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Atomic Parity Violation and Related Physics in Ytterbium by Dimitri

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Atomic Parity Violation and Related Physics in Ytterbium by Dimitri Atomic Parity Violation and Related Physics in Ytterbium by Dimitri Robert Dounas-Frazer A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Dmitry Budker, Chair Professor Hartmut H¨affner Professor Robert Harris Fall 2012 Atomic Parity Violation and Related Physics in Ytterbium Copyright 2012 by Dimitri Robert Dounas-Frazer 1 Abstract Atomic Parity Violation and Related Physics in Ytterbium by Dimitri Robert Dounas-Frazer Doctor of Philosophy in Physics University of California, Berkeley Professor Dmitry Budker, Chair 2 1 3 Atomic parity violation has been observed in the 408 nm 6s S0 ! 5d6s D1 forbidden −10 transition of ytterbium. The parity-violating amplitude is 8:7(1:4) × 10 ea0, two orders of magnitude larger than in cesium, where the most precise experiments to date have been performed. This is in accordance with theoretical predictions and constitutes the largest atomic parity-violating amplitude yet observed. This also opens the way to future measure- ments of neutron skins and anapole moments by comparing parity-violating amplitudes for various isotopes and hyperfine components of the transition. We present a detailed description of the observation. Linearly polarized 408 nm light interacts with ytterbium atoms in crossed electric (E) and magnetic fields (B). The proba- 2 1 3 bility of the 6s S0 ! 5d6s D1 transition contains a parity-violating term, proportional to (E · B)[(E × E) · B], arising from interference between the amplitudes of transitions induced by the electroweak interaction and the Stark effect (E is the optical electric field). The 3 transition probability is detected by measuring the population of the metastable 6s6p P0 3 state, to which 65% of the atoms excited to the 5d6s D1 state spontaneously decay. The 3 population of the 6s6p P0 state is determined by resonantly exciting the atoms with 649 nm 3 light to the 6s7s S1 state and collecting the fluorescence resulting from its decay. Systematic corrections due to imperfections in the applied electric and magnetic fields are determined in auxiliary experiments. The statistical uncertainty is dominated by parasitic frequency ex- cursions of the 408-nm excitation light due to imperfect stabilization of the optical reference with respect to the atomic resonance. The present uncertainties are 9% statistical and 8% systematic. Methods of improving the accuracy for the future experiments are discussed. We further present a measurement of the dynamic scalar and tensor polarizabilities of 3 ytterbium's 5d6s D1 state. The polarizabilities were measured by analyzing the spectral 2 1 3 lineshape of the 6s S0 ! 5d6s D1 transition. Due to the interaction of atoms with the standing wave, the lineshape has a characteristic polarizability-dependent distortion. A the- oretical model was used to simulate the lineshape and determine a combination of the polar- izabilities of the ground and excited states by fitting the model to experimental data. This combination was measured with a 13% uncertainty, only 3% of which is due to uncertainty 2 in the simulation and fitting procedure. By comparing two different combinations of polar- 3 izabilities, the scalar and tensor polarizabilities of the state 5d6s D1 were measured to be 3 −2 3 −2 α0( D1) = 0:151(36) Hz · (V=cm) and α2( D1) = −0:205(53) Hz · (V=cm) , respectively. We show that this technique can be applied to similar atomic systems. Finally, we propose two methods for improving future measurements of atomic parity violation using two-photon transitions. The first method is characterized by the absence of static external electric and magnetic fields. Such measurements can be achieved by observing the interference of parity-conserving and parity-violating two-photon transition amplitudes between energy eigenstates of zero electronic angular momentum. General expressions for induced two-photon transition amplitudes are derived. The two-photon scheme using the 2 1 1 3 6s S0 ! 6s6p P1 ! 6s6p P0 transition in ytterbium (λ1 = 399 nm, λ2 =1280 nm) is proposed as a crosscheck of the APV experiment which uses the single-photon 408 nm 2 1 3 6s S0 ! 5d6s D1 transition. We estimate that the signal-to-noise ratio of the proposed experiment is comparable to that achieved in the 408 nm system. The second method allows for measurement of nuclear spin dependent atomic parity violation without nuclear spin independent background. Such measurements can be achieved by driving parity-violating two-photon J = 0 ! 1 transitions driven by identical photons in the presence of an external static magnetic field. We discuss two promising applications: the 2 1 1 2 1 3 462 nm 5s S0 ! 5s9p P1 transition in strontium-87, and the 741 nm 7s S0 ! 7s7p P1 transition in unstable radium-225. i To my brother, Alexi, for being a constant reminder that there are things in life more important than physics. ii Contents Contents ii List of Figures iv List of Tables v 1 Introduction 1 1.1 History and background . 2 1.2 Implications . 4 1.3 The case for ytterbium . 7 2 Observation of APV in ytterbium 8 2.1 Experimental technique for the APV measurement . 9 2.2 PV signature: Ideal case . 11 2.3 PV signature: Impact of apparatus imperfections . 14 2.4 Experimental apparatus . 17 2.5 Results and analysis . 22 2.6 Error budget . 25 3 Measurement of ac polarizabilities in ytterbium 29 3.1 Atomic system . 30 3.2 Spectral lineshape . 33 3.3 Application to ytterbium . 43 3.4 Summary and Outlook . 50 4 Novel schemes for measuring APV 52 4.1 APV in J = 0 ! 0 two-photon transitions . 52 4.2 APV in J = 0 ! 1 two-photon transitions . 62 5 Future APV experiments 71 Bibliography 73 iii A Details of the Yb APV experiment 82 A.1 Derivation of transition amplitudes . 82 A.2 Characterization of the PBC mirrors . 84 A.3 Impact of the phase mixing effect on the harmonics ratio . 86 B Details of the AC polarizability experiment 89 B.1 Frequency dependence of dynamic polarizabilities . 89 B.2 System of equations used in numerical model . 90 C Derivation of transition amplitudes for the AOS 91 D Derivation of transition amplitudes for the DPS 94 D.1 Bose-Einstein statistics selection rules . 94 D.2 Wigner-Eckart theorem . 95 D.3 E1-M1 and E1-E2 transition amplitudes . 95 D.4 Induced E1-E1 transitions . 96 iv List of Figures 1.1 Electromagnetic and electroweak radiative processes . 2 1.2 Running of the weak mixing angle . 5 2.1 Energy levels and atomic transitions for APV in Yb . 10 2.2 Experimental apparatus . 12 2.3 Effects of electric field modulation . 14 2.4 Power build-up cavity . 17 2.5 Optical setup . 18 2.6 Wire frame electrodes . 20 2.7 Spectroscopic profile . 22 2.8 APV asymmetry in ytterbium . 25 2.9 Frequency excursions of Fabry-P´erot´etalon . 27 3.1 Energy-level diagram for Lineshape Simulation Method . 33 3.2 Parameters of atomic trajectory . 34 3.3 Absorption prpfile . 37 3.4 Simulated lineshapes . 41 3.5 Ytterbium energy levels and transitions for LSM . 44 3.6 Experimental apparatus for LSM . 46 3.7 Results of LSM fitting program . 47 4.1 Energy level diagram for All-Optical Scheme . 54 4.2 Ytterbium energy levels and transitions for AOS . 60 4.3 Energy level diagram for Degenerate Photon Scheme . 64 A.1 Finesse of power build-up cavity . 85 v List of Tables 1.1 Stable isotopes of ytterbium . 7 2.1 Effects of stray fields on partial asymmetries . 15 2.2 Parasitic sources of asymmetry . 16 2.3 Measured values of stray fields . 23 2.4 Error budget for APV asymmetry . 28 3.1 Summary of results from LSM . 48 3.2 Error budget for LSM . 50 4.1 Atomic data for application of AOS to ytterbium . 61 4.2 Atomic data for application of DPS to strontium and radium . 69 5.1 Summary of APV methods . 72 vi Acknowledgments When I started grad school at Berkeley in 2007, the Physics Department was still in the habit of administering two sets of preliminary exams: written exams and oral ones. They were tough, but the Colorado School of Mines prepared me well enough that I passed them all on the first try. I sent a jubilant email to several CSM faculty and staff thanking them for being such great teachers and mentors, so I won't list them all by name here; instead, I'll just acknowledge the wonderful education I received at CSM. The preliminary exams served not only as an introduction to the Berkeley Physics De- partment, but as an introduction to Dima Budker as well. Dima co-administered my oral exam on modern physics. By the end of my first year, I'd joined his research group and started working on the ytterbium experiment. Throughout my time in his group, Dima has been a great mentor, striking a good balance between skepticism, curiosity, and friendliness. He's also been supportive of my interest in physics education. I'm incredibly grateful to Dima for his guidance over the years. The results in this dissertation are due to the hard work of a number of people over the course of about 17 years. During my relatively short time at Berkeley, I've only had the pleasure of meeting a small handful of them. I've been fortunate to work with a talented team of people, including: Kostya Tsigutkin, who led the ytterbium project when I first joined the group; Damon English, with whom I collaborated on several projects; Nathan Leefer, a good friend and colleague; Afrooz Family, Jim Tang, and Pasha Reshetikhin, all who worked on the ytterbium project as undergraduates; and many others.
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