Li-Bang Wang, National Tsing Hua University

Precision Measurement in Atomic Physics

NCTU IOP Colloquium 5/12/2011NCTU IOP Colloquium 5/12/2011

On Growth and Form, 1917

numerical precision is the

very soul of science

Thompson, D'Arcy Wentworth

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

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

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

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

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-

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

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

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

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

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

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)

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

Neutron EDM: historyNeutron EDM: history

By Ramsey

figure from Wikipedia

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

How to measure EDMHow to measure EDM

Problem: reverse E field cause leakage current,huge noise from B field

figure from M. Romalis, Princeton

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

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

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)

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

Frequency standardFrequency standard

Figure: S.A. Diddams et al.,Science 306, 1318, 2004

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

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).

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

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

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)

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

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

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)

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

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:

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

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

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

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

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

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)

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

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

548.5 nm light source548.5 nm light source

Referenced to I2 Power > 10 mW

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

In trap developmentIn trap development

ICurrent supply with biased voltage

Electron-emitting filament

Trap

Oven for atomic beam

collimator

collimator

e-

RF

Ground

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

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

Optical detectionOptical detection

Ca+ trap being the easiest for laser cooling397 nm cooling laser +

866 nm repump795 nm input

397nmoutput LBO crystal

PDPD

DCM

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