1. Antihydrogen Charge Measurements Joel Fajans U.C. Berkeley and the ALPHA Collaboration M. Ahmadi, C. Amole, M.D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, E. Butler, A. Capra, C. Carruth, C.L. Cesar, M. Charlton, A.E. Charman, S. Eriksson, L.T. Evans, N. Evetts, T. Friesen, M.C. Fujiwara, D.R. Gill, A. Gutierrez, J.S. Hangst, W.N. Hardy, M.E. Hayden, C.A. Isaac, A. Ishida, S.A. Jones, S. Jonsell, L. Kurchaninov, A. Little, N. Madsen, D. Maxwell, J.T.K. McKenna, S. Menary, J.M. Michan, T. Momose, J.J. Munich, S.C. Napoli, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, C.O. Rasmussen, F. Robicheaux, R.L. Sacramento, M. Sameed, E. Sarid, D.M. Silveira, C. So, T.D. Tharp, R.I. Thompson, D.P. van der Werf, Z. Vendeiro, J.S. Wurtele, and A.I. Zhmoginov Work supported by: DOE/NSF Partnership in Basic Plasma Science, DOE Office of High Energy Physics (Accelerator Science) 2011-2012 LBNL LDRD Also supported by CNPq, FINEP/RENAFAE (Brazil), ISF (Israel), MEXT (Japan), FNU, Carlsberg Foundation (Denmark), VR (Sweden), NSERC, NRC/TRIUMF AIF FQRNT(Canada), and EPSRC, the Royal Society and the Leverhulme Trust (UK).

2. ALPHA Antihydrogen Collaboration CERN’s ALPHA collaboration has been trapping antihydrogen atoms since 2010. Over 1000 atoms have been trapped and detected. ALPHA: In operation between 2007 and 2011 ALPHA-II: Began operation in late 2012 ALPHA, Trapped Antihydrogen, Nature 468, 673 (2010). Positron Accumulator

3. ALPHA Antihydrogen Collaboration ALPHA creates antihydrogen by mixing positron and antiproton plasmas. Some of the resultant antiatoms are cold enough to be trapped in a minimum-B field. The magnetic minimum is created by mirror coils (axially) and an octupole coil (radially). Force on a magnet moment from a magnetic gradient:

4. ALPHA’s Antiatoms Typical antiatoms have energy just less than the trap depth of about 540mK. Antiatoms have been trapped for as long as 1000s. Typically only one antiatom is observed in an experimental cycle, though as many as four have been observed. Experimental cycles now take as little as six minutes. We detect the antiatoms by ramping down the confining magnetic fields, and detecting the resulting annihilation pions with a silicon vertex detector. ALPHA, Confinement of antihydrogen for 1000s, Nature Physics 7, 558 (2011). ALPHA, Antihydrogen trapping apparatus, Nuclear Instruments and Methods in Physics Research Section A, 735 319, (2014). ALPHA, Antihydrogen annihilation reconstruction with the ALPHA silicon detector, Nuclear Instruments and Methods in Physics Research Section A, 684 73-81, (2012) Pion tracks resulting from the release of a trapped antihydrogen atom, ALPHA 2014 Octupole and Mirror shutdown currents

5. “Mainstream” Antihydrogen Research Physicists have long discussed two classes of measurements with antihydrogen. Spectral measurements: ALPHA has measured the microwave spin flip frequency to approximately 0.1%. To excite the 1s-2s transition, ALPHA has illuminated antiatoms with 243nm light. Power in our laser cavity is not yet sufficient (650mW in build up cavity) to observe transitions. We have also begun operation with a 121nm system. ALPHA, Resonant quantum transition in trapped antihydrogen atoms, Nature 483, 439 (2012). ALPHA 243nm Laser Setup Cryogenic 243nm Cavity Finesse

6. “Mainstream” Antihydrogen Research Green dots---simulated annihilations Red circles---434 Observed annihilations ALPHA, Description and first application of a new technique to measure the gravitational mass of antihydrogen, Nature Comm 4, 1785 (2013). A. Zhmoginov, A. Charman, J. Fajans, and J.S. Wurtele Nonlinear dynamics of antihydrogen in magnetostatic traps: implications for gravitational measurements, Class. And Quantum Grav. 30 205014 (2013). P. Hamilton, A. Zhmoginov, F. Robicheaux, J, Fajans, J.S. Wurtele and H. Mueller,, Antimatter interferometry for gravity measurements, Phys. Rev. Lett. 112 121102 (2014). Proposed ALPHAg Apparatus

7. Antihydrogen Charge Bressi, G. et al. Testing the neutrality of matter by acoustic means in a spherical resonator. Phys. Rev. A 83, 052101 (2011). Greenland, P. T. Antimatter, Contemporary Physics 38, 181 (1997). Olive, K. A. et al. Review of particle physics. Chinese Phys. C 38, 090001 (2014). Fee, M. S. et al. Measurement of the positronium 1 3 S 1 –2 3 S 1 interval by continuous-wave two-photon excitation. Phys. Rev. A 48, 192 (1993). Hori, M. et al. Two-photon laser spectroscopy of antiprotonic helium and the antiproton-to-electron mass ratio. Nature 475, 484 (2011). Hughes, R. J. & Deutch, B. I. Electric charges of positrons and antiprotons. Phys. Rev. Lett.69, 578 (1992).

8. Our particle detector is sensitive to pions only, and, thus, cannot tell the difference between antihydrogen atom and antiproton annihilations. To discriminate between antiatoms and antiprotons, we apply large electric fields when we release the trapped particles from our trap. These fields would deflect antiprotons either left or right, conditions that we call Bias-Left or Bias-Right Antihydrogen/Antiproton Discrimination

9. Observed antihydrogen atoms after release from the ALPHA Trap Observed antiprotons after release from the ALPHA trap ALPHA, Discriminating between antihydrogen and mirror-trapped antiprotons in a minimum-B trap, New J. Phys., 14 015010, (2012). Antihydrogen/Antiproton Discrimination

10. Antiatom Annihilation Deflection Position vs. Antiatom Charge Simulations The bias fields will deflect particles with a charge far less than the unit charge. By searching for such deflection, we can bound the antihydrogen charge. Most systematic errors are eliminated by comparing Bias-Left with Bias-Right results.

11. Antihydrogen Deflection Observations ALPHA, An experimental limit on the charge of antihydrogen, Nature Comm, 5, 3955 (2014). Bias-Left Bias-Right Note that this was a retrospective analysis of data primarily taken for other purposes. The Bias-Left and Bias-Right data was not strictly alternated. The Bias-Left data were collected in 2010. The Bias-Right data were primarily collected in 2011. The detector performance was carefully examined for uniformity across the data collection years. No significant variations were observed.

12. Antihydrogen Deflection Predictions ALPHA, An experimental limit on the charge of antihydrogen, Nature Comm, 5, 3955 (2014).

13. Antihydrogen Charge ALPHA, An experimental limit on the charge of antihydrogen, Nature Comm, 5, 3955 (2014). This bound is marginally better than the bound inferred by superposition.

14. Deflection Measurement Limitations ALPHA, An experimental limit on the charge of antihydrogen, Nature Comm, 5, 3955 (2014). The bound error is set by the uncertainty in measuring the average positions under Bias-Right and Bias-Left conditions. Because of: The limited number of antiatoms. The natural spread in the annihilation position of these antiatoms. The detector resolution. the precision of this deflection measurement is hard to improve.

15. Improving the Antihydrogen Charge Bound Using Stochastic Acceleration Stochastic acceleration (Fermi acceleration) can eject putatively charged antiatoms from the trap. Stochastic acceleration: the acceleration of a charged particle by randomly time- varying electric fields. This is a “textbook” problem in nonlinear dynamics. M. Baquero-Ruiz and A. E. Charman and J. Fajans and A. Little and A. Povilus and F. Robicheaux and J.S. Wurtele and A. I. Zhmoginov, Measuring the electric charge of antihydrogen by stochastic acceleration, New J. Phys. 16 083013, (2014).

16. Stochastic Acceleration: Experimental Fields

18. Stochastic Acceleration Scaling M. Baquero-Ruiz and A. E. Charman and J. Fajans and A. Little and A. Povilus and F. Robicheaux and J.S. Wurtele and A. I. Zhmoginov, Measuring the electric charge of antihydrogen by stochastic acceleration, New J. Phys. 16 083013, (2014). ALPHA, An improved limit on the charge of antihydrogen from stochastic acceleration, Nature, 529, 373 (2016).

19. Stochastic Potential Oscillations ALPHA, An improved limit on the charge of antihydrogen from stochastic acceleration, Nature, 529, 373 (2016).

20. Trap antihydrogen. Subject antiatoms to oscillating electrostatic potentials for 114.9s. Antiatoms with a sufficiently large Q will be ejected. Hold antiatoms for 114.9s. Turn off trapping fields and count surviving antiatoms. Stochastic Acceleration Experimental Cycle M. Baquero-Ruiz and A. E. Charman and J. Fajans and A. Little and A. Povilus and F. Robicheaux and J.S. Wurtele and A. I. Zhmoginov, Measuring the electric charge of antihydrogen by stochastic acceleration, New J. Phys. 16 083013, (2014). ALPHA, An improved limit on the charge of antihydrogen from stochastic acceleration, Nature, 529, 373 (2016). Stochastic TrialsNull Trials

21. Aside: Stochasticity M. Baquero-Ruiz and A. E. Charman and J. Fajans and A. Little and A. Povilus and F. Robicheaux and J.S. Wurtele and A. I. Zhmoginov, Measuring the electric charge of antihydrogen by stochastic acceleration, New J. Phys. 16 083013, (2014). ALPHA, An improved limit on the charge of antihydrogen from stochastic acceleration, Nature, 529, 373 (2016). M. Baquero-Ruiz, Studies on the Neutrality of Antihydrogen, Ph.D. Thesis, U.C Berkeley, (2013). Antiatom Orbits Drive Randomization vs. Escape Time Experimental Drive Randomization

22. Stochastic Acceleration Simulation Results

23. Stochastic Acceleration Experimental Results ALPHA, An improved limit on the charge of antihydrogen from stochastic acceleration, Nature, 529, 373 (2016). Capra, A. Testing CPT and antigravity with trapped antihydrogen at ALPHA, Ph.D. Thesis, York University (2015). Number of TrialsObserved Antiatoms Stochastic Trials1012 Null Trials1012 Cosmic background is negligible.

24. Systematic Errors The dominant source of systematic error in the stochastic measurement is the uncertainty in the antiatom energy distribution function. Escape Time Measurement of the Antiatom Energy Distribution Function Survival Probability for Different Antiatom Energy Distributions ALPHA, An experimental limit on the charge of antihydrogen, Nature Comm, 5, 3955 (2014). ALPHA, An improved limit on the charge of antihydrogen from stochastic acceleration, Nature, 529, 373 (2016).

25. Conclusions and Implications ALPHA, An improved limit on the charge of antihydrogen from stochastic acceleration, Nature, 529, 373 (2016).

26. Simulations Simulations follow: Employ a symplectic stepper. Simulations have been benchmarked against other aspects of the data. Employ an accurate model of the magnetic fields. Field model has been benchmarked with antiprotons. Typically, about one thousand trajectories are followed for a given condition.

27. Polarization Effects The stochastic measurement also sets limits on polarization of antihydrogen. Interpreted as a limit on the polarizability, ALPHA, An improved limit on the charge of antihydrogen from stochastic acceleration, Nature, 529, 373 (2016).