International Accelerator Facility for Improved …International Accelerator Facility for Beams of...

International Accelerator Facility for

Beams of Ions and Antiprotons at Darmstadt

Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint

Improved Determination ofthe Electron Mass in Atomic Mass Units

Wolfgang Quint

GSI Darmstadt and Univ. Heidelberg




B

g-Factor of the electron

h

sg

B⋅=

µ

µµ: magnetic moment

g: g-factor

s: spin

µB: Bohr magneton




g = 2 + α / πα / πα / πα / π




gfree= 2 (1 + C1αααα/ππππ + C2(αααα/ππππ)2 + C3(αααα/ππππ)3 + C4(αααα/ππππ)4 + C5(αααα/ππππ)5 +....

1st order in αααα:

Schwinger termC1 = ½

QED contributions to the g-factor of the free electron

magnetic field

Ref.:J. Schwinger, Phys. Rev. 73, 416 (1948); Hanneke et al., PRL 100, 120801 (2008)

The theory of quantum electrodynamics is,I would say, the jewel of physics

- our proudest possession.R. Feynman

The theory of quantum electrodynamics is,I would say, the jewel of physics

- our proudest possession.R. Feynman




gfree= 2 (1 + C1αααα/ππππ + C2(αααα /ππππ)2 + C3(αααα /ππππ)3 + C4(αααα /ππππ)4 + C5(αααα /ππππ)5 +....

Free electron: QED contributions of 2nd and 3rd order

2nd order in αααα: C2 = - 0.328 478 966

7 graphs

3rd order in αααα: C3 = 1.176572 graphs

Ref.:B. Lautrup et al., Phys. Rep. 3, 193 (1972)

not shown:4th order in α:α:α:α:

C4 = -1.9108891 graphs




Bm

e

e

e

c =ωBm

eg

e

e

L2

=ω

cyclotron frequency:cyclotron frequency:Larmor precession

frequency:

Larmor precession

frequency:

e

c

e

Leg

ω

ω⋅= 2

g-Factor of the free electron

B: magnetic field in

Penning trap

e

c

e

aeg

ω

ω⋅=− 22or ratheror rather (get 3 orders of magnitude

in accuracy by Nature)

(get 3 orders of magnitude

in accuracy by Nature)

q1

Folie 7

q1 quint_local; 18.05.2003




Ref.:T. Beier, Physics Reports 339, 79 (2000)

QED and highly charged ions

self energy vacuum polarization vertex correction

basic processes in bound-state QED:

bound-state QED: quantum physics in strong fields

bound-state QED coupling parameter for U91+: Zα ≈ 0.67




Ref.:U.D. Jentschura, P.J. Mohr, G. Soff, PRL 82, 53 (1999); T. Beier, Physics Reports 339, 79 (2000)

Bound-state QED: treatment non-perturbative in Zαααα

non-perturbativetreatment

no expansionin Zαααα

perturbative treatment: expansion in Zαααα

Non-perturbative bound-state QED was developed in the last 20 years by excellent theoreticians like:

Beier, Blundell, Breit, Czarnecki, Glazov, Jentschura, Johnson, Karshenboim, Lindgren, Lee, Milstein, Mohr, Pachucki, Persson, Plunien, Salomonson, Sapirstein,

Shabaev, Soff, Sunnergreen, Terekhov, Tupitsyn, Volotka, Yerokhin, and others.




SELFENERGY

VACUUMPOLARIZATION

gbound/gfree ≈≈≈≈ 1 - (Zαααα)2/3 + αααα(Zαααα)2/4ππππ + ....+ ....+ ....+ ....

bound-state QEDDirac theory

Bound-electron g-factor:Feynman graphs 1st order in α/πα/πα/πα/π





Bound-electron g-factor:Feynman graphs 2nd order in α/πα/πα/πα/π


50505050 graphs




Bound-electron g-factor

Ref.:D. Glazov

NUCLEAR CHARGE Z

CO

NT

RIB

UT

ION

TO

G-F

AC

TO

R

1-loop QED free electron

2-loop QED free electron




BM

Q

ion

ion

c =ωBm

eg

e

Je

L2

=ω

Ion cyclotron frequency:Ion cyclotron frequency:Larmor precession

frequency of the

bound electron:

Larmor precession

frequency of the

bound electron: B

g-Factor of the bound electron ina hydrogen-like ion(nucleus has no spin, e.g. 12C5+, 16O7+, 28Si13+, 40Ca19+)

e

Q

M

mg

ion

ion

e

ion

c

e

LJ ⋅⋅⋅=

ω

ω2

our

measurement

our

measurement

external input

parameter

external input

parameter

→ 'experimental

g-factor'

→ comparison

with theory

→ 'experimental

g-factor'

→ comparison

with theory




A single highly charged ion stored in a Penning trap

potential

z

axial confinement

ion

radial confinement

ring

endcap

endcap

U0

magnetic

B0

physical electric

(MODIFIED) CYCLOTRON MOTION

w+

MAGNETRON DRIFT

w-

AXIAL MOTION

wz

B

combined ion motion




Precision trap (PT)

� Very homogeneous magnetic field

Analysis trap (AT)

� Magnetic bottle for spin detection

Creation trap (CT)

� In-trap ion creation of

highly-charged ions

~1

4 c

m7mm

Triple Penning Trap System




Precision trap (PT)

� Very homogeneous magnetic field

Analysis trap (AT)

� Magnetic bottle for spin detection

Creation trap (CT)

� In-trap ion creation of

highly-charged ions

Triple Penning Trap System




HCI g-factor apparatus

SUPERCONDUCTINGSOLENOIDS

PENNING TRAP @ 4K

CRYOELECTRONICS

@ 4 K

SUPERCONDUCTING MAGNETWITH ROOM TEMPERATUR BORE

CRYOSTAT

MAGNETIC BOTTLE

SINGLE IONIN TRAP

PRECISION TRAP

TARGET

FEP

MICROWAVE INLET

MINI EBIS

`DOUBLE TRAP‘




g-Factor trap in Mainz(GSI/Heidelberg collaboration)




νz = 360 kHz

B

compensationelectrode

ring electrode

end cap

end cap

compensationelectrode

dEp/dt = Pcool = -I2R

resistive cooling

LRCU = I R

Electronic detection andresistive cooling of trapped ions

νc2 = ν-

2 + νz2 + ν+

2




Mass-to-charge ratio [Volt]

Ele

ctr

. D

ete

cti

on

sig

nal

hydrogen-like ionshydrogen-like ions

Charge breeding of carbon and oxygen ionsin cryogenic EBIS (electron-beam ion source)




Isolating a single highly charged ion




High-resolution cyclotron frequency measurementof a single highly charged silicon ion

28Si13+




� Other modes can be coupled to

axial motion via rf-sideband coupling

-1500 -1000 -500 0 500 1000 1500

0

2

4

6

8

10

12

-2 -1 0 1 2

0

3

6

9

12

Sig

na

l (d

BV

rms)

Frequency / Hz -670900

-15 -10 -5 0 5 10 15

0

2

4

6

8

10

12

14

16

Sig

na

l (d

BV

rms)

Frequency / Hz -670900

� Axial frequency directly measured as

narrow “dip”

RLzrfv νννν ++−=+

zv

Eigenfrequency Measurement

)( zv

),( −+ vv

RνLνRLzrfv νννν −−+=−

300mHz




Continuous Stern-Gerlach effect:Determination of spin direction

B2B1

z

1

2

2B

KE

Lz

m=D

2B

mz

z

w

mw =D

CLASSICALSTERN-GERLACH

CONTINUOUSSTERN-GERLACH

SEPARATION IN POSITION SPACE SEPARATION IN FREQUENCY SPACE




Quantum jump spectroscopy:Spin-flip transitions in the analysis trap




Anke

WagnerSven

SturmBirgit

Schabinger

The lab team(before spinflip)




The lab team (after spinflip)




Measurement Cycle

704790 704820 704850 704880

-210

-200

-190

-180

Sig

nal (d

BV

)

Axial Frequency (kHz)

6 0 7 0 8 0 9 0 1 0 0

-0 .5

-0 .4

-0 .3

-0 .2

-0 .1

0 .0

0 .1

0 .2

0 .3

0 .4

0 .5

F

ractio

na

l a

xia

l fr

eq

uen

cy d

iffe

ren

ce

(H

z)

M e a s u re m e n t n u m b e r

AT PT

2. PT: Measurement of eigenfrequencies and

simultaneous irradiation with microwaves

1. AT: Detection of spin orientation: → spin up

0 1 0 2 0 3 0 4 0 5 0

-0 .5

-0 .4

-0 .3

-0 .2

-0 .1

0 .0

0 .1

0 .2

0 .3

0 .4

0 .5

Fra

ctio

na

l a

xia

l fr

equ

en

cy d

iffe

rence (

Hz)

M e a s u re m e n t n u m b e r

3. AT: Detection of spin orientation → spin down

+vzv cv

Lv

c

L

ν

ν=Γ

4. Spin flip in PT? → spin has flipped!

−v(offline)

Precision measurement of bound electron g-factor in hydrogen-like silicon




Bound electron magnetic moment measurementon hydrogen-like silicon 28Si13+

Sp

infl

ip p

rob

abil

ity (

%)




gJ(12C5+) = 2.001 041 590 18 (3) theoretical value

gJ(12C5+) = 2.001 041 596 4 (10)(44) our measurement

gJ(12C5+) = 2.001 041 590 18 (3) theoretical value

gJ(12C5+) = 2.001 041 596 4 (10)(44) our measurement

Comparison of theory and experiment:g-Factor of the bound electron in

H-like carbon 12C5+, oxygen 16O7+ and silicon 28Si13+

Lit.:

T. Beier et al., PRL 88, 011603 (2002)

V. Shabaev et al., PRL 88, 091801 (2002)

V. Yerokhin et al., PRL 89, 143001 (2002)

K. Pachucki, V. Yerokhin et al., PRA 72, 022108 (2005)

S. Sturm et al., PRL 107, 023002 (2011)

gJ(16O7+) = 2.000 047 020 32 (11) theoretical value

gJ(16O7+) = 2.000 047 025 4 (15)(44) our measurement

gJ(16O7+) = 2.000 047 020 32 (11) theoretical value

gJ(16O7+) = 2.000 047 025 4 (15)(44) our measurement

gJ(28S13+) = 1.995 348 958 0 (17) theoretical value

gJ(28S13+) = 1.995 348 958 7 (5)(3)(8) our measurement

gJ(28S13+) = 1.995 348 958 0 (17) theoretical value

gJ(28S13+) = 1.995 348 958 7 (5)(3)(8) our measurement




BM

Q

ion

ion

c =ωBm

eg

e

Je

L2

=ω

Ion cyclotron frequency:Ion cyclotron frequency:Larmor precession

frequency of the

bound electron:

Larmor precession

frequency of the

bound electron: B

Q

eg

M

me

L

ion

cJ

ion

e⋅⋅=

ω

ω

2

Electron mass

our

measure-

ment

our

measure-

ment

→ determination

of electron mass

→ determination

of electron mass

theory as

input

parameter

theory as

input

parameter




� Several Г-resonances at different

cyclotron energies to check systematics

→ extrapolation to zero energy

Experimental Result

0

10

20

30

40

50

1.00.0-1.0 0.5

(Γ/Γι

0-1) / 10

-9

Fra

ction

al sp

inflip

ra

te /

%

FWHM: 7·10-10

-0.5

0,00 0,05 0,10 0,15 0,20 0,25

0,0

0,2

0,4

0,6

0,8

1,0

1,2

Γ/Γ

0 -

1 / 1

0-9

U2

exc (V

2)

Г0 = 4 736. 210 500 89 (11)(7)(stat.) (syst.)

� Probing Zeeman transition at different Γ’s

several 100 times:

→ Г-resonance

� Γ0’ is extracted from fit

� Resonance width and thus statistical error

limited by magnetic field fluctuations

� Dominant systematics:

� image charge shift: -282(14) ppt




Result

me=0,000 548 579 909 067 (14)(9)(2) u(stat)(syst)(theo)

δme/me=3·10-11

Г0 = 4 736. 210 500 89 (11)(7)(stat.) (syst.)

gtheo = 2. 001 041 590 176 (6)

0

1

2 Γ=

ion

theoione

q

egmm

TheoryExperiment

[S. Sturm et al., Nature 506, 467-470 (2014)]

2013

2010

2007

2004

2001

1998

1995

-6 -4 -2 0 2 4 6

Farnham

Hori

this work

Verdú

me/m

this work

e-1 (parts per billion)

Year

CODATAHäffner




Result

me=0,000 548 579 909 067 (14)(9)(2) u(stat)(syst)(theo)

δme/me=3·10-11

Г0 = 4 736. 210 500 89 (11)(7)(stat.) (syst.)

gtheo = 2. 001 041 590 176 (6)

0

1

2 Γ=

ion

theoione

q

egmm

TheoryExperiment

[S. Sturm et al., Nature 506, 467-470 (2014)]

2013

2010

2007

2004

2001

1998

1995

-6 -4 -2 0 2 4 6

Farnham

Hori

this work

Verdú

me/m

this work


Yea

r

CODATAHäffner

2013

2010

2007

2004

2001

1998

1995

-6 -4 -2 0 2 4 6

Farnham

Hori

this work

Verdú

me/m

this work


Yea

r

CODATAHäffner




Who has forgotten the walnut?Who has forgotten the walnut?

500000 tons500000.000015 tons

Relative Precision: 3·10-11




Profit of an improved electron mass me

Important ingredient in fine-structure constant measurement:

Rbe

Rb

e

recoilM

h

m

M

c

R

cm

hR ∞∞ ==222α

Rb

recoilM

kv

h=

5 ppt,

CODATA (T. Hänsch) 2010

115 ppt,

E. Myers 2010

1241 ppt,

F. Biraben 2011

30 ppt, our value




Measurements of the electron mass over the years

Mq

em

electron

c

ion

ce

ν

ν=

Bm

e

e

electron

cπ

ν2

=

Ion

B

e-

BM

qion

cπ

ν2

=

1970 1980 1990 2000 201010

-10

10-9

10-8

10-7

10-6

10-5

rela

tive

un

ce

rta

inty

of m

e

year

CODATA Indirect measurement via µB/µΝ

Gärtner: vc via particle loss (first direct)

Gräff: vc via ToF

Van Dyck: vc via image currents (first non-destructive)

Wineland: vc via laser fluorescence + vL + gtheo

(first bound electron)

Gabrielse: vc via image currents

Farnham: vc via image currents (first single ion)

Häffner: vc/vL of 12

C5+

+ gtheo

Verdú: vc/vL of 16

O7+

+ gtheo

Hori: antiprotonic helium

common

mass spectrometry




• “Abteilung für gespeicherte und gekühlte Ionen” at MPIK, Heidelberg

• Atomic Physics Division at GSI Helmholtzzentrum, Darmstadt

• QUANTUM group at the Institut für Physik, Mainz

• International Max Planck Research School – Quantum Dynamics

Special thanks to

Experiment: Jiamin Hou, Sven Sturm, Anke Wagner,

Günter Werth, Klaus Blaum

Theory: Jacek Zatorski, Zoltán Harman, Christoph H. Keitel

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