3 The proton and antiproton magnetic moments9.2.4 A single electron as a qubit . . . . . . . . . .9.3 Summary . . . . . . . . . . . . . . . . . . . . . . . 235237A Derivation of Single-Mode Coupling with Axial Oscillations238Bibliography242
List of Figures1.11.21.31.41.5Electron g-value comparisons . . . . . . . . . . . . .Sample Feynman diagrams . . . . . . . . . . . . . . .Theoretical contributions to the electron g . . . . . .Various determinations of the fine structure constantThe energy levels of a trapped electron . . . . . . . .2589322.12.22.32.42.52.62.72.82.9Cartoon of an electron orbit in a Penning trap . . .Sectioned view of the Penning trap electrodes . . .The entire apparatus . . . . . . . . . . . . . . . . .Trap electrode wiring diagram . . . . . . . . . . . .Typical endcap bias configurations . . . . . . . . .Radiofrequency detection and excitation schematicMagnetic bottle measurement . . . . . . . . . . . .Two quantum leaps: a cyclotron jump and spin flipThe microwave system . . . . . . . . . . . . . . . .3738444749545758603.13.23.33.4. . . .the. . . . . . . . . .vac. . . . . . .7072743.53.6The subway effect . . . . . . . . . . . . . . . . . . . . . . . .Magnet settling time . . . . . . . . . . . . . . . . . . . . . .Trap support structure and room temperature regulation . .Typical floor vibration levels and improvements from movinguum pumps . . . . . . . . . . . . . . . . . . . . . . . . . . .Daytime field noise . . . . . . . . . . . . . . . . . . . . . . .A new high-stability apparatus . . . . . . . . . . . . . . . .4.14.24.34.44.54.64.74.8The relativistic shift of the cyclotron frequency . . .The energy levels of a trapped electron . . . . . . . .The theoretical lineshape for various parameters . . .Cyclotron quantum jump spectroscopy . . . . . . . .Anomaly quantum jump spectroscopy . . . . . . . . .Field drift removal from monitoring the cyclotron lineAxial frequency dip . . . . . . . . . . . . . . . . . . .Sample cyclotron and anomaly line fits . . . . . . . .ix. . . . . . . . . . .edge. . . . .77788083859098100102104112
List of Figuresx5.15.2Examples of cylindrical cavity modes . . . . . . . . . . . . . . . . . .Characteristic regions of the damped Mathieu equation and the hysteretic parametric lineshape . . . . . . . . . . . . . . . . . . . . . . .5.3 Parametric mode maps . . . . . . . . . . . . . . . . . . . . . . . . . .5.4 Modes TE127 and TE136 with sidebands . . . . . . . . . . . . . . . . .5.5 Image charges of an electron offset from the midpoint of two parallelconducting plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.6 Calculated cyclotron damping rates at various z . . . . . . . . . . . .5.7 Typical cyclotron damping rate measurement . . . . . . . . . . . . .5.8 Lifetime data with fit . . . . . . . . . . . . . . . . . . . . . . . . . . .5.9 Comparison of lifetime fit results . . . . . . . . . . . . . . . . . . . .5.10 Measurement of the axial offset between the electrostatic and modecenters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.11 Cavity shift results . . . . . . . . . . . . . . . . . . . . . . . . . . . .66.7Lineshape analysis from 2006 . . . . . . . . . . . . . . . . . . . . . .Cyclotron and anomaly lines from each field with fits . . . . . . . . .Comparing methods for extracting g from the cyclotron and anomalylines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Study of cyclotron and anomaly power shifts . . . . . . . . . . . . . .The energy levels of a trapped electron . . . . . . . . . . . . . . . . .g-value data before and after applying the cavity shift . . . . . . . . .Comparison of the new g-value data and their average . . . . . . . . .1731831881911947.17.27.37.4Sideband cooling and heating lines . . . .Enhanced cavity coupling near a mode . .Measured axial–cyclotron sideband heatingThe energy levels of a trapped electron . .2032062072118.18.2Anomaly excitations binned by sidereal time . . . . . . . . . . . . . . 224Lorentz violation results . . . . . . . . . . . . . . . . . . . . . . . . . 2269.1Electron g-value comparisons . . . . . . . . . . . . . . . . . . . . . . 232. . . . . . . . . . .resonance. . . . . .171172
List of Tables1.11.21.3Tests of QED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Contributions to the theoretical charged lepton magnetic moments . .Current and proposed reference quantities for the SI . . . . . . . . . .1325272.12.2Typical trap parameters . . . . . . . . . . . . . . . . . . . . . . . . .Trap frequencies and damping rates . . . . . . . . . . . . . . . . . . .39415.15.21295.45.5Mode frequencies and Qs . . . . . . . . . . . . . . . . . . . . . . . . .Comparison of mode parameters from single and multi-electron techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Limits on the radial alignment between the electrostatic and modecenters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Parameters used in calculating the cavity shifts . . . . . . . . . . . .Calculated cavity shifts . . . . . . . . . . . . . . . . . . . . . . . . . .6.16.26.36.46.56.6Summary of the lineshape model analysis . . . . . . . . . .Fitted axial temperatures . . . . . . . . . . . . . . . . . .Summary of power-shift searches . . . . . . . . . . . . . .Calculated cavity shifts . . . . . . . . . . . . . . . . . . . .Corrected g and uncertainties from the 2006 measurementCorrected g and uncertainties . . . . . . . . . . . . . . . .1751761831901921937.1Mode geometric factors for cavity-assisted sideband cooling . . . . . . 2045.3xi.151157160161
AcknowledgmentsThis thesis is the seventh stemming from electron work in our lab over two decades.I am indebted to those who came before me, including Joseph Tan (thesis in 1992),Ching-hua Tseng (1995), Daphna Enzer (1996), Steve Peil (1999), and postdoc KamalAbdullah. In particular, my own training came through close interaction with BrianD’Urso (2003), who designed the amplifiers and electron self-excitation scheme thatprovide our signal, and Brian Odom (2004), whose passion and dedication led to our2006 result. It was a privilege to work with these two fine scientists.Professor Jerry Gabrielse had the vision for an improved electron magnetic moment measurement using a cylindrical Penning trap and lower temperatures as wellas the stamina to pursue it for 20 years. He has been generous with his experimental knowledge and advice, constantly available in person or by phone, and adept atacquiring support. I am grateful for the opportunity to learn from him.Shannon Fogwell has kept the apparatus running while I analyzed results andwrote this thesis. She took much of the data contained herein, and her positron trapis the future for this experiment. Yulia Gurevich helped briefly before embarking ona quest for the electron’s “other” dipole moment. I have truly enjoyed working withmany graduate students and postdocs throughout my tenure, especially those in theGabrielse Lab: Andrew Speck, Dan Farkas, Tanya Zelevinsky, David LeSage, NickGuise, Phil Larochelle, Josh Goldman, Steve Kolthammer, Phil Richerme, RobertMcConnell, and Jack DiSciacca, as well as Ben Levitt, Jonathan Wrubel, Irma Kuljanishvili, and Maarten Jansen. Each has helped this work in his or her own way,whether helping with magnet fills, letting me “borrow” cables, or simply ponderingphysics.xii
AcknowledgmentsxiiiIt has been a pleasure having undergraduates around the lab, including five whomI supervised directly: Verena Martinez Outschoorn, Aram Avetisyan, Michael vonKorff, Ellen Martinsek, and Rishi Jajoo. They performed tasks as diverse as characterizing laboratory vibrations, designing a pump room and vacuum system, andcalculating the magnetic field homogeneity and inductance matrix for a new solenoid.The Army Research Office funded my first three years as a graduate studentthrough a National Defense Science and Engineering Graduate (NDSEG) Fellowship.The National Science Foundation generously supports this experiment.Numerous teachers have encouraged me throughout the years. Without the loveand support of my family I could not have made it this far. My wife, Mandi Jo, hasbeen particularly supportive (and patient!) as I finish my graduate studies.
Chapter 1IntroductionA particle in a box is the prototype of a simple and elegant system. This thesisdescribes an experiment with a particle, a single electron trapped with static magneticand electric fields, surrounded by a cylindrical metal box. The interaction between theelectron and the electromagnetic modes of the box induces frequency shifts, inhibitsspontaneous emission, and, with the box cooled to freeze out blackbody photons,prepares the electron cyclotron motion in i
A single electron in a quantum cyclotron yields new measurements of the electron magnetic moment, given by g 2 1:00115965218073(28)[0:28 ppt], and the ne structure constant, 1
Cavities of the Body Organs are located within body cavities. Cavities are large internal spaces. There are two major cavities: Dorsal cavity – made up of 2 divisions, the spinal (vertebral) cavity and the cranial cavity. Ventral cavity – made up of 2 divisions; the thoracic cavity and abdominopelvic cavity. Dorsal Cavity
SRF2005 Workshop Cornell University, July 10,2005 2 Outline of the Tutorial Introduction: applications for high-b SC cavities and machine requirements Features important in cavity design RF design and optimization (fundamental mode): Figures of merit for good accelerating cavity design Codes used for calculation and example results An example of cavity shape optimization: The Low Loss Cavity,
RMAX Cavity Battens The RMAX cavity battens are an integral component of the RMAX Batten Cavity EIFS Cladding wall system and must be applied as part of the RMAX EIFS system for the RMAX Statutory Warranty to apply. The RMAX cavity battens measure 1250mm x 40mm x 25mm and are manufactured by RMAX from high density X28 grade, Isolite Expanded
The Purpose of Cavity Filler on Ball Valve . The cavity filled ball valves are with . over 92% PTFE or TFM filler for the valve cavity. Most of the usage on cavity filled valve is in: . STEEL PIPER. PTFE PTFE. 6803 Theall Rd Building B, Houston, Texas. 77066 Phone : 1 (832) 666-5576 www.morrisvalve.com .
The oral cavity, known sometimes as “buccal cavity”, is the start of the alimentary canal. The content of the oral cavity determines its function. It houses the structures necessary for mastication and speech, which include teeth,
Body organization 1. Body cavities – hollow spaces within the human body that contain internal organs. a) The dorsal cavity: located toward the back of the body, is divided into the cranial cavity (which holds the brain) and vertebral or spinal cavity (which holds the spinal cord). b) The ventral cavity:
circuit used to obtain the approximate frequency of the front-cavity resonance of the config-uration in (a). The volume of the front cavity is represented by Cf, and the constrictions poste-rior and anterior to the cavity are represented by R, M, R,, and M,. Zb is the impedance of the cavity behind the constriction. I
cavity entrance (if necessary) with opening instrument (hatchet), (b) excavation of caries with spoon excavators, resulting in a clean enamel-dentino junction and affected dentin in the central part of the cavity, (c) cleaning of cavity with wet and dry cotton pellets, (d) application of cavity
