Atomic Physics

Wolfgang Quint (w.quint@gsi.de)

GSI Darmstadt, Germany

Penning trap measurement of thePenning trap measurement of themagnetic moment of the antiprotonmagnetic moment of the antiproton

Villars Meeting, Sept. 25, 2004Villars Meeting, Sept. 25, 2004

Atomic Physics

B

g-Factor of the antiproton

hs

gpN

p

p: magnetic momentgp: g-factors: spinN: nuclear magneton

proton: gp = 2×2.792847337(29)*accuracy: 10-8

antiproton: gpbar = 2×2.800(8)* accuracy: 10-3

*Particle Data Group

Atomic Physics

Bm

eg

p

pL 2 B

m

e

pc

cyclotron frequency:cyclotron frequency:Larmor precessionfrequency:

Larmor precessionfrequency:

c

Lpg

2

g-Factor of the antiproton

B: magnetic field in Penning trap

Atomic Physics Geonium: Single electron in a Penning trap

anomaly transition

(2 , )

(1 , )

(0 , )

(nc , )

(1 , )

(0 , )

(nc , )

Electron

CPT

Positron

(2 , )

(1 , )

(0 , )

(nc , )

(1 , )

(0 , )

(nc , )

anomaly transition

(nc: cyclotron quantum number)

Figure of merit for CPT violation(Bluhm, Kostelecky, Russell):

212 102,12/)( cmeaa

(Dehmelt, Van Dyck)

Atomic Physics Single antiproton in a Penning trap

Proton

CPT

Figure of merit for CPT violation(Bluhm, Kostelecky, Russell):

252 1012/)( cmpaa

spinflip transition

(nc , )

(nc , )spinflip transition

(nc , )

(nc , )

Antiproton

(expected accuracy)

Atomic Physics

z = 1 MHz

B

compensationelectrode

ring electrode

end cap

end cap

compensationelectrode

dEp/dt = Pcool = -I2R

cooling

LRCU = I R

Electronic detection of a single antiproton

c2-

2 z

2+2

Atomic Physics

-0,2 -0,1 0,0 0,1 0,2 0,3 0,4 0,5

0,00

0,02

0,04

0,06

0,08

0,10

0,12

relativistic frequency shift:D

c/

c = - E

c/mc2, E

c = 5 eV

Dc = - 0,5 Hz

g = (1 - ß2)-1/2 = 1,000 000 005

mgeB

c =

(This antiproton wastrapped for 60 days,until Jan. 18, 1993,7 o'clock)

Cyclotron Resonance of aSingle Antiproton

Dc = 11 mHz

linewidthDc/

c = 1,2 . 10-10

elec

tron

ic s

igna

l [m

V2 ]

cyclotron frequency c - 89 258 427 Hz

Cyclotron resonance of a single antiproton

measured at LEAR,1993(G. Gabrielse,D. Phillips,W. Quint)

Atomic Physics

BM

q

ionc

Ion cyclotron frequency:Ion cyclotron frequency:

Bm

eg

e

JL 2

Larmor precession fre-quency of bound electron:

Larmor precession fre-quency of bound electron:

B

ion

qM

ee

m

ionc

L

Jg

2

G-Factor of the bound electron in H-like ions

new value for the electron mass

Atomic Physics

-20 -10 0 10 20

60µV

80µV

100µV

120µV

140µV

160µV

° non-destructive detection at T = 4 Kelvin

2,2 Hz

Measurement of the axial frequency

of a single C5+

-ion

elec

tron

ic d

etec

tion

sig

nal

axial frequency - 343 033 Hz

Atomic Physics

0 200 400 600 800364343.0

364343.5

364344.0

364344.5

axia

l fre

quen

cy [

Hz]

time [min]

spin up

spin down

Quantum jumps of a single hydrogen-like ion

• Axial frequency depends on spin direction due to continuous Stern-Gerlach effect

Atomic Physics

spin has magneticmoment

magnetic bottle:B(z) = B0 + B2z2

magnetic energy:Emagn(z) = B0 B2z2

attractive orrepulsive force

axial frequency =f (spin direction

Continuous Stern-Gerlach effect

Atomic Physics

precisiontrap

analysistrap E

lectric potential shape

Mag

netic

fiel

d lin

es

Principle:

• Excitation of spin-flip in precision trap (homogeneous magnetic field)

• Detection of spin-flip in analysis trap (inhomogeneous magnetic field for spin-flip detection)

Principle:

• Excitation of spin-flip in precision trap (homogeneous magnetic field)

• Detection of spin-flip in analysis trap (inhomogeneous magnetic field for spin-flip detection)

Double-Trap Technique for g-Factor Measurements

Atomic Physics

-15 -10 -5 0 5 10 150

10

20

30

40 C5+

Frequency ratio L/

c in rel. units [10-9]

Sp

in-f

lip p

rob

abili

ty [

% ]

• Measurement of the g-factor of the bound electron with an accuracy of 7 x 10-10

• Measurement of the g-factor of the bound electron with an accuracy of 7 x 10-10

G-Factor of bound electronin highly charged ions

Atomic Physics

Electron

(Van Dyck/

Dehmelt)

C5+

(Mainz/ GSI)

O7+

(Mainz/ GSI)

Antiproton

(proposed)

Magnetic moment

gB/2 gB/2 gB/2 gN/2

g-Factor g = 2.00... g = 2.00... g = 2.00... g = 5.58…

‘Magnetic

bottle‘

0.15 mT/mm2 10 mT/mm2 10 mT/mm2 230 mT/mm2

Dz due to

spinflip

1.3 Hz 0.7 Hz 0.46 Hz 0.25 Hz

Parameters of g-factor experiments

Atomic Physics

Improvement of accuracy in gpbar by six orders of magnitude Improvement of accuracy in gpbar by six orders of magnitude

Conclusions

Important test of CPT invariance for baryons Important test of CPT invariance for baryons

• Measurement of the magnetic moment of the bound electron with an accuracy of 7 x 10-10.• This experimental technique can be employed for the measurement of the magnetic moment of the antiproton.

• Measurement of the magnetic moment of the bound electron with an accuracy of 7 x 10-10.• This experimental technique can be employed for the measurement of the magnetic moment of the antiproton.