Intrnational Bound-Stat Acclrator Quantum Facility Elctrodynamics for Bams in Strong of Ions and Filds Antiprotons Byond at Darmstadt th Furry Pictur by g-factor Masurmnts Wolfgang Quint GSI Darmstadt and Univ. Hidlbrg
Quantum mchanics, Rlativity, and P.A.M. Dirac Quantum mchanics Spcial Rlativity Dirac thory lctron magntic momnt nrgy lvls of bound lc. ngativ nrgy stats xistnc of antimattr g-factor Lamb-shift fw-l. ions CPT tsts
Dirac sa of ngativ nrgy stats Ngativ nrgy stats: obsrvabl in nrgy lvls and g-factors of fw-lctron ions Rf.: W. Grinr, Adv. in Quantum Chmistry, vol. 53, 99 (2008)
Quantum Elctrodynamics (QED) QED = Dirac thory + quantizd radiation fild basic procsss in QED: slf nrgy vacuum polarization vrtx corrction QED coupling paramtr: fin-structur constant α = 2 /2ε 0 hc 1/137 0.007 Rf.: T. Bir, Physics Rports 339, 79 (2000)
Quantum Elctrodynamics Th g-factor: r µ = Most stringnt tst: r s g µ B h g-factor of th fr lctron: h Bohr magnton: µ B 2m Schwingr trm: g 2 1 α α = 1 + C1 + C 2 + π π = 1.001 159 652 181 2 3 α C3 π 78 (77) [T. Aoyama t al., PRL 109, 111807 (2012)] g 2 =1.001 + C 4 α π 4 + C 5 α π 5 +... 159 652 180 73 (28) [D. Hannk t al., Phys. Rv. A 83, 052122 (2011)] 5
Fr lctron: QED contributions 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) 5 +... 2 nd ordr in α: C 2 = - 0.328 478 966 7 graphs 3 rd ordr in α: C 3 = 1.1765 72 graphs not shown: 4 th ordr in α: C 4 = -1.9108 891 graphs Rf.: B. Lautrup t al., Phys. Rp. 3, 193 (1972)
Fr lctron: QED contributions of 5 th 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) 5 +... Harvard g-2 masurmnt 2011: g fr = 2 (1.001 159 652 180 73 (28)) dtrmination of α 5 th ordr in α: C 5 = 9.16 12672 graphs I am digging at th roots of physics to s whthr thr is som trasur thr. Toichiro Kinoshita Rf.: Kinoshita t al., arxiv:1205.5368v1 [hp-ph] 24 May 2012
ω Larmor prcssion frquncy: L = g 2 g-factor of th fr lctron 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)
Intrnational Acclrator Hans Facility Dhmlt for Nobl Priz 1989 "for th dvlopmnt of th ion trap tchniqu" 9
g-factor of th lctron and positron Elctron: g = 2 1.001 159 652 188 4 (43)* Positron: g = 2 1.001 159 652 187 9 (43)* *CODATA
QED and highly chargd ions (HCI) 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 H-lik uranium U 91+ : Zα 0.67 Rf.: T. Bir, Physics Rports 339, 79 (2000)
Intrnational Bound-lctron Acclrator Facility g-factor: for Bams of Fynman Ions and Antiprotons graphs at 1 st Darmstadt ordr 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)
Bams of Ions and QED Antiprotons in strong at Darmstadt filds Common thortical approach: Furry pictur of bound-stat QED - for 28 Si 13+ : < E > 2 10 15 V/m for 40 Ca 19+ : < E > 8 10 15 V/m Wndll Hinkl Furry 1907-1984 Prof. at Harvard Univrsity 13
Masurmnt principl E spin = hv L Larmor prcssion frquncy v L g = 4π m B B - - Cyclotron frquncy of th ion B ν c qion = 2π m ion B g= 2 m m ion q ion v v L c Our task: Masurmnt of Г=v L /v c 14
A singl highly chargd ion 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
7mm Tripl Pnning trap systm 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
Highly chargd ion g-factor apparatus SUPERCONDUCTING MAGNET WITH ROOM TEMPERATUR BORE MICROWAVE INLET CRYOSTAT CRYO ELECTRONICS @ 4 K SINGLE ION IN TRAP PRECISION TRAP `DOUBLE TRAP MAGNETIC BOTTLE SUPERCONDUCTING SOLENOIDS PENNING TRAP @ 4K MINI EBIS TARGET FEP
Ion oscillation frquncis Masurmnt of th tiny imag currnts (~ fa) on th trap lctrods rquirs: Suprconducting tank circuit: Ultra-low nois cryognic amplifirs: A Fourir transformation: FFT: 25 Hlical rsonator: Q= 3200 n = 400 pv/ Hz i n 10 fa/ Hz Voltag-Nois Dnsity (dbv) 20 15 10 5 0-1500 -1000-500 0 500 1000 1500 (Axial Frquncy / Hz) -671000 A hot ion is dtctd as a pak abov th Johnson nois of th rsonator. 18
High-rsolution cyclotron frquncy masurmnt of a singl highly chargd silicon ion 28 Si 13+
Continuous Strn-Grlach ffct: Dtrmination of spin 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
Quantum jump spctroscopy: Spin-flip transitions in th analysis trap
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 (%)
Bound lctron magntic momnt masurmnt on lithium-lik silicon 28 Si 11+ g xp ( 28 Si 11+ ) = 2.000 889 889 9(21) g tho ( 28 Si 11+ ) = 2.000 889 909 (51) thortical calculations by D.A. Glazov, A.V. Volotka, V.M. Shabav Larmor rsonanc Prcision tst of lctron-lctron intraction scrnd QED contributions Rf.: A. Wagnr t al. PRL 110, 033003 (2013)
Dirac Intrnational sa: contribution Acclrator of Facility ngativ for nrgy stats to Bams bound of Ions lctron and Antiprotons magntic at momnt Darmstadt in Li-lik HCI intgration ovr ngativ nrgy stats for intrnal lctron lins Rf.: D. Glazov
Quantum Elctrodanymics in strong filds: Intrnational Acclrator Facility for non-prturbativ Bams of Ions and Antiprotons tratmnt Darmstadt in Zα byond th Furry pictur - Extrnal fild approximation: Nuclus approximatd as an xtrnal Coulomb fild, V(r), r r [ iα + β + V( r) ] ψ( r) = Eψ( r) r r Common thortical approach: Furry pictur of bound-stat QED - rducing a 2-body systm to a 1-body systm Wndll Hinkl Furry 1907-1984 Prof. at Harvard Univrsity
Quantum Elctrodanymics in strong filds: Intrnational Acclrator Facility for non-prturbativ Bams of Ions and Antiprotons tratmnt Darmstadt in Zα byond th Furry pictur Isotop shift in bound-lctron g-factors All contributions cancl xcpt for: - Nuclar rcoil - Nuclar siz Not includd in Furry pictur Our tst systm: g( 40 Ca 17+ ) g( 48 Ca 17+ ) - nuclar rcoil dominats th isotop shift (99.96%), sinc nuclar siz: Rf.: F. Köhlr, S. Sturm r nucl. ( 40 Ca) = 3.4776(19) 10-15 fm r nucl. ( 48 Ca) = 3.4771(20) 10-15 fm [I. Angli t al., Atomic Data and Nuclar Data Tabls 99 (2013)]
g-factors of lithium-lik calcium 40 Ca 17+ and 48 Ca 17+ snsitiv tst of QED byond th Furry pictur Masurd g-factors: m g=2γ m ion (stat) (syst) (m ion ) g( 40 Ca 17+ ) = 1.999 202 040 55 (10) (12) (110) 10-10 δg/g = 5.6 10-10 g( 48 Ca 17+ ) = 1.999 202 028 85 (12) (13) (80) 10-10 δg/g = 4.1 10-10 g xp = g( 40 Ca 17+ ) - g( 48 Ca 17+ ) = 11.70 (16) (3) (138) 10-9 q ion Most prcis g-factors of lithium-lik ions! g tho = g( 40 Ca 17+ ) - g( 48 Ca 17+ ) = 10.305 (27) 10-9 [Sz. Nagy t al. Eur. Phys. J. D 39, (2006)] comparison to thory: [A. V. Volotka t. al., PRL 112, 253004 (2014)] V. Shabav t al.
g-factors of lithium-lik calcium 40 Ca 17+ and 48 Ca 17+ snsitiv tst of QED byond th Furry pictur
HITRAP at th Exprimntal Storag Ring ESR at GSI Darmstadt UNILAC xprimnts with particls at rst or at low nrgis coolr Pnning trap postdclrator SIS EXPERIMENTS WITH HIGHLY CHARGED IONS AND ANTIPROTONS AT EXTREMELY LOW ENERGIES: g-factor masurmnts of th bound lctron lasr spctroscopy mass masurmnts of xtrm accuracy raction microscop, collisions at vry low vlocitis surfac studis and hollow-atom spctroscopy x-ray spctroscopy U 91+ strippr targt ESR lctron cooling and dclration down to 4 MV/u U 73+ U 91+
Acknowldgmnts Hlmholtz-Institut Jna Fridrich-Schillr-Univrsität Jna Thank you for your attntion!