Atomic Physics in Traps

Transcription

1 Atomic Physics in Traps QED Fundamental Constants CPT Invariance Wolfgang Quint GSI Darmstadt and Univ. Heidelberg

2 Quantum mechanics, Relativity, and P.A.M. Dirac Quantum mechanics Special Relativity Dirac theory electron magnetic moment energy levels of H-like ions negative energy states existence of antimatter g-factor Lamb shift few-el. ions CPT tests

3 Quantum Electrodynamics (QED) QED = Dirac theory + quantized radiation field basic processes in QED: self energy vacuum polarization vertex correction QED coupling parameter: finestructure constant α =e 2 /2ε 0 hc 1/ Ref.: T. Beier, Physics Reports 339, 79 (2000)

4 QED and highly charged ions bound-state QED: quantum physics in strong fields basic processes in bound-state QED: self energy vacuum polarization vertex correction bound-state QED coupling parameter for U 91+ : Zα 0.67 Ref.: T. Beier, Physics Reports 339, 79 (2000)

5 Magnetic moment (g-factor) of the electron B µ = g e 2 m J m: magnetic moment g: g-factor e: charge m: mass J: angular momentum

6 g = 2 + α / π

7 QED contributions to the g-factor of the free electron g free = 2 (1 + C 1 α/π + C 2 (α/π) 2 + C 3 (α/π) 3 + C 4 (α/π) 4 + C 5 (α/π) magnetic field 1 st order in α: Schwinger term C 1 = ½ Ref.: J. Schwinger, Phys. Rev. 73, 416 (1948); Hanneke et al., PRL 100, (2008) The The theory theory of of quantum electrodynamics is, is, I I would would say, say, the the jewel jewel of of physics --our our proudest possession. R. R. Feynman

8 Free electron: QED contributions of 2 nd and 3 rd order g free = 2 (1 + C 1 α/π + C 2 (α /π) 2 + C 3 (α /π) 3 + C 4 (α /π) 4 + C 5 (α /π) nd order in α: C 2 = graphs 3 rd order in α: C 3 = graphs not shown: 4 th order in α: C 4 = graphs Ref.: B. Lautrup et al., Phys. Rep. 3, 193 (1972)

9 Free electron: QED contributions of 5 th order g free = 2 (1 + C 1 α/π + C 2 (α/π) 2 + C 3 (α/π) 3 + C 4 (α/π) 4 + C 5 (α/π) Harvard g-2 measurement 2008: g free = 2 ( (28)) determination of α 5 th order in α: C 5 = graphs I am digging at the roots of physics to see whether there is some treasure there. Toichiro Kinoshita Ref.: Kinoshita et al., arxiv: v1 [hep-ph] 24 May 2012

10 Determinations of the finestructure constant α Ref.: M. Vogel ACCURACY IN ALPHA [-LOG( α -1 )(α -1 )]

11 Bound-electron g-factor: Feynman graphs 1 st order in α/π g bound /g free 1 - (Zα) 2 /3 + α(zα) 2 /4π +... Dirac theory SELF ENERGY bound-state QED VACUUM POLARIZATION Ref.: T. Beier, Physics Reports 339, 79 (2000)

12 Bound-electron g-factor

13 g-factor of the electron bound in a hydrogen-like ion ω Larmor precession frequency of of the the bound bound electron: e L = g J 2 g J e m = e 'experimental g-factor' comparison with with theory B 2 e L ion c ω ω m M e ion B Ion Ion cyclotron frequency: ion ω c = Q ion e our our external input measurement parameter Q M ion B

14 A single highly charged ion stored in a Penning trap z U 0 radial confinement endcap axial confinement ring ion B AXIAL MOTION z endcap MAGNETRON DRIFT - B 0 potential (MODIFIED) CYCLOTRON MOTION + magnetic physical electric combined ion motion

15 Highly charged ion g-factor apparatus SUPERCONDUCTING MAGNET WITH ROOM TEMPERATUR BORE MICROWAVE INLET CRYOSTAT CRYO 4 K SINGLE ION IN TRAP PRECISION TRAP `DOUBLE TRAP MAGNETIC BOTTLE SUPERCONDUCTING SOLENOIDS PENNING 4K MINI EBIS TARGET FEP

16 Electronic detection of a single trapped ion: Resistive cooling and active feedback cooling B end cap ν z = 680 khz feedback cooling G φ compensation electrode ring electrode compensation electrode C R L U = I R end cap de k /dt = P cool = -I 2 R resistive cooling

17 Resistive Cooling of C 5+ -ions in a Penning Trap Resistive cooling of trapped 12 C 5+ ions - final temperature: T = 4 Kelvin axial energy [arb. units] Τ = 4 Κ τ cool = 132 ms cooling time [s]

18 High-resolution cyclotron frequency measurement of a single highly charged silicon ion 28 Si 13+

19 Bound electron magnetic moment measurement on hydrogen-like silicon 28 Si 13+ Spinflip probability (%)

20 Comparison of theory and experiment: g-factor of the bound electron in H-like carbon 12 C 5+, oxygen 16 O 7+ and silicon 28 Si 13+ g J ( J ( C )) = (3) (3) theoretical value g J ( J ( C )) = (10)(44) our ourmeasurement g J ( J ( O )) = (11) (11) theoretical value g J ( J ( O )) = (15)(44) our ourmeasurement g J ( J ( Si Si )) = (17) (17) theoretical value g J ( J ( Si Si )) = (5)(3)(8) our ourmeasurement Lit.: T. Beier et al., PRL 88, (2002) V. Shabaev et al., PRL 88, (2002) V. Yerokhin et al., PRL 89, (2002) K. Pachucki, V. Yerokhin et al., PRA 72, (2005) S. Sturm et al., PRL 107, (2011)

21 Bound-electron g-factor CONTRIBUTION TO G-FACTOR Häffner 2000 Verdu 2004 Dirac Sturm 2011 Sturm 2013 Köhler 2013, preliminary 1-loop QED-BS nuclear size 2-loop QED-BS 1-loop QED free electron 2-loop QED free electron Ref.: D. Glazov NUCLEAR CHARGE Z

22 Determination of electron mass ω Larmor precession frequency of of the the bound bound electron: e L = g J 2 e m e B B Ion Ion cyclotron frequency: ion ω c = Q M ion B m M e ion determination of of electron mass = g J 2 ω theory as as input parameter ω ion c e L e Q our our measurement

23 Determination of the electron mass from g-factor measurements on H-like carbon 12 C 5+ and oxygen 16 O C 5+ g-factor measurement m e e (( C )) = (29) u 16 O 7+ g-factor measurement m e e (( O )) = (41) u Van Dyck et al., comparison of cycl. frequencies ν e /ν(c 6+ ) m e e (UW) = (120) u Outlook: 1) Improved measeurement on carbon C 5+, work in progress by F. Köhler and S. Sturm 2) measurements on lighter ions, e.g. 4 He 1+

24 Bound electron magnetic moment measurement on lithium-like silicon 28 Si 11+ g exp ( 28 Si 11+ ) = (21) g theo ( 28 Si 11+ ) = (51) theoretical calculations by D.A. Glazov, A.V. Volotka, V.M. Shabaev Larmor resonance Precision test of electron-electron interaction screened QED contributions Ref.: A. Wagner et al. PRL 110, (2013)

25 Dirac sea: contribution of negative energy states to bound electron magnetic moment in Li-like HCI integration over negative energy states for internal electron lines Ref.: D. Glazov

26 HITRAP at the ESR storage ring / GSI UNILAC experiments with particles at rest or at low energies cooler Penning trap postdecelerator EXPERIMENTS EXPERIMENTS WITH WITH HIGHLY HIGHLY CHARGED CHARGED IONS IONS AND AND ANTIPROTONS ANTIPROTONS AT AT EXTREMELY EXTREMELY LOW LOW ENERGIES: ENERGIES: g-factor g-factor measurements measurements of of the the bound bound electron electron laser laser spectroscopy spectroscopy mass mass measurements measurements reaction reaction microscope, microscope, atomic atomic collisions collisions surface surface studies studies x-ray x-ray spectroscopy spectroscopy U 91+ SIS stripper target ESR electron cooling and deceleration down to 4 MeV/u 400 MeV/u U 73+ U 91+

27 Determination of the proton g-factor ωc = e B mp ωl = g ωl g=2 ωc Cyclotron frequency r B e B 2mp Larmor frequency hωl e m ω ' z ( ) ω ' z ( ) = ω z ωc = ω+ 2 + ω 2 + ωz 2 ω+ 2π 29 MHz ω z 2π 690 khz ω 2π 8.5 khz analysis trap precision trap

28 A single trapped proton and the continuous Stern-Gerlach effect axial frequency shift due to spinflip: 1 µ B ν z z 2 2 2π mν z Proton measurement is times harder compared to electron g-2 measurement. B 2 = 0.3 T/mm 2 ν z = 190 mhz

29 First Larmor resonance curve of a single proton in the Penning trap Axial temperature reduced Larmor resonance narrower νl νl = g = ν L 2 ν c Next steps: Reduce axial frequency fluctuations further 20 khz Direct observation of spinflips Apply double-trap method. Magnetic field in precision trap is more homogeneous by 4 orders of magnitude improvement to g g =10 9 expected

30 Proton g-factor measurement with and without active feedback cooling reduction of axial temperature by application of active electronic feedback g p = (50) Ref.: C. Rodegheri et al., NJP 2012

31 Baryon-Antibaryon Symmetry Experiment The BASE Collaboration at AD / CERN

32 Acknowledgements Group at the institute of physics - Mainz Group of Klaus Blaum at MPIK Heidelberg Atomic Physics Division at GSI Darmstadt VH-NG-037 Thank you for your attention!

33 Electronic detection of a single ion by resonance circuit Particle acts as a perfect short Q = 5600 ν = 680 khz R e n p = 36MΩ = 1.3 nv Hz Amplitude (dbm) Ref.: A. Mooser Frequency (Hz) 2.5 Hz Line width δν z N p Line Width (Hz) Single Proton Number of Particles

34 Continuous Stern-Gerlach effect: Determination of spin direction CLASSICAL STERN-GERLACH SEPARATION IN POSITION SPACE CONTINUOUS STERN-GERLACH SEPARATION IN FREQUENCY SPACE z B 1 B 2 L 2 z B1 2KE z B2 m z

35 Quantum jumps of a single HCI in a Penning trap FREQUENCY DIFFERENCE [Hz] ,1 12 C O Si 13+ AXIAL FREQUENCY [Hz] - OFFSET 0,6 0,4 0,2 0,0-0,2-0,4-0,6-0, TIME [min] B 2 =10mT/mm ION MASS M [u]