precision measurement in atomic physics - nctu institute of physics ... · · 2011-06-07li-bang...
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Li-Bang Wang, National Tsing Hua University
Precision Measurement in Atomic Physics
NCTU IOP Colloquium 5/12/2011NCTU IOP Colloquium 5/12/2011
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On Growth and Form, 1917
numerical precision is the
very soul of science
Thompson, D'Arcy Wentworth
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How precise?How precise?
Magnetic moment of electron,
ge (exp) = 2.0023193043617(15)
Rydberg constant =
= 109,737.31568639(91)
Electric dipole moment of electron
|de| < 1.61027 ecm
Time variation of fine structure constant
/ = (-6.2 6.5)x10-17/year
cheme
3
422
[1] G. Gabrielse et al., Phys. Rev Lett. 97, 30802 (2006)[2] Th. Udem et al., Phys. Rev. Lett. 79, 2646 (1997)[3] B. C. Regan et al., Phys. Rev. Lett. 88: 071805 (2002)[4] T. M. Fortier et al., Phys. Rev. Lett. 98, 070801 (2007)
13712 c
e
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OutlineOutline
Historical Review:
Precision measurement lead to new physics
Selected topics
Atomic spectroscopy: techniques utilizing
resonance, frequency measurement very
precise
Precision spectroscopy in our lab @NTHU
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New Physics Discovered by Atomic SpectroscopyNew Physics Discovered by Atomic Spectroscopy
microwave region
Detector
A magnet B magnet
source
NMR for Deuteron
Isidor Isaac Rabi
Norman F. Ramsey
First Motivated by Stern-Gerlach experiment, 1922 First atomic spectroscopy by resonance method
NMR, Rabi and Ramsey, 1934-1939
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Electric Electric QuadrupoleQuadrupole Moment of DeuteronMoment of Deuteron
J. M. Kellogg, I. I. Rabi, N. F. Ramsey, and J. R. Zacharias Phys. Rev. 57, 677 (1940)
Electric Quadrupole moment of Deuteron discovered Nuclear force is Non-central! Tensor force
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The Lamb ShiftThe Lamb Shift
Willis Eugene LambNobel Prize in 1955"for his discoveries concerning the fine structure of the hydrogen spectrum"
H2source
1 S1/2
2 S1/22 P1/2
e- gun
Microwave region
2 P3/2
1947 by Lamb ~1060 MHznow: 1057.846(4) MHz
Detector
e+
e-
p
p e-
e-
p
pe-
e-
LS QED
p
pe-
e-
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QEDQED
Sin-Ichiro Tomonaga ( ), Julian Schwinger, Richard P. FeynmanNobel Prize in Physics 1965
"for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles"
Quantum Electrodynamics
The most precisely tested theory
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Selected topics in precision measurementSelected topics in precision measurement
Test QED: the g-2 of electron and muonNew source of CP violation: electric dipole
moment of electron and nucleon Strong interaction: size of proton Time and frequency standard: making a better
clock Constancy of fundamental constant: can speed of
light change?Weak interaction: parity violation in atom Spectroscopy of simple atom
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gg--2 of electron2 of electron
sg
B
What is g-factor?The magnetic moment of the electron is proportional to the electron spin
Classical non-relativistic g=1
In QM, Dirac Theory predict g=2
In reality, g= 2.002319304
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Why measure g factorWhy measure g factor
Test QED
Search for structure of electrons
g can be expanded as a function of
weakhadronic aaa
CCCg
......1
2
3
6
2
42
-1 = 137.035 999 070 (98)Gabrielse, Hanneke, Kinoshita, Nio, and Odom, Phys Rev Lett 97, 30802 (2006)
13712 c
e
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How to measure gHow to measure g
Spin precession (Larmor) frequency
Bgm BsL Calibration of magnetic field by cyclotron frequency:
BMq
C
C
L
C
L
Mm
eqg
22
Measurement performed on a single electron in Penning trap
me
B 2
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Current statusCurrent status
g-2 experiment of electron and muon:
ge (exp) = 2.0023193043617(15), ge (th) to determine fundamental constant
g (exp) = 2.0023318416(12)*g (th) = 2.0023318367(13)*
5 deviation
G.W. Bennett et al., Phys Rev Lett 92, 1618102 (2004)
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Permanent electric dipole momentPermanent electric dipole moment
1957 Landau first pointed out the electric dipole moment (EDM) of a fundamental particle would suggest P and T violation
d: electric dipole moment = vectoru: spin or magnetic moment = pseudo-vector, (like r x p)
figure from Wikipedia
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Neutron EDM: historyNeutron EDM: history
By Ramsey
figure from Wikipedia
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CP violation without strangenessCP violation without strangeness
Matterantimatter asymmetry suggest
another source of CP violationElectron: intrinsic ?Quark: intrinsic ?Neutron/proton:
from quark EDM ? New interaction?Atoms, molecules:
large enhancement factors
Atoms: Tl, Cs, Hg, Xe, Rn, Ra, FrMolecule: PbO, YbF, TlFIons, solid state systems, etc
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How to measure EDMHow to measure EDM
Problem: reverse E field cause leakage current,huge noise from B field
figure from M. Romalis, Princeton
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Current statusCurrent status
Typical valueE ~ 10 kV/cm~ 10Hz, ~ nHz
Sensitivity approachingsome Standard Model extension
figure from M. Romalis, Princeton
What if someone observes EDM?Theories ready with many parameters
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Size of protonSize of proton
Fundamental quantity bothering for decades Very important for nuclear calculation Lattice QCD not able to calculate precisely
)2/(tan)(2
41
)(4
)(222
2
2
2
2
222
222
QGMQ
MQ
QGMQQG
dd
dd
M
ME
MottRosenbluth
02
22
2
)(6
Q
Ec dQ
QdGr
Charge radius of proton by electron scattering
Simon et al, (1980) Rrms = 0.862(12) fm
I. Sick, (2003). Rrms = 0.895(18) fm
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Laser spectroscopy methodLaser spectroscopy method
Measure H transition frequency 1s 2s at 121nm,
uncertainty: (th) 16kHz, (exp) 22kHz
charge radius of proton Rrms = 0.883(14) fm
Lack of precision (only1~2%) very annoying!
Kirill Melnikov and Timo van Ritbergen, Phys. Rev. Lett. 84, 1673(2000)
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MuonicMuonic hydrogenhydrogen
muon decay e
proton -
m/me ~ 200 Bohr radius
Energy level
Wave function
Energy shift due to nuclear size~
Sensitivity ~ (m/me)2
2
20
04
ema
e
220
4
)4(2 nmeE en
220 r
0/2/30~ arear
at PSI, aiming 0.1% measurementRrms = 0.84184(67)fm
The size of the proton, Nature 466, 213216, 2010
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Frequency standardFrequency standard
Figure: S.A. Diddams et al.,Science 306, 1318, 2004
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Why better clock?Why better clock?
When you measure something very precisely,
new physics will come out by itself!
Applications:
GPS
Test special relativity, gravitational red-shift
Gravitational wave radiation in binary pulsar
Test linearality of quantum mechanics
Variation of fundamental constant
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Results From Searches for dResults From Searches for d/dt/dt
refquantitymethod
11
10
9
8
7
6
5
43
2
1
Quasar spectra(6.4 1.4) 10-16
(m/qcd)0.5Oklo nuclear reactor-(2.3 +0.7/-0.3) 10-17
(m/qcd)0.5Oklo nuclear reactor < 0.8 10-17
gCs/gRb0.44Rb Cs(0.02 0.7) 10-15
gCsme/mp2.8Opt-H Cs(-0.9 2.9) 10-15
gCsme/mp6.0Opt-Hg+ Cs(-6.2 6.5) 10-17
gCsme/mp1.9Opt-Yb+ Cs(0.3 2.0) 10-15
Dy atomic beam(-2.7 2.6) 10-15Quasar spectra(4.4 1.6) 10-16Quasar spectra(0.6 0.6) 10-16
Quasar spectra(7.2 1.8) 10-16
/ per year
[1] S. K. Lamoreaux and J. R. Torgerson, Phys. Rev. D 69, 121701R (2004).[2] Y. Fujii et al., Nuclear Physics B 573, 377 (2000).[3] J. K. Webb et al., Phys. Rev. Lett. 87, 091301 (2001).[4] M. T. Murphy, J. K. Webb, and V. V. Flambaum, Mon. Not. R. Astron. Soc. 345,609 (2003).[5] R. Srianand et al., Phys. Rev. Lett. 92, 121302 (2004).[6] M. T. Murphy, J. K. Webb, and V. V. Flambaum, astro-ph/0612407 (2006).[7] A. Cingz et al., Phys. Rev. Lett. 98, 040801 (2007).[8] M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004).[9] E. Peik et al., Phys. Rev. Lett. 93, 170801 (2004).[10] H. Marion et al., Phys. Rev. Lett. 90, 150801 (2003).[11] T. M. Fortier et al., Phys. Rev. Lett. 98, 070801 (2007).
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Parity violation in atomParity violation in atom
interaction between nucleus and electron involves coherent sum of neutral weak and electromagnetic amplitudes
e N e N
Z0+
2
|M|2
opposite parity states (e.g. 2s and 2p of H)
are mixed by weak interaction
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In HydrogenIn Hydrogen
111080/122
~ L
HzL
QE
pHs Wweak
conventional characterization in atomic
physics: weak charge
NZ4sin1NZ,Q W2W Mixing between 2s and 2p state
Measure asymmetry in transition rate under
reversed E, B field
Weak mixing angle SinW
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Weinberg angleWeinberg angle
Only success: Cs APV by C. WiemanRecently, D. Budker, large APV effect in Yb
Bismuth: M. Macpherson et al, PRL 67, 2684 (1991)Lead: D. Meekhof et al, PRL 71, 3442 (1993)Thallium: P. Vetter et al, PRL 74, 2658 (1995) Cesium: C. Wieman et al, PRL 82, 2484 (1999)Ytterbium: K. Tsigutkin et al, PRL. 103, 071601 (2009)
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Hydrogen energy levelHydrogen energy level
2222 6.13
21
neV
nmcEn
23
)2/1(2
41
224
ln
nmc
)2/1)(2/1(1),(
41
325
ljlnk
nmc
23
)2/1(2
41
224
jn
nmc
2/3)1(34
224
ff
nmc
mm p
p
protonrZe 222 )0(
32
non-relativistic
relativistic correction
spin-orbit interaction(LS, fine structure)QED effect (Lamb shift)
nuclear magnetic moment (hyperfine structure)nuclear size effect
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Nuclear size effectNuclear size effect
transition from s to p state decrease transition frequency
rE
s
pr
E
p
s
b) finite size nucleusa) point nucleusV ~ - 1/r
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Result for hydrogenResult for hydrogen
Measure total transition frequency:uncertainty: theory 16kHz, experiment 22kHz charge radius of proton = 0.883(14) fmMeasure isotope shift, 1s 2s 121 nm = 670 994.33464(15) MHz
nuclear mass
nuclear sizenuclear polarizability
nuclear magnetic susceptibility
Reference: [1] Kirill Melnikov and Timo van Ritbergen, Phys. Rev. Lett. 84, 1673(2000)[2] A. Huber, Th. Udem, B. Gross, J. Reichert, M. Kourogi, K. Pachucki, M. Weitz, and T.W. Hnsch. Phys. Rev. Lett. 80, 468 (1998)
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Isotope shiftIsotope shift
Mass shift: due to nucleus recoil
Isotope Shift = MS + FS
Field shift: due to nuclear size
MS ''
AAAA FS
[(0)]2 < rc2 >
Nuclear mass precisely known Atomic structure (0) calculable,H, He, Li.
This method widely used in H-D, 4He-3He, and 6Li-7Li
and determine the difference in the nuclear size
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Summary of QED uncertaintySummary of QED uncertainty
H: 10 kHz, He: 1 MHz, Li: > 10 MHz
Typical nuclear effect: several MHz
Except for H, precise measurement of total
transition frequency cannot get nuclear effect
First pointed out by G. Drake, QED uncertainty
largely cancel in isotope shift measurement
Uncertainty in IS:
H:
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Previous attempt for heliumPrevious attempt for helium
Theory
23P1-2
150 160 170 180 190
Pachucki '06 [4]
Drake '02 [5]
Frequency - 2291000 kHz
Harvard '05
York '00
N. Texas '00
940 945 950 955 960
Pachucki '06 [4]
Drake '02 [5]
LENS '04
Harvard '05
York '01
Frewquency - 29616000 kHz
23P0-1
Experiment Theory Experiment
uncertainty of theory and exp < 1kHzdifference = 10kHz and 20kHz
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Discrepancy in lithiumDiscrepancy in lithium
0 1 2 3 4 5 6 7 8 9 10 11 12 130.0
0.2
0.4
0.6
0.8
1.0
1.2
Austria
Austria
India
D2
York
York
R
2 (6 L
i-7Li
) fm
2
Measurement #
electron scattering
laser spectroscopy
GSI two photon
D1
Test QED calculation, but discrepancy exist
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Neutral Li and Li ionNeutral Li and Li ion
Neutral Li D1 and D2 line by atomic beam Li+ in discharge and ion trap for better theoretical
calculation
metastable
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Our approachOur approach
Diode Laser 1@ 670 nm
Diode Laser 2@ 670 nm
lock to I2 transition or Li hollow cathode lamp
Measure beat frequencyTo atomic beam for spectroscopy
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ResultsResults
150 200 250 300 350
0
20
40
60
80
100
120
140
160
Atom
ic s
igna
l (A
rb. U
nit)
Frequency (Arb. Unit)
atomic signal laser PZT scan
92 MHzS/N ~ 50
0 1000 2000 3000 4000 5000
0
20
40
60
80
100
120
140
Ato
mic
sig
nal (
Arb
. Uni
t)
Frequency (Arb. Unit)
atomic signal laser PZT scan
800 MHz
S/N ~ 40
D1 line: both ground state and excited state hyperfine structure are resolved
D2 line: only the excited state hyperfine structure is resolved
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Reference laserReference laser
Relative Frequency (GHz)100 6
7Li D1I26Li D2 7Li D2
-10
6Li D1
-23
I2I2
weak
Error signal by frequency modulation Magnetic field shielding by mu-metal ~ 10 mG
160 240 320
-60
0
60
Sign
al (A
rb. U
nit)
Frequency (MHz)
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Iodine frequency standardIodine frequency standard
RF~10 MHz
PBS
HWP
lock in EOM
40 MHz
PD
LIR
LIR
highpass
chopped at ~10 kHz
low pass
signal out
I2 vapor cell at 100oC
I2 cold finger at 25oC
DBM
RF
DL1
RF Amplifier
AOM
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LiLi+ + for its better theory for its better theory
Previous attempt: using accelerated ion beam Strathclyde UK, York Canada (still working) Bothered by asymmetric line shape Approach: saturation absorption in discharge cell
548.5 nmoutput
Diode Laser @ 1097nm
FiberAmplifier
FrequencydoublingAOM
Heated discharge cell
Frequency modulatedsaturation absorption
548.5 nm ready at several mW, referenced to Iodine
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548.5 nm light source548.5 nm light source
Referenced to I2 Power > 10 mW
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Ion Trap DevelopmentIon Trap Development
yx
z0 cos( )V t
1U 2U
z
02Z
D=6m m, d=2.54mm, R=1.8mm, =1mm, L=42mm, 2Z0=13mm
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In trap developmentIn trap development
ICurrent supply with biased voltage
Electron-emitting filament
Trap
Oven for atomic beam
collimator
collimator
e-
RF
Ground
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Ion Trap BasicsIon Trap Basics Trapping of charged particles by electric field
Required: 3-dimensional force towards center
Convenience: harmonic force
Laplace equation:
a,b,c can not be all positive
UeF
222 czbyaxU
02 U
Solutions: Apply RF field: dynamical trapping: Paul trapDC voltage + magnetic field: Penning trap
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Paul Trap BasicsPaul Trap BasicsIdeal Paul Trap Potential: =(U0+V0cost)(x2+y2-2z2)/d02: RF frequency typically /2 = 1MHz ~ 100MHzd0: trap size U0,V0: strength of DC and RF field
2/,
24
28
220
0
220
0
tzru
qmd
eVq
amd
eUa
rz
rz
equation of motion:
0)2cos2(22
uqadt
ud
This is the Mathieu equationWhen u remains finite :stable solutionsWhen u goes to infinity: unstable solutions
Approximate solution for a,q
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Optical detectionOptical detection
Ca+ trap being the easiest for laser cooling397 nm cooling laser +
866 nm repump795 nm input
397nmoutput LBO crystal
PDPD
DCM
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Conclusion and OutlookConclusion and Outlook
Precision atomic measurement keeps
producing interesting physics
Our direction in NTHU: Precision
spectroscopy on simple atoms, Li and Li+
with aid of optical frequency comb
Ion trap development
People involved: Post-doc:Graduate students: , , , Supported by NSC