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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