Correlated cyclotron and spin
measurements to make an
improved measurement of the
electron magnetic moment
Elise Novitski
Harvard University
Lepton Moments
21 July 2014
Correlated cyclotron and spin
measurements to make an
improved measurement of the
electron magnetic moment
Elise Novitski Shannon Fogwell Hoogerheide
Harvard University
Lepton Moments
21 July 2014
Acknowledgements
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)
2
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 Model
Electron:
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)
3
Fine Structure Constant
uncertainty in  in ppb
• Most Precise determination of α
0.4
total uncertainty
0.3
from theory
from
exp't
0.2
0.1
0.0
(g/2)
(C8)
(C10)
(ahadronic)
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)
(aweak)
4
Fine Structure Constant
uncertainty in  in ppb
• Most Precise determination of α
0.4
total uncertainty
0.3
from theory
from
exp't
We want to improve the
experimental precision!
0.2
0.1
0.0
(g/2)
(C8)
(C10)
(ahadronic)
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)
(aweak)
5
Ingredients of a g/2 measurement
• Measure cyclotron frequency
• Measure anomaly frequency
• Measure axial frequency (less
precision needed)
• Calculate special relativistic shift ( )
• Calculate ww from measured
cavity mode couplings
6
D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)
Ingredients of a g/2 measurement
• Measure cyclotron frequency
• Measure anomaly frequency
• Measure axial frequency (less
precision needed)
• Calculate special relativistic shift ( )
• Calculate ww from measured
cavity mode couplings
7
D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)
Ingredients of a g/2 measurement
• Measure cyclotron frequency
• Measure anomaly frequency
• Measure axial frequency (less
precision needed)
• Calculate special relativistic shift ( )
• Calculate ww from measured
cavity mode couplings
8
D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)
Uncertainties in the 2008 measurement
g/2 = 1.001 159 652 180 73 (28) [0.28 ppt]
Uncertainties for g in parts-per-trillion.
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
Leading uncertainty is lineshape model
uncertainty– limits precision to which
it is possible to split our anomaly and
cyclotron lines
9
D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)
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:
æ1
ö
2
H z0 + H 'z = ç mw z0
- ms,c B2 ÷ z 2
è2
ø
Dn z
1 g
-9
» 7 ´10 (n + + ms )
nz
2 2
10
L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)
Coupling to axial motion broadens
cyclotron and anomaly lines
normalized excitation fraction
Tz = 16 K
Tz = 5 K
Tz = 0.32 K
0
50
100
150
200
250
frequency offset from nc / ppb
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)
11
New Technique: Correlated Measurement
2008 Protocol
New Protocol
• Cyclotron attempts followed by
anomaly attempts
• Apply cyclotron and anomaly
drives simultaneously
fc
na
• Combine data, adjust for field
drift, fit both lines to extract g/2
• Generate 2-D correlated
lineshape, extract g/2
cyclotron detuning
12
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
L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)
B. D’Urso, Ph.D. thesis, Harvard University (2003)
cyclotron frequency detuning
14
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)
15
Axial decoupling and the discrete lineshape limit
• 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
L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)
B. D’Urso, Ph.D. Thesis, Harvard University, 2003
20
Cavity-assisted axial sideband cooling
• Decouple axial motion from amplifier
• Apply a drive at w C - w z 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
21
L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)
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)
22
Cavity mode structure of the 2008 trap was not
conducive to cavity-assisted axial sideband cooling
Trap dimensions
Measurements
done in this range
Strong cyclotron damping modes:
cause short lifetime and cavity
shift, so must be avoided
Cooling modes:
enable axial-cyclotron
sideband cooling
Trap radius/height ratio
• 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)
24
Cavity mode structure of the new trap will
enable cavity-assisted axial sideband cooling
New trap dimensions
Strong cyclotron damping modes:
cause short lifetime and cavity
shift, so must be avoided
New g-2
measurements
will be done here
Cooling modes:
enable axial-cyclotron
sideband cooling
Trap radius/height ratio
• Can drive directly on good cooling mode
• Axial ground state should be achievable
25
S. Fogwell Hoogerheide, Ph.D. Thesis, Harvard University, 2013
Additional techniques for improving
cyclotron and anomaly frequency
measurements
• 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)
26
D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)
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
Uncertainties for g in parts-per-trillion.
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
na
28
D. Hanneke, S. Fogwell, and G. Gabrielse, Phys. Rev Lett. 100, 120801 (2008)
Status and outlook
Improvements that have already been implemented
• New apparatus with positrons, improved stability, smaller
magnetic bottle, etc
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
29
Bound electron g-value and Electron
mass
Larmor precession frequency
of the bound electron:
wL e 
B
gJ e
B
2 me
Ion cyclotron frequency:
wc ion 
Q
B
Mion
g J wc
me
e



e
Mion
2 wL Q
ion
→ determination
of electron mass
theory
measurement
me=0,000 548 579 909 067 (14)(9)(2) u
[S. Sturm et al., Nature 506, 467-470 (2014)]
(stat)(syst)(theo)
δme/me=3∙10-11
31
Wolfgang Quint, GSI/Heidelberg
Bound electron g-value and Electron
mass
Larmor precession frequency
of the bound electron:
wL e 
B
gJ e
B
2 me
Ion cyclotron frequency:
wc ion 
Q
B
Mion
g J wc
me
e
h 2 R M

e
2
R
h
Rb


Mion
2 wL Q


cme theory c measurement
me M Rb
ion

2
recoil
→ determination
of electron mass
me=0,000 548 579 909 067 (14)(9)(2) u
[S. Sturm et al., Nature 506, 467-470 (2014)]
(stat)(syst)(theo)
δme/me=3∙10-11
32
Wolfgang Quint, GSI/Heidelberg
Bound electron g-value and Electron
mass
Larmor precession frequency
of the bound electron:
wL e 
gJ e
B
2 me
B
Ion cyclotron frequency:
wc ion 
Q
B
Mion
POSTER:
ion
g J wc
me
e
WOLFGANG
 2 R h e 2R M
h
2
Rb


M
ion  2
QUINT
wL Q
 recoil
cme measurement
c me M Rb
theory
WEDNESDAY
→ determination
of electron mass
AFTERNOON
me=0,000 548 579 909 067 (14)(9)(2) u
[S. Sturm et al., Nature 506, 467-470 (2014)]
(stat)(syst)(theo)
δme/me=3∙10-11
33
Wolfgang Quint, GSI/Heidelberg