1. Correlated cyclotron and spin measurements to make an improved measurement of the electron magnetic moment Elise Novitski Harvard University Lepton Moments 21 July 2014

2. Correlated cyclotron and spin measurements to make an improved measurement of the electron magnetic moment Elise Novitski Harvard University Lepton Moments 21 July 2014 Shannon Fogwell Hoogerheide

3. Acknowledgements 2 Prof. Gerald Gabrielse PhD Students: Ronald Alexander (new student) Maryrose Barrios (new student) Elise Novitski (PhD in progress…) Joshua Dorr (PhD, Sept. 2013) Shannon Fogwell Hoogerheide (PhD, May 2013)

4. Standard Model Triumph Most Precisely Measured Property of an Elementary Particle Tests the Most Precise Prediction of the Standard Model Experiment: Standard Model: Testing the CPT Symmetry built into the Standard Model Electron: Positron: 3 D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008) R. Boucjendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, Phys. Rev. Lett. 106, 080801 (2011) T. Aoyama, M. Hayakawa, T. Kinoshita, and M. Nio, Phys. Rev. Lett. 109, 111808 (2012)

5. Fine Structure Constant Most Precise determination of α 4 D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008) R. Boucjendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, Phys. Rev. Lett. 106, 080801 (2011) T. Aoyama, M. Hayakawa, T. Kinoshita, and M. Nio, Phys. Rev. Lett. 109, 111808 (2012)

6. Fine Structure Constant Most Precise determination of α 5 D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008) R. Boucjendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, Phys. Rev. Lett. 106, 080801 (2011) T. Aoyama, M. Hayakawa, T. Kinoshita, and M. Nio, Phys. Rev. Lett. 109, 111808 (2012) We want to improve the experimental precision!

7. Ingredients of a g/2 measurement 6 Measure cyclotron frequency Measure anomaly frequency Measure axial frequency (less precision needed) Calculate special relativistic shift (  ) Calculate  from measured cavity mode couplings D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

8. Ingredients of a g/2 measurement 7 Measure cyclotron frequency Measure anomaly frequency Measure axial frequency (less precision needed) Calculate special relativistic shift (  ) Calculate  from measured cavity mode couplings D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

9. Ingredients of a g/2 measurement 8 Measure cyclotron frequency Measure anomaly frequency Measure axial frequency (less precision needed) Calculate special relativistic shift (  ) Calculate  from measured cavity mode couplings D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

10. Uncertainties in the 2008 measurement c / GHz = 147.5149.2150.3151.3 Statistics0.390.17 0.24 Cavity shift0.130.060.070.28 Uncorrelated lineshape model 0.560.000.150.30 Correlated lineshape model 0.24 Total0.730.300.340.53 Uncertainties for g in parts-per-trillion. g/2 = 1.001 159 652 180 73 (28) [0.28 ppt] 9 Leading uncertainty is lineshape model uncertainty– limits precision to which it is possible to split our anomaly and cyclotron lines D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

11. Spin and cyclotron detection 10 Magnetic bottle creates z-dependent B field, which adds another term to axial Hamiltonian Modifies axial frequency to depend on spin and cyclotron states: L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)

12. Coupling to axial motion broadens cyclotron and anomaly lines L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986) B. D’Urso et al., Phys. Rev. Lett. 94, 113002 (2005) D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008) 11

13. New Technique: Correlated Measurement 2008 Protocol Cyclotron attempts followed by anomaly attempts Combine data, adjust for field drift, fit both lines to extract g/2 New Protocol Apply cyclotron and anomaly drives simultaneously Generate 2-D correlated lineshape, extract g/2 12 cyclotron detuning

14. 1)Cyclotron transition attempts at range of frequencies 1)Anomaly transition attempts at range of frequencies 1)Repeat steps 1 and 2 several times 2)Measure magnetic field 1)Repeat steps 1-4 several times 1)Combine data, adjusting for measured magnetic field drift 2)Fit to both lineshapes to determine g-value The 2008 measurement protocol corrects only for slow magnetic field drifts 13 D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

15. Advantages of the correlated measurement protocol Eliminates magnetic field drifts between a given anomaly and cyclotron data point In low-axial-damping limit, system stays in single axial state during a measurement, creating discrete peaks Combined with cooling to axial ground state, each point is a full g-2 measurement cyclotron frequency detuning 14 L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986) B. D’Urso, Ph.D. thesis, Harvard University (2003)

16. Technical challenges of the correlated measurement protocol Need to be in low axial damping limit to take full advantage, so must develop a method of decoupling particle from amplifier Lower transition success rate, so statistics could be an issue – Both cyclotron and anomaly drive attempts must be successful to get an excitation – Much narrower lines, and must still know B-field well enough to drive transitions 15 L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986) B. D’Urso, Ph.D. thesis, Harvard University (2003)

17. Spin and cyclotron detection 16 Magnetic bottle creates z-dependent B field, which adds another term to axial Hamiltonian Modifies axial frequency to depend on spin and cyclotron states: L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)

18. Coupling to axial motion broadens cyclotron and anomaly lines L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986) B. D’Urso et al., Phys. Rev. Lett. 94, 113002 (2005) D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008) 17

19. How cyclotron and anomaly lines are affected by axial temperature 18 cyclotron frequency detuning anomaly frequency detuning excitation fraction Cyclotron line: Axial damping slow compared to measurement time Width proportional to axial temperature Anomaly line: Axial damping fast compared to measurement time Width proportional to square of axial temp Both lines: weighted mean offset from “zero-axial-amplitude” frequency by an amount proportional to axial temperature L. S. Brown, Ann. of. Phys. 159, 62-98 (1984)

20. Techniques for improving cyclotron and anomaly frequency measurements 19 D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008) Narrower lines – Smaller magnetic bottle – Lower axial state via cavity-assisted axial sideband cooling Cleaner lineshapes for finer linesplitting – Reduce vibrational noise (improve support structure to maintain alignment) – Improve magnet stability (changes to cryogen spaces and magnet design) – Reduce effect of magnetic field fluctuations by switching to correlated measurement protocol

21. Axial decoupling and the discrete lineshape limit 20 L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986) B. D’Urso, Ph.D. Thesis, Harvard University, 2003 A technical challenge: decoupling particle from amplifier to prevent reheating of axial motion A consequence of decoupling: reaching the discrete-lineshape limit in one or both lines, where quantum nature of axial motion is evident With cavity-assisted axial sideband cooling, goal is to reach lowest axial state

22. Cavity-assisted axial sideband cooling L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986) 21 Apply a drive at to couple axial and cyclotron motions Cooling limit: Cooling rate: Interaction with the resonant microwave cavity mode structure: a challenge that can be converted into an advantage Decouple axial motion from amplifier

23. Trap as a resonant microwave cavity Power coupling efficiency: TE 111 27.4 GHz 22 L. S. Brown, G. Gabrielse, K. Helmerson, and J. Tan, Phys. Rev. Lett. 51, 44-47 (1985) L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986) J. Tan and G. Gabrielse, Phys. Rev. A 48, 3105-3122 (1993) D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

24. Cooling modes and damping modes Only certain modes cool: need electric field like at trap center These modes both couple power into cavity and give geometrical E field enhancement factor Plots: transverse E-field on cross sections of a cooling mode in the trap 23 Some other modes strongly damp cyclotron motion, shifting g-value and limiting cyclotron lifetime L. S. Brown, G. Gabrielse, K. Helmerson, and J. Tan, Phys. Rev. Lett. 51, 44-47 (1985) L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986) J. Tan and G. Gabrielse, Phys. Rev. A 48, 3105-3122 (1993) D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

25. Cavity mode structure of the 2008 trap was not conducive to cavity-assisted axial sideband cooling Strong cyclotron damping modes: cause short lifetime and cavity shift, so must be avoided Cooling modes: enable axial-cyclotron sideband cooling Trap dimensions Trap radius/height ratio Measurements done in this range Frequencies good for avoiding cyclotron modes were 30 linewidths away from good cooling modes Cooling was attempted but axial ground state was never reached 24 D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008) D. Hanneke, Ph.D. thesis, Harvard University (2007)

26. Cavity mode structure of the new trap will enable cavity-assisted axial sideband cooling New g-2 measurements will be done here New trap dimensions Trap radius/height ratio Strong cyclotron damping modes: cause short lifetime and cavity shift, so must be avoided Cooling modes: enable axial-cyclotron sideband cooling Can drive directly on good cooling mode Axial ground state should be achievable 25 S. Fogwell Hoogerheide, Ph.D. Thesis, Harvard University, 2013

27. Additional techniques for improving cyclotron and anomaly frequency measurements 26 D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008) Narrower lines – Smaller magnetic bottle – Lower axial state via cavity-assisted axial sideband cooling Cleaner lineshapes for finer linesplitting – Reduce vibrational noise (improved support structure to maintain alignment) – Improve magnet stability (changes to cryogen spaces and magnet design)

28. Techniques for improving cyclotron and anomaly frequency measurements Narrower lines – Smaller magnetic bottle – Lower axial state via cavity-assisted axial sideband cooling Cleaner lineshapes for finer linesplitting – Reduce vibrational noise (improve support structure to maintain alignment) – Improve magnet stability (changes to cryogen spaces and magnet design) – Reduce effect of magnetic field fluctuations by switching to correlated measurement protocol 27 D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

29. Another frontier: better statistics Rate-limiting step: wait for cyclotron decay after anomaly transition attempt (or correlated transition attempt) To speed this step, sweep down with adiabatic fast passage or π-pulse c / GHz = 147.5149.2150.3151.3 Statistics0.390.17 0.24 Cavity shift0.130.060.070.28 Uncorrelated lineshape model 0.560.000.150.30 Correlated lineshape model 0.24 Total0.730.300.340.53 Uncertainties for g in parts-per-trillion. 28 D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

30. Status and outlook Remaining basic preparation Transfer positrons from loading trap into precision trap to prepare for positron measurement Characterize apparatus (cavity mode structure, systematic checks, etc) New techniques in development Develop method for detuning particle from amplifier Demonstrate cavity-assisted axial sideband cooling and correlated measurement protocol New measurements of positron and electron g-2 at greater precision than the 2008 electron measurement Improvements that have already been implemented New apparatus with positrons, improved stability, smaller magnetic bottle, etc 29

31. Acknowledgements Gerald Gabrielse (Principal Investigator) Joshua Dorr (2013) Shannon Fogwell Hoogerheide (2013) David Hanneke (2007) Brian Odom (2004) Brian D’Urso (2003) Steve Peil (1999) Daphna Enzer (1996) Kamal Abdullah (Postdoc) Ching-hua Tseng (1995) Joseph Tan (1992) 30

32. Bound electron g-value and Electron mass 31 Ion cyclotron frequency: Larmor precession frequency of the bound electron: Larmor precession frequency of the bound electron: B measurement → determination of electron mass theory m e =0,000 548 579 909 067 (14)(9)(2) u (stat)(syst)(theo) [S. Sturm et al., Nature 506, 467-470 (2014)] Wolfgang Quint, GSI/Heidelberg δm e /m e =3∙10 -11

33. Bound electron g-value and Electron mass 32 Ion cyclotron frequency: Larmor precession frequency of the bound electron: Larmor precession frequency of the bound electron: B measurement → determination of electron mass theory m e =0,000 548 579 909 067 (14)(9)(2) u (stat)(syst)(theo) [S. Sturm et al., Nature 506, 467-470 (2014)] Wolfgang Quint, GSI/Heidelberg δm e /m e =3∙10 -11

34. Bound electron g-value and Electron mass 33 Ion cyclotron frequency: Larmor precession frequency of the bound electron: Larmor precession frequency of the bound electron: B measurement → determination of electron mass theory m e =0,000 548 579 909 067 (14)(9)(2) u (stat)(syst)(theo) [S. Sturm et al., Nature 506, 467-470 (2014)] Wolfgang Quint, GSI/Heidelberg δm e /m e =3∙10 -11 POSTER: WOLFGANG QUINT WEDNESDAY AFTERNOON

35. PSAS, Rio de Janeiro, 26 May 2014, Wolfgang Quint PHYSIKALISCHES INSTITUT UNIVERSITÄT HEIDELBERG Ion cyclotron frequency: Larmor precession frequency of the bound electron: Larmor precession frequency of the bound electron: B Electron mass our measure- ment our measure- ment → determination of electron mass theory as input parameter theory as input parameter

36. PSAS, Rio de Janeiro, 26 May 2014, Wolfgang Quint PHYSIKALISCHES INSTITUT UNIVERSITÄT HEIDELBERG New electron mass m e =0,000 548 579 909 067 (14)(9)(2) u (stat)(syst)(theo) δm e /m e =3∙10 -11 g theo = 2. 001 041 590 176 (6) Theory [S. Sturm et al., Nature 506, 467-470 (2014)]

37. PSAS, Rio de Janeiro, 26 May 2014, Wolfgang Quint PHYSIKALISCHES INSTITUT UNIVERSITÄT HEIDELBERG → Improve most stringent QED test: - comparison : → physics beyond Standard Model → inner structure of electron → light dark matter hypothesis Profit of an improved electron mass m e -Important ingredient in fine-structure constant determination: Mass of Rb87: 86.909 180 535(10)u 115ppt in EdMyers Group in 2010; http://pra.aps.org/abstract/PRA/v82/i4/e042513http://pra.aps.org/abstract/PRA/v82/i4/e042513 Rydberg Constant: 5ppt in CODATA 2010 Our value: 31 ppt h/MRb: 1241 ppt in Paris, 2011 http://prl.aps.org/abstract/PRL/v106/i8/e080801 5 ppt, CODATA (T. Hänsch) 2010 115 ppt, E. Myers 2010 1241 ppt, F. Biraben 2011 30 ppt, our value Hint for physics beyond SM: 2.5 σ discrepancy at muon g-2 (0.54 ppm) - enhanced sensitivity to „new physics“ due to masses: (m µ /m e ) 2 =40000; - with a precision of 37 ppt for α you could check this effect with the electron: - α from the free electron g-factor and theory has to improve by a factor of 8 - α recoil has to improve by a factor of 20 → precision of m e (30ppt) now sufficient