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New Apparatus and Methods for the Measurement of the Proton and Antiproton Magnetic Moments

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New Apparatus and Methods for the Measurement of the Proton and Antiproton Magnetic Moments New Apparatus and Methods for the Measurement of the Proton and Antiproton Magnetic Moments A thesis presented by Mason Claflin Marshall 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 May 2019 May 2019 - Mason Claflin Marshall All rights reserved. Dissertation advisor Author Gerald Gabrielse Mason Claflin Marshall New Apparatus and Methods for the Measurement of the Proton and Antiproton Magnetic Moments Abstract The first direct measurement of the antiproton magnetic moment was performed using a single particle in a Penning trap. The result, μpˉ/μN = 2.792 845 (12) [4.4 ppm], is 680 times more precise than the previous best measurement. Together with a prior measurement of the proton magnetic moment in the same apparatus, this was the first direct comparison of the proton and antiproton magnetic moments. This stringent test of CPT invariance gave μpˉ/μp = 1.000 000 (5) [5.0 ppm]. The − observation of individual spin flips of a single proton, also reported here, opened the possibility of further improving measurement precision by orders of magnitude. Improving this result by a factor of 104 requires measuring μ outside the large ∼ magnetic field gradient needed to detect spin flips. Two methods are proposedto avoid the leading uncertainties in such a high-precision two-trap measurement. One of these is to measure single spin-flips of a single proton or antiproton. The otheris to induce multiple spin flips in the presence of a spin-cyclotron coupling drive, and observe the resulting change in the cyclotron energy. The design, construction, and commissioning of an appropriate apparatus, with high-quality particle detection and newly designed Penning trap electrodes, is reported. iii Contents Title Page .................................... i Abstract ..................................... iii Table of Contents ................................ iv List of Figures .................................. vi List of Tables .................................. vii Acknowledgments . viii 1 Introduction 1 1.1 Proton and antiproton magnetic moments ............... 2 1.2 Measurement history ........................... 3 1.3 CPT symmetry .............................. 5 1.4 Overview of work presented ....................... 8 2 Proton in a Penning Trap 12 2.1 Penning Trap Principles ......................... 12 2.1.1 Axial motion ........................... 13 2.1.2 Cyclotron and magnetron frequencies . 17 2.1.3 Measuring g: the Larmor frequency . 18 2.1.4 Experimental frequencies and parameters . 18 2.2 The magnetic gradient .......................... 19 2.3 Image current detection ......................... 23 2.4 Measuring and driving the axial frequency . 25 2.4.1 Driven axial detection ...................... 25 2.4.2 Axial dips ............................. 27 2.4.3 Feedback and the self-excited oscillator . 29 2.5 Cyclotron driving and detection ..................... 31 2.5.1 Obtaining a single proton .................... 34 2.6 Magnetron sideband cooling ....................... 36 2.6.1 Using sideband drives for initial particle detection . 36 2.6.2 Magnetron frequency measurement – "split dips" and avoided crossing .............................. 39 iv Contents 2.7 Spin flip and anomaly drives ....................... 40 3 Antiproton Magnetic Moment Measurement 43 3.1 Trapping and cooling antiprotons .................... 44 3.2 2013 measurement methodology ..................... 51 3.2.1 Measurement procedure in the analysis trap . 51 3.2.2 Measuring transition probability via the Allen deviation . 53 3.2.3 Axial stability and selecting a cold cyclotron state . 54 3.3 Magnetic field stability .......................... 56 3.4 Lineshapes ................................. 56 3.5 Antiproton magnetic moment measurement . 59 4 Observing Single-Proton Spin Flips 62 4.1 Identifying single spin flips from frequency differences . 64 4.2 Experimental demonstration of single spin flip identification . 67 4.3 Improving spin-state detection for quantum jump spectroscopy . 72 4.3.1 Reduced background fluctuations and multiple trials . 73 4.3.2 Adiabatic fast passage ...................... 76 4.4 Conclusion ................................. 79 5 Precision Measurement Methods with Single Spin Flips 80 5.1 Historical two-trap measurement methods . 81 5.2 Separated oscillatory fields measurement of νc . 83 5.2.1 Measuring ρc in the analysis trap . 88 5.2.2 Estimated cyclotron frequency measurement precision using SOF 94 5.3 Separated oscillatory fields measurement of νs . 98 6 Quantum Walk Measurement of the Magnetic Moment 105 6.1 Measurement scheme . 106 6.2 Single-drive Rabi frequencies and lineshapes . 111 6.2.1 Residual magnetic bottle linewidth and relativistic shift . 112 6.2.2 Power-broadened linewidth and drive strength . 114 6.3 Quantum state evolution under the simultaneous anomaly and spin drives ................................... 117 6.3.1 Rotating wave approximation for simultaneous drives . 118 6.3.2 Quantum walk overview . 120 6.3.3 Quantum walk of the cyclotron state . 121 6.4 Lineshape and Precision . 126 6.4.1 Detuning and Power Broadened Linewidth . 126 6.4.2 Estimating Background - Noise and Cyclotron State Change . 129 6.4.3 Magnetic Field Drift and Signal-To-Noise . 131 6.5 Cyclotron detuning Δcd . 133 v Contents 6.6 Numerical estimates of statistical precision for different experimental parameters ................................ 136 6.7 Comparison between Anomaly and Single-Spin-Flip methods . 141 6.8 Conclusion ................................. 145 6.9 Appendix: rotating wave approximation for simultaneous drives . 146 7 Cryogenic Single-Particle Detection 150 7.1 Detection Overview ............................ 151 7.2 The axial tuned circuit . 152 7.2.1 Superconducting toroid design principles . 154 7.2.2 Measuring and comparing amplifiers . 157 7.2.3 Improvements to axial coil construction and materials . 160 7.2.4 The cryogenic FET and circuitboard . 166 7.2.5 Feedback and stability . 171 7.2.6 Feedback and transconductance-dependent amplifier Q . 172 7.2.7 Experimentally Realized Axial Amplifiers . 179 7.2.8 Prospects for further improvement of axial detection . 180 7.3 Second stage amplifiers . 187 7.4 Cyclotron amplifiers . 191 7.4.1 Precision trap cyclotron amplifier and FET switch . 192 7.4.2 The cooling trap cyclotron amp . 194 7.4.3 Superconducting cyclotron amplifiers and magnetic field . 196 8 A New Apparatus for Sub-ppb Measurements 199 8.1 Penning trap design and construction . 200 8.1.1 Magnetic design in the precision trap . 202 8.1.2 Analysis, cooling, and loading traps . 206 8.1.3 Trap electrode construction . 211 8.2 Trapcan, pinbase, and tripod . 218 8.3 Experiment cryostat and mechanical structure . 222 8.3.1 Titanium cryostat . 222 8.3.2 Thermal gradients in titanium . 223 8.3.3 Thermoacoustic oscillations . 225 8.3.4 Thermal isolation stage . 228 8.4 DC Wiring ................................. 230 8.5 Tuned circuit drive lines . 230 8.5.1 Transmission line resonator . 234 8.5.2 2012-13 results with transmission line resonator . 237 8.5.3 2017 improvements – LC drive resonator . 240 8.6 Cryogenic alignment system . 246 8.6.1 Cryogenic gearbox . 246 8.6.2 FEP-resistive anode alignment sensor . 251 vi Contents 9 Results and Status of the New Apparatus 255 9.1 Experiment cryostat . 255 9.2 Particle loading and alignment . 256 9.3 Axial signals in the precision trap . 257 9.4 Cyclotron signals in the precision trap . 261 9.5 Commissioning the analysis trap . 264 9.6 Conclusion ................................. 266 10 Next Steps Towards a Sub-ppb Measuremetn 267 10.1 Steps to a sub-ppb measurement . 267 10.1.1 Characterizing the analysis trap . 268 10.1.2 The self-excited oscillator . 269 10.1.3 Feedback and axial temperature . 270 10.1.4 Cyclotron quantum number measurement . 270 10.1.5 Characterization of the FET switch and cyclotron energy back- ground noise ............................ 270 10.1.6 Developing cyclotron frequency measurement techniques . 272 10.1.7 Evaluate the magnetic field . 274 10.1.8 Commissioning the cooling trap . 275 10.1.9 Selecting a sub-ppb measurement method . 277 10.2 Further apparatus improvements . 277 10.2.1 Improvements to detection . 278 10.2.2 Cyclotron amplifier decoupling . 278 10.2.3 Improvements to wiring . 279 10.2.4 Controlling the magnetic bottle . 280 11 Conclusion 285 11.1 Results in the first-generation apparatus . 285 11.2 Two methods for sub-ppb precision . 286 11.3 A new, improved apparatus . 287 Bibliography 289 vii List of Figures 1.1 History of proton and antiproton magnetic moment measurements . 5 2.1 Motions of a charged particle in a Penning trap . 13 2.2 Coordinate system and trap dimensions for the precision trap. 14 2.3 Penning trap stacks ............................ 20 2.4 Analysis trap and magnetic bottle field . 22 2.5 Simplified schematic of circuits for axial and cyclotron image current detection. ................................. 23 2.6 Drive scans at different voltage ratios in the new apparatus . 27 2.7 One-particle dip in the new apparatus . 28 2.8 Dip spectra at different ratios ...................... 28 2.9 Schematic of circuit for axial feedback . 29 2.10 Axial signals in the apparatus used for the 2013 antiproton measurement. 31 2.11 Excited cyclotron signals for different particle numbers. 32 2.12 Cyclotron decay in the new apparatus . 34 2.13 Two-particle cyclotron decay ....................... 35 2.14 Axial
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