Precision Physics and g-Factor Experiment in Quantum Electrodynamics

1. The ALPHATRAP g-factorexperiment International Conference on Precision Physics and Fundamental Physical Constants FFK 2019 11.06.2019 Alexander Egl

2. Quantum Electrodynamics (QED) In Strong Fields • QED describesinteractionof light/photonsandchargedparticles • Impressivetheorypredictionsandmostprecise experimental results, e.g. electron magnetic moments: g-2, g-factor in highly charged ions (HCI) [1] • Most stringently tested theory in weak fields • Validityof QED in strong fields? Test ofboundstate QED (BS-QED) underextreme conditions in high electricandmagneticfieldsof heavy HCI • g-factormeasurements in H or Li-like systems • Fine structure and hyperfine structurespectroscopy  Combine strongestfieldandhighestprecision (V/cm) Nuclearcharge [1] H. Häffner, et al., Phys. Rev. Lett. 85, 5308 (2000) J.Verdu, et al., Phys. Rev. Lett. 92, 093002 (2004) [2] S. Sturm, et al., Nature 506, 7489 (2014) [3] S. Sturm, et al., Phys. Rev. Lett. 107, 023002 (2011) [4] F. Köhler, et al. Nat. Comm. 7, 10246 (2016) [2] [3] [4]

3. Measurement principle h Measure the free cyclotron frequency todetermine magnetic field Measure the Larmor frequency in a well-known magnetic field Precision values from literature: electron mass1: atomic mass2, e.g. 208Pb: Independent precision experiments 1: Sturm et al., Nature 506, 467 (2014); 2: Audi et al., Chinese Phys. C 36, 1287 (2012)

4. Penning Trap - Principle • Experimental Conditions: • Single, cold ion • Homogeneous magnetic field: 4T • Cryogenic temperature: 4.2 K • Extremely high vacuum: 10-17mbar • Long storage times: months B UCE2 UCE1 URE UCE1 UCE2

5. Spin statedetection- Continuous Stern Gerlach Effect Introducingmagneticbottleinhomogeneity B e • ferromagnetic • ring • Magneticbottle • B2≈ 45000 T/m² ContinuousStern-Gerlach effect: • axial frequency offset between “up” and “down” spin orientation 40Ar13+

6. The ALPHATRAP setup • Access to externally produced ions • Laser ion source (Be+) • HC-EBIT • HD-EBIT (commissioning phase) • Transport through room-temperature beamline into 4K section • Separated by cryogenic valve

7. Double Trap System Capture section -dynamicioncapturing -storageofions (months) Precision Trap (PT) -homogeneousB -measurementof -spin flipsinduction -Laser spectroscopy Analysis Trap (AT) -strong () -Spin statedetectionand preparation B

8. Measurement cycle PT e AT microwave horn

9. Measurement cycle PT AT: Detectionandpreparationofspinorientation e AT

10. Measurement cycle PT: Measurement ofmotionalfrequencies and probe withspectroscopyfrequency PT & AT: Detectionandpreparationofspinorientation e AT

11. Measurement cycle PT: Measurement ofmotionalfrequencies and probe withspectroscopyfrequency PT AT: Detectionandpreparationofspinorientation e AT

12. Measurement cycle PT: Measurement ofmotionalfrequencies and probe withspectroscopyfrequency PT AT: Detectionandpreparationofspinorientation e AT Compare spinstate

13. Measurements so far 40Ar13+measurements The ALPHATRAP g-factor experiment

14. Measurements so far 40Ar13+measurementofg-factor: firsthigh precisionmeasurementof 5 electrong-factor The ALPHATRAP g-factor experiment

15. Measurement of the g-factor of 40Ar13+ (preliminary results) boronlike Argon: g ≈ 2/3 • 3 different theoreticalvalues: • 120 σdeviationbetweenfirst 2 • Measured2 resonances [1] Physical Review A 94, 042504 (2016) [2] HCI 2018 Conference Talk, Group ofVolotka, Shabaevet al. [3] J. Phys. Conf. Ser. 583 012001 [4] At. Data Nucl. Data Tables 100, 1111 (2014); no error given

16. Measurement of the g-factor of 40Ar13+ (preliminary results) preliminary results preliminary results Gaussianfittedbymaximumlikelihoodestimation (binneddataonlyforrepresentation)

17. Comparison with Current Theory Theo. [1] Theo. [2] Theo. [3] Theo. [4] This work Exp. [4] http://arxiv.org/abs/1906.00881 • A maximum of 120σdeviation comparing the existing theoretical predictions • Our experimental result shows the agreement with the current theory at 10-7 level. (Experiment precision at 10-9) [1] A. A. Shchepetno et al., J. Phys. Conf. Ser. 583 012001 [2] J. P. Marques et al., PHYSICAL REVIEW A 94, 042504 (2016) [3] V. A. Agababaev et al., HCI 2018 Conference Talk, Group of Volotka, Shabaev et al. [4] I. Arapoglou et al., Phy. Rev. Lett accepted, http://arxiv.org/abs/1906.00881

18. Measurements so far 40Ar13+measurements The ALPHATRAP g-factor experiment

19. For hydrogenlikeionstransitionenergyscaling: forprincipal, for HFS, for FS • Similarscalingforfewelectronsystems • boronlike40Ar13+: I = 0 Measurements so far 40Ar13+measurementoffinestructuretransition: laserspectroscopy on magneticfinestructuretranstionusing a novel detectionscheme The ALPHATRAP g-factor experiment

20. Measurements so far • For hydrogenlikeionstransitionenergyscaling: forprincipal, for HFS, for FS • Similarscalingforfewelectronsystems • boronlike40Ar13+: I = 0 The ALPHATRAP g-factor experiment

21. Results – Resonancefor |1/2,-1/2> ↔ |3/2,+1/2> ( = |J,mj> ) • Derivedtemperaturefrom FWHM  19.5 ± 4.4 K preliminary results

22. Results – Resonancefor |1/2,-1/2> ↔ |3/2,+1/2> ( = |J,mj> ) • Derivedtemperaturefrom FWHM  1.0 ± 0.3 K • Negative electronic feedbackapplied, expectedlowertemperatureoffactor ≈ 3 • Adiabaticcoolingbyloweringoftrapping potential depthbyfactorof 3.8  lowered temperature by ≈ 3×3.8 = 11.4 preliminary results

23. Summary & Perspectives Sturm, Sven, et al. "The ALPHATRAP experiment." The European Physical Journal Special Topics 227.13 (2019): 1425-1491. • First high precisionmeasurementofboronlikeg-factor • Fine structure spectroscopy without fluourescence detection • ALPHATRAP: accessto heavy HCI via HD-EBIT: • control over single ion states and preparation • longstoragetimes • lowenergy • QED testsof heavy HCI e.g. HFS splitting in hydrogen- andlithiumlike209Bi82+,80+ • Isotope shift measurement for g-factor in HCI  high sensitivity to nuclear effects

24. Thankyouforyourattention + for Ar13+ FS Laser spectroscopy: W. Nörtershäuser1, K. König1, T. Ratajczyk1 1 IKP, TU Darmstadt The ALPHATRAP Team: Klaus Blaum Sven Sturm Bingsheng Tu Andreas Weigel Ioanna Arapoglou Alexander Egl Tim Sailer & … + for Ar13+ g-factormeasurement: H. Cakir1, V. A. Yerokhin1,2, N. S. Oreshkina1, V. A. Agababaev3,4, A. V. Volotka3,5,6, D. V. Zinenko3, D. A. Glazov3, Z. Harman1, C.H. Keitel1 1 MPIK 2 Peter the Great St. Petersburg University 3 St Petersburg State University 4 St Petersburg Electrotechnical University 5 Helmholtz-Institut Jena 6 GSI Darmstadt

26. Considerationsforlineshape • Ion bound in a harmonic potential • Axial motion: • Doppler shift: • modulation index indicates by how much the modulated variable varies around its unmodulated level. It relates to variations in the carrier frequency. The Bessel function gives then the strength of the sideband

27. Simulations • Sidebandspectrumforonespecifictemperaturepicked out ofthisdistribution

28. Center ofresonances

29. Outlook • Isotope shiftmeasurementfor g-factor in HCI • Groundstate g-factorof HCI • Precision increasedbysympatheticallasercooling, developmentofcoolingschemefor HCI ↔ Be+ ions • Improvedlasersystem: linewidthnarrowing e.g. ULE cavities, absolute frequencydetermination via frequencycomb • Spectrocsopy, e.g. of Li-like and H-like Bismuth

30. Laser Coolingfor ALPHATRAP • Increase precisionby • SympatheticCoolingof a highly-chargedion • Phase Sensitive DetectionMethodsbenefitfromsmall radial kineticenergiesduringthephaseevolutiontime → smallermagneticandrelativisticshifts • Facilitationofthe Spin-Flip measurement in the AT • Open upnew type ofmeasurements: Coulomb Crystals in Penning traps ( crystalmadeof a single Be1+ionand a single HCI) → measurementsof→ α

31. Considerationsforlineshape • Sidebandspectrumforonespecificenergy out ofthe thermal Boltzmann distribution

32. Considerationsforlineshape • SmoothingandcomparisonoftheGaussianlineshape (Doppler broadening)