Wolfgang Quint GSI Darmstadt and Univ. Heidelberg. Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint

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1 Intrnational Improvd Acclrator Dtrmination Facility for of Bams th of Ions Elctron and Antiprotons Mass in at Darmstadt Atomic Mass Units Wolfgang Quint GSI Darmstadt and Univ. Hidlbrg

2 Intrnational Acclrator Facility for Bams of Ions and Antiprotons at Darmstadt

3 Intrnational Acclrator Facility for Bams of Ions and g-factor Antiprotons of th at Darmstadt lctron B µ µ B = g s h µ: magntic momnt g: g-factor s: spin µ B : Bohr magnton

4 Intrnational Acclrator Facility for Bams of Ions and Antiprotons at Darmstadt g = 2 + α / π

5 Intrnational Acclrator Facility for QED Bams contributions of Ions and Antiprotons to th g-factor at Darmstadt of th fr lctron g fr = 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) magntic fild 1 st ordr in α: Schwingr trm C 1 = ½ Rf.: J. Schwingr, Phys. Rv. 73, 416 (1948); Hannk t al., PRL 100, (2008) Th thory of quantum lctrodynamics is, I would say, th jwl of physics - our proudst possssion. R. Fynman

6 Intrnational Acclrator Facility for Fr Bams lctron: of Ions QED and Antiprotons contributions at Darmstadt of 2 nd and 3 rd ordr g fr = 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 ordr in α: C 2 = graphs 3 rd ordr in α: C 3 = graphs not shown: 4 th ordr in α: C 4 = graphs Rf.: B. Lautrup t al., Phys. Rp. 3, 193 (1972)

7 q1 Intrnational g-factor Acclrator of th Facility fr for lctron Bams of Ions and Antiprotons at Darmstadt ω Larmor prcssion frquncy: L = g 2 m or rathr B g g = 2 2 = 2 ω ω L c ω ω B: magntic fild in Pnning trap a c cyclotron frquncy: ω c = m B (gt 3 ordrs of magnitud in accuracy by Natur)

8 Foli 7 q1 quint_local;

9 Intrnational Acclrator Facility for Bams of Ions and QED Antiprotons and highly at Darmstadt chargd ions bound-stat QED: quantum physics in strong filds basic procsss in bound-stat QED: slf nrgy vacuum polarization vrtx corrction bound-stat QED coupling paramtr for U 91+ : Zα 0.67 Rf.: T. Bir, Physics Rports 339, 79 (2000)

10 Intrnational Acclrator Facility for Bams Bound-stat of Ions and QED: Antiprotons tratmnt Darmstadt non-prturbativ in Zα non-prturbativ tratmnt prturbativ tratmnt: xpansion in Zα no xpansion in Zα Non-prturbativ bound-stat QED was dvlopd in th last 20 yars by xcllnt thorticians lik: Bir, Blundll, Brit, Czarncki, Glazov, Jntschura, Johnson, Karshnboim, Lindgrn, L, Milstin, Mohr, Pachucki, Prsson, Plunin, Salomonson, Sapirstin, Shabav, Soff, Sunnrgrn, Trkhov, Tupitsyn, Volotka, Yrokhin, and othrs. Rf.: U.D. Jntschura, P.J. Mohr, G. Soff, PRL 82, 53 (1999); T. Bir, Physics Rports 339, 79 (2000)

11 Intrnational Bound-lctron Acclrator g-factor: Facility for Bams of Fynman Ions and Antiprotons graphs 1 st at ordr Darmstadt in α/π g bound /g fr 1 - (Zα) 2 /3 + α(zα) 2 /4π +... Dirac thory SELF ENERGY bound-stat QED VACUUM POLARIZATION Rf.: T. Bir, Physics Rports 339, 79 (2000)

12 Intrnational Bound-lctron Acclrator Facility g-factor: for Bams of Ions Fynman and Antiprotons graphs at Darmstadt 2 nd ordr in α/π 50 graphs Rf.: T. Bir, Physics Rports 339, 79 (2000)

13 Intrnational Acclrator Facility for Bams of Ions and Bound-lctron Antiprotons at Darmstadt g-factor CONTRIBUTION TO G-FACTOR 1-loop QED fr lctron 2-loop QED fr lctron Rf.: D. Glazov NUCLEAR CHARGE Z

14 g-factor Intrnational of th Acclrator bound lctron Facility in for a hydrogn-lik Bams of Ions and ion Antiprotons at Darmstadt (nuclus has no spin,.g. 12 C 5+, 16 O 7+, 28 Si 13+, 40 Ca 19+ ) ω Larmor prcssion frquncy of th bound lctron: L = g J 2 g J m = 'xprimntal g-factor' comparison with thory B 2 L ion c ω ω our masurmnt m M ion B Ion cyclotron frquncy: ion ω c = Q xtrnal input paramtr ion Q M ion B

15 Intrnational Acclrator Facility for Bams A singl of Ions highly and Antiprotons chargd ion at Darmstadt stord in a Pnning trap z U 0 radial confinmnt ndcap axial confinmnt ring ion B AXIAL MOTION z ndcap MAGNETRON DRIFT - B 0 potntial (MODIFIED) CYCLOTRON MOTION + magntic physical lctric combind ion motion

16 Intrnational Acclrator Facility for Bams of Ions Tripl and Antiprotons Pnning at Darmstadt Trap Systm 7mm Prcision trap (PT) Vry homognous magntic fild ~14 cm Analysis trap (AT) Magntic bottl for spin dtction Cration trap (CT) In-trap ion cration of highly-chargd ions

17 Intrnational Acclrator Facility for Bams of Ions Tripl and Antiprotons Pnning at Darmstadt Trap Systm Prcision trap (PT) Vry homognous magntic fild Analysis trap (AT) Magntic bottl for spin dtction Cration trap (CT) In-trap ion cration of highly-chargd ions

18 Intrnational Acclrator Facility for Bams of Ions and Antiprotons HCI g-factor at Darmstadt 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

19 Intrnational g-factor Acclrator trap Facility in for Mainz Bams of Ions and Antiprotons at Darmstadt (GSI/Hidlbrg collaboration)

20 Intrnational Acclrator Facility for Elctronic dtction and Bams of Ions and Antiprotons at Darmstadt rsistiv cooling of trappd ions B nd cap ν c 2 = ν -2 + ν z 2 + ν + 2 ν z = 360 khz compnsation lctrod ring lctrod compnsation lctrod C R L U = I R nd cap de p /dt = P cool = -I 2 R rsistiv cooling

21 Charg Intrnational brding Acclrator of carbon Facility for and oxygn ions Bams in of cryognic Ions and Antiprotons EBIS (lctron-bam at Darmstadt ion sourc) Elctr. Dtction signal hydrogn-lik ions Mass-to-charg ratio [Volt]

22 Intrnational Isolating Acclrator a singl Facility highly for chargd ion Bams of Ions and Antiprotons at Darmstadt

23 Intrnational Acclrator Facility for Bams of Ions and Antiprotons at Darmstadt High-rsolution cyclotron frquncy masurmnt of a singl highly chargd silicon ion 28 Si 13+

24 Intrnational Acclrator Facility for Bams of Ions and Antiprotons at Darmstadt Eignfrquncy Masurmnt Signal (dbv rms ) mHz Axial frquncy ( v z ) dirctly masurd as narrow dip 0 v z Signal (dbv rms ) Frquncy / Hz ν L Frquncy / Hz ν R Othr mods ( v, v + ) can b coupld to axial motion via rf-sidband coupling v v + = ν ν + ν + ν = ν rf rf + ν z z ν L L ν R R

25 Intrnational Continuous Acclrator Strn-Grlach Facility for ffct: Bams of Ions Dtrmination and Antiprotons of at spin Darmstadt dirction 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

26 Intrnational Acclrator Facility for Quantum jump spctroscopy: Bams of Ions and Antiprotons at Darmstadt Spin-flip transitions in th analysis trap

27 Intrnational Acclrator Th Facility lab tam for Bams of Ions and Antiprotons (bfor at spinflip) Darmstadt Birgit Schabingr Svn Sturm Ank Wagnr

28 Intrnational Th Acclrator lab tam Facility (aftr forspinflip) Bams of Ions and Antiprotons at Darmstadt

29 Intrnational Acclrator Masurmnt Facility Cycl for Bams of Ions and Antiprotons at Darmstadt AT PT v L Fractional axial frquncy diffrnc (Hz) M a s u r m n t n u m b r 1. AT: Dtction of spin orintation: spin up v -180 z v + νl Γ= ν c vc 2. PT: Masurmnt of ignfrquncis and simultanous irradiation with microwavs Signal (dbv) v (offlin) M a s u r m n t n u m b r Fractional axial frquncy diffrnc (Hz) Axial Frquncy (khz) 3. AT: Dtction of spin orintation spin down 4. Spin flip in PT? spin has flippd!

30 Prcision masurmnt of bound lctron g-factor in hydrogn-lik silicon

31 Bound lctron magntic momnt masurmnt Intrnational Acclrator Facility for Bams on of hydrogn-lik Ions and Antiprotons silicon at 28 Darmstadt Si 13+ Spinflip probability (%)

32 Comparison of thory and xprimnt: g-factor of th bound lctron in H-lik carbon 12 C 5+, oxygn 16 O 7+ and silicon 28 Si 13+ Intrnational Acclrator Facility for Bams of Ions and Antiprotons at Darmstadt g J ( 12 C 5+ ) = (3) thortical valu g J ( 12 C 5+ ) = (10)(44) our masurmnt g J ( 16 O 7+ ) = (11) thortical valu g J ( 16 O 7+ ) = (15)(44) our masurmnt g J ( 28 S 13+ ) = (17) thortical valu g J ( 28 S 13+ ) = (5)(3)(8) our masurmnt Lit.: T. Bir t al., PRL 88, (2002) V. Shabav t al., PRL 88, (2002) V. Yrokhin t al., PRL 89, (2002) K. Pachucki, V. Yrokhin t al., PRA 72, (2005) S. Sturm t al., PRL 107, (2011)

33 Intrnational Acclrator Facility for Bams of Ions and Antiprotons Elctron at Darmstadt mass ω Larmor prcssion frquncy of th bound lctron: L = g J 2 m B B Ion cyclotron frquncy: ion ω c = Q M ion B m M ion dtrmination of lctron mass = g J 2 thory as input paramtr ω ω ion c L Q our masurmnt

34 Intrnational Acclrator Facility for Bams of Ions and Antiprotons at Darmstadt Exprimntal Rsult Probing Zman transition at diffrnt Γ s svral 100 tims: Г-rsonanc Γ 0 is xtractd from fit Rsonanc width and thus statistical rror limitd by magntic fild fluctuations Svral Г-rsonancs at diffrnt cyclotron nrgis to chck systmatics xtrapolation to zro nrgy (stat.) (syst.) Г 0 = (11)(7) Dominant systmatics: imag charg shift: -282(14) ppt Fractional spinflip rat / % Γ/Γ 0-1 / ,2 1,0 0,8 0,6 0,4 0,2 0,0 FWHM: (Γ/Γ ι -1) / ,00 0,05 0,10 0,15 0,20 0,25 U 2 xc (V2 )

35 Intrnational Acclrator Facility for Bams of Ions and Antiprotons Rsult at Darmstadt Exprimnt Г 0 = (11)(7) (stat.) (syst.) m = m ion g tho = (6) gtho 1 2 q Γ ion 0 Thory m =0, (14)(9)(2) u [S. Sturm t al., Natur 506, (2014)] (stat)(syst)(tho) 1995 Farnham δm /m = Yar Häffnr CODATA Vrdú Hori this work this work m /m -1 (parts pr billion)

36 Intrnational Acclrator Facility for Bams of Ions and Antiprotons Rsult at Darmstadt Г 0 = (11)(7) Yar Exprimnt m (stat.) (syst.) = m =0, (14)(9)(2) u δm /m = m [S. Sturm t al., Natur 506, (2014)] g tho = (6) gtho 1 2 q Γ ion Häffnr 2013 (stat)(syst)(tho) Yar ion 0 Thory this work 2010 m /m this work Farnham CODATA Vrdú Hori -1 (parts pr billion) this work Farnham Vrdú Hori this work m /m -1 (parts pr billion) Häffnr CODATA

37 Intrnational Acclrator Facility for Bams of Ions and Antiprotons at Darmstadt

38 Intrnational Acclrator Facility for Bams of Ions and Antiprotons at Darmstadt Who has forgottn th walnut? tons tons Rlativ Prcision:

39 Intrnational Acclrator Facility for Bams of Ions and Antiprotons at Darmstadt Profit of an improvd lctron mass m Important ingrdint in fin-structur constant masurmnt: α 2 rcoil = 5 ppt, CODATA (T. Hänsch) R h cm = 2R c M m Rb 115 ppt, E. Myrs 2010 h M Rb 1241 ppt, F. Birabn 2011 hk vrcoil = M Rb 30 ppt, our valu

40 Intrnational Acclrator Facility for Bams of Ions and Antiprotons at Darmstadt B Ion Masurmnts of th lctron mass ovr th yars - ν ν lctron c ion c = = 2π m q 2π M B B m = νc q ν ion lctron c M rlativ uncrtainty of m 10-5 common mass spctromtry yar CODATA Indirct masurmnt via µ B /µ Ν Gärtnr: v c via particl loss (first dirct) Gräff: v c via ToF Van Dyck: v c via imag currnts (first non-dstructiv) Winland: v c via lasr fluorscnc + v L + g tho (first bound lctron) Gabrils: v c via imag currnts Farnham: v c via imag currnts (first singl ion) Häffnr: v c /v L of 12 C 5+ + g tho Vrdú: v c /v L of 16 O 7+ + g tho Hori: antiprotonic hlium

41 Intrnational Acclrator Facility for Bams of Ions and Antiprotons Spcial at thanks Darmstadt to Exprimnt: Jiamin Hou, Svn Sturm, Ank Wagnr, Güntr Wrth, Klaus Blaum Thory: Jack Zatorski, Zoltán Harman, Christoph H. Kitl Abtilung für gspichrt und gkühlt Ionn at MPIK, Hidlbrg Atomic Physics Division at GSI Hlmholtzzntrum, Darmstadt QUANTUM group at th Institut für Physik, Mainz Intrnational Max Planck Rsarch School Quantum Dynamics