Correlated cyclotron and spin measurements to make an

improved measurement of the electron magnetic moment

Elise NovitskiHarvard UniversityLepton Moments

21 July 2014

Correlated cyclotron and spin measurements to make an

improved measurement of the electron magnetic moment

Elise NovitskiHarvard UniversityLepton Moments

21 July 2014

Shannon Fogwell Hoogerheide

Acknowledgements

3

Prof. Gerald Gabrielse

PhD Students: • Ronald Alexander (new student)• Maryrose Barrios (new student)• Elise Novitski (PhD in progress…)• Joshua Dorr (PhD, Sept. 2013)• Shannon Fogwell Hoogerheide (PhD, May

2013)

4

Standard Model Triumph

• Most Precisely Measured Property of an Elementary Particle• Tests the Most Precise Prediction of the Standard Model

Experiment: Standard Model:

• Testing the CPT Symmetry built into the Standard ModelElectron:Positron:

D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)R. Boucjendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, Phys. Rev. Lett. 106, 080801 (2011)T. Aoyama, M. Hayakawa, T. Kinoshita, and M. Nio, Phys. Rev. Lett. 109, 111808 (2012)

5

Fine Structure Constant

• Most Precise determination of α

D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)R. Boucjendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, Phys. Rev. Lett. 106, 080801 (2011)T. Aoyama, M. Hayakawa, T. Kinoshita, and M. Nio, Phys. Rev. Lett. 109, 111808 (2012)

unce

rtai

nty

in

in p

pb

0.0

0.1

0.2

0.3

0.4

(g/2) (C8) (C10) (ahadronic) (aweak)

from theoryfromexp't

total uncertainty

6

Fine Structure Constant

• Most Precise determination of α

D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)R. Boucjendira, P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, Phys. Rev. Lett. 106, 080801 (2011)T. Aoyama, M. Hayakawa, T. Kinoshita, and M. Nio, Phys. Rev. Lett. 109, 111808 (2012)

unce

rtai

nty

in

in p

pb

0.0

0.1

0.2

0.3

0.4

(g/2) (C8) (C10) (ahadronic) (aweak)

from theoryfromexp't

total uncertainty

We want to improve the experimental precision!

7

Ingredients of a g/2 measurement• Measure cyclotron frequency• Measure anomaly frequency• Measure axial frequency (less precision needed)• Calculate special relativistic shift ( )• Calculate / Dw w from measured cavity mode couplings

D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

8

Ingredients of a g/2 measurement• Measure cyclotron frequency• Measure anomaly frequency• Measure axial frequency (less precision needed)• Calculate special relativistic shift ( )• Calculate / Dw w from measured cavity mode couplings

D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

9

Ingredients of a g/2 measurement• Measure cyclotron frequency• Measure anomaly frequency• Measure axial frequency (less precision needed)• Calculate special relativistic shift ( )• Calculate / Dw w from measured cavity mode couplings

D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

10

Uncertainties in the 2008 measurement

nc / GHz = 147.5 149.2 150.3 151.3

Statistics 0.39 0.17 0.17 0.24

Cavity shift 0.13 0.06 0.07 0.28

Uncorrelated lineshape model

0.56 0.00 0.15 0.30

Correlated lineshape model

0.24 0.24 0.24 0.24

Total 0.73 0.30 0.34 0.53

Uncertainties for g in parts-per-trillion.

g/2 = 1.001 159 652 180 73 (28) [0.28 ppt]

Leading uncertainty is lineshape model uncertainty– limits precision to which it is possible to split our anomaly and cyclotron lines

D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

11

Spin and cyclotron detection• Magnetic bottle creates z-dependent B field, which adds another term to axial Hamiltonian• Modifies axial frequency to depend on spin and cyclotron states:

L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)

12

Coupling to axial motion broadens cyclotron and anomaly lines

L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)B. D’Urso et al., Phys. Rev. Lett. 94, 113002 (2005)D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

frequency offset from c / ppb

0 50 100 150 200 250

no

rma

lize

d e

xcita

tion

fra

ctio

n

Tz = 16 K

Tz = 5 K

Tz = 0.32 K

13

New Technique: Correlated Measurement2008 Protocol• Cyclotron attempts followed by

anomaly attempts

• Combine data, adjust for field drift, fit both lines to extract g/2

New Protocol• Apply cyclotron and anomaly

drives simultaneously

• Generate 2-D correlated lineshape, extract g/2

cyclotron detuning

anom

aly

detu

ning

15

Advantages of the correlated measurement protocol

• Eliminates magnetic field drifts between a given anomaly and cyclotron data point

• In low-axial-damping limit, system stays in single axial state during a measurement, creating discrete peaks

• Combined with cooling to axial ground state, each point is a full g-2 measurement

cyclotron frequency detuning

anom

aly

freq

uenc

y de

tuni

ng

L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)B. D’Urso, Ph.D. thesis, Harvard University (2003)

16

Technical challenges of the correlated measurement protocol

• Need to be in low axial damping limit to take full advantage, so must develop a method of decoupling particle from amplifier

• Lower transition success rate, so statistics could be an issue– Both cyclotron and anomaly drive attempts must

be successful to get an excitation– Much narrower lines, and must still know B-field

well enough to drive transitions

L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)B. D’Urso, Ph.D. thesis, Harvard University (2003)

21

Axial decoupling and the discrete lineshape limit

L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)B. D’Urso, Ph.D. Thesis, Harvard University, 2003

• A technical challenge: decoupling particle from amplifier to prevent reheating of axial motion

• A consequence of decoupling: reaching the discrete-lineshape limit in one or both lines, where quantum nature of axial motion is evident

• With cavity-assisted axial sideband cooling, goal is to reach lowest axial state

22

Cavity-assisted axial sideband cooling

L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)

• Apply a drive at to couple axial and cyclotron motions

• Cooling limit:

• Cooling rate:

• Interaction with the resonant microwave cavity mode structure: a challenge that can be converted into an advantage

• Decouple axial motion from amplifier

23

Trap as a resonant microwave cavity

Power coupling efficiency:

TE111 27.4 GHz

L. S. Brown, G. Gabrielse, K. Helmerson, and J. Tan, Phys. Rev. Lett. 51, 44-47 (1985)L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)J. Tan and G. Gabrielse, Phys. Rev. A 48, 3105-3122 (1993)D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

25

Cavity mode structure of the 2008 trap was not conducive to cavity-assisted axial sideband cooling

Strong cyclotron damping modes:cause short lifetime and cavity

shift, so must be avoided

Cooling modes: enable axial-cyclotron

sideband cooling

Trap dimensions

Cyc

lotr

on fr

equ

ency

(G

Hz)

Trap radius/height ratio

Measurementsdone in this range

• Frequencies good for avoiding cyclotron modes were 30 linewidths away from good cooling modes• Cooling was attempted but axial ground state was never reached

D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)D. Hanneke, Ph.D. thesis, Harvard University (2007)

26

Cavity mode structure of the new trap will enable cavity-assisted axial sideband cooling

New g-2 measurementswill be done here

New trap dimensions

Cyc

lotr

on fr

equ

ency

(G

Hz)

Trap radius/height ratio

Strong cyclotron damping modes:cause short lifetime and cavity

shift, so must be avoided

Cooling modes: enable axial-cyclotron

sideband cooling

• Can drive directly on good cooling mode• Axial ground state should be achievable

S. Fogwell Hoogerheide, Ph.D. Thesis, Harvard University, 2013

27

Additional techniques for improving cyclotron and anomaly frequency

measurements

D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

• Narrower lines– Smaller magnetic bottle– Lower axial state via cavity-assisted axial sideband cooling

• Cleaner lineshapes for finer linesplitting– Reduce vibrational noise (improved support structure to maintain

alignment)– Improve magnet stability (changes to cryogen spaces and magnet design)

29

Another frontier: better statistics

• Rate-limiting step: wait for cyclotron decay after anomaly transition attempt (or correlated transition attempt)

• To speed this step, sweep down with adiabatic fast passage or π-pulse

nc / GHz = 147.5 149.2 150.3 151.3

Statistics 0.39 0.17 0.17 0.24

Cavity shift 0.13 0.06 0.07 0.28

Uncorrelated lineshape model

0.56 0.00 0.15 0.30

Correlated lineshape model

0.24 0.24 0.24 0.24

Total 0.73 0.30 0.34 0.53

Uncertainties for g in parts-per-trillion.

D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)

30

Status and outlook

Remaining basic preparation• Transfer positrons from

loading trap into precision trap to prepare for positron measurement

• Characterize apparatus (cavity mode structure, systematic checks, etc)

New techniques in development

• Develop method for detuning particle from amplifier

• Demonstrate cavity-assisted axial sideband cooling and correlated measurement protocol

New measurements of positron and electron g-2 at greater precision than the 2008 electron measurement

Improvements that have already been implemented

• New apparatus with positrons, improved stability, smaller magnetic bottle, etc

32

Bound electron g-value and Electron mass

BM

Q

ion

ionc B

m

eg

e

JeL 2

Ion cyclotron frequency:Ion cyclotron frequency:Larmor precession frequencyof the bound electron:

Larmor precession frequencyof the bound electron: B

Q

eg

M

meL

ioncJ

ion

e

2

measurementmeasurement→ determination of electron mass

→ determination of electron mass

theorytheory

me=0,000 548 579 909 067 (14)(9)(2) u(stat)(syst)(theo)[S. Sturm et al., Nature 506, 467-470 (2014)]

Wolfgang Quint, GSI/Heidelberg

δme/me=3∙10-11

33

Bound electron g-value and Electron mass

BM

Q

ion

ionc B

m

eg

e

JeL 2

Ion cyclotron frequency:Ion cyclotron frequency:Larmor precession frequencyof the bound electron:

Larmor precession frequencyof the bound electron: B

Q

eg

M

meL

ioncJ

ion

e

2

measurementmeasurement→ determination of electron mass

→ determination of electron mass

theorytheory

me=0,000 548 579 909 067 (14)(9)(2) u(stat)(syst)(theo)[S. Sturm et al., Nature 506, 467-470 (2014)]

Wolfgang Quint, GSI/Heidelberg

δme/me=3∙10-11

Rbe

Rb

erecoil M

h

m

M

c

R

cm

hR 222

34

Bound electron g-value and Electron mass

BM

Q

ion

ionc B

m

eg

e

JeL 2

Ion cyclotron frequency:Ion cyclotron frequency:Larmor precession frequencyof the bound electron:

Larmor precession frequencyof the bound electron: B

Q

eg

M

meL

ioncJ

ion

e

2

measurementmeasurement→ determination of electron mass

→ determination of electron mass

theorytheory

me=0,000 548 579 909 067 (14)(9)(2) u(stat)(syst)(theo)[S. Sturm et al., Nature 506, 467-470 (2014)]

Wolfgang Quint, GSI/Heidelberg

δme/me=3∙10-11

Rbe

Rb

erecoil M

h

m

M

c

R

cm

hR 222

POSTER: WOLFGANGQUINTWEDNESDAY AFTERNOON