JLee PhD Defense Presentation 2012

1 m

Optical Spectroscopy of Tungsten Carbide

for electron EDM Measurement

Jeongwon Lee Leanhardt AMO group

Department of Physics, University of Michigan

Portrait of Edward James Rene Magritte (1937)

P-violation

S ed+

_

Electron with

Non-zero EDM

1. Introduction

- what is an electron Electric Dipole Moment (eEDM)?

- eEDM measurement scheme

- advantages of WC molecules

2. Experimental Results

- 1st generation : continuous supersonic beam source

- 2nd generation : pulsed supersonic beam source

3. Uncertainty Analysis

- Systematic uncertainty

- Statistical uncertainty

4. Summary

Contents

1. Introduction

Contents

electron EDM violates symmetry

Non-zero electron Electric Dipole Moment

Violates both time (T) and parity (P) reversal symmetry

e- EDM : not detected yet d

e [e

*cm

]

10-38

10-28

10-30

10-32

10-34

10-36

10-40

SU

SY

Mu

lti-H

igg

s

Le

ft-R

igh

t

10-24

10-26

Current Experimental Limit :

|de| < 1.05 x 10-27 e*cm [~10-18 Debye]

Improving the precision of e-EDM measurement

=> Probe for new physics beyond Standard Model

Standard Model

Too far from current experimental limit

S ed1m

1m

deE

S ed

BB

BB

deE

E B

+

_ +

_

EDM Measurement Scheme

- Case 1 : E & B Field Parallel

Total Shift 1:

0m

h

EdB emtotal

221,

S ed1m

1m

deE

S ed

BB

BB

deE

E B

+

_ +

_

EDM Measurement Scheme

- Case 2 : E & B Field anti-Parallel

0m

Reversing E field relative to B field

=> Stark Shift in opposite direction Total Shift 2:

h

EdB emtotal

222,

E

vvd

totaltotal

e4

2,1,

Elab

[1] B.C. Regan, E.D. Commins, C.J. Schmidt & D. DeMille [PRL 88, 071805 (2002)]

[2] J.J. Hudson, D.M. Kara, I.J. Smallman, B.E. Sauer, M. R. Tarbutt & E.A. Hinds [Nature 473, 493-496 (2011)]

Effective Electric Field : E-field seen by e- inside

atoms and molecules

- Maximum Elab ~ 105 V/cm

- High Z atoms : Eeff ~ 107 V/cm

Upper Limit from Tl expt.[1] : |de| < 1.6 x 10-27 e*cm [~10-18 Debye]

- Heavy Polar Molecules : Eeff ~ 1010 V/cm

Upper Limit from YbF expt.[2] : |de| < 1.05 x 10-27 e*cm

Advantage 1: Large Electric Field

- Heavy Polar Molecule

When g ~ 2 and g ~ 1, g ~ 0

Very Small magnetic moment:

measured to be g = 0.022 [1]

1

3

1

2

1

spin:

orbital:

spin + orbital:

+ = Spin & orbital projection

in opposite direction

Advantage 2: Small Magnetic Moment

- 3 1 state of WC

[1] F. Wang & T.C. Stemlie, JCP 135 104313 (2011)

Elab

Advantage 3: Internal Comagnetometer

- -doublet structure of WC

0effE

0effE

1m 0m 1m

elElab elElab

elElab elElab

Small doublet splitting (nearly degenerate opposite parity states)

=> Efficient Zeeman Shift Cancellation

B

2. Experimental Results

Contents

LIF Spectroscopy

3 transitions per J level.

WC Molecular Spectrum

Ro-vibrational ground state => EDM state

X 3 1

[20.6] =2

R(1) line

R transition : J = +1

Q transition : J = 0

P transition : J = - 1

e = 983.2 cm-1

~ 1400 K

B = 0.509 cm-1 ~ 0.7 K

Rotational Temperature Requirement

Fractional ro-vibrational

ground state @ 1000 K ~ .001

@ 100 K ~ .01

We want colder molecules!

Most general way of Cooling to

1K level : supersonic expansion

(Fractional EDM state)

B = 0.509 cm-1 ~ 0.7 K

e = 983.2 cm-1 ~ 1400 K

1st generation experiment:

Continuous WC molecular beam apparatus

1. Evaporation

Zone

(Seeding Zone)

3. Optical

Spectroscopy

Zone

2. Differential

Pumping Zone

1. Evaporation Zone

- Seeding Technique

Resistive Heating Method

24 2HWCCHW

W WC 182W

183W

184W 186W

1% molecular formation

Tungsten Vapor Pressure

=> 1 X 10-6 Torr at 2700K

Compare with,

Ytterbium Vapor Pressure

=> 7 Torr at 1000K

1. Evaporation Zone

- Cooling Mechanism

Tungsten Filament (~150W)

(Resistive Heating Method)

1. Far from the throat of the nozzle, Thermalization process dominates

=> Energy Transfer from W / WC to Buffer gas molecule

2. Closer to the throat, Supersonic Effect dominates

=> Converting thermal energy into direct kinetic motion

Thermalization E. Conversion

Supersonic Effect

Continuous WC molecular beam apparatus 2. Differential Pumping Zone

- Pumping Capacity Issue

Too Much Flux is Lost!

Continuous WC molecular beam apparatus 2. Differential Pumping Zone

- How to overcome the pumping capacity

2cm

25 cm

Flux regained by

decreasing the

nozzle-skimmer distance

3. Optical Spectroscopy Zone

Tungsten Supersonic Beam Characterization

Top View

Side View of

Spectroscopy

Chamber

Calculated

Photon

Collection

efficiency

= 0.063

Radial Probe

@ 384.9nm

Axial Probe

@ 384.9nm

Laser Induced Fluorescence

Spectroscopy of Tungsten 5D0 5F1

384.9nm

5D0 (Ground State)

5F1

Atomic /

Molecular Beam

Flux Separation Technique

- Atom Flux / Radiated Light Flux

Flux passing through nozzle & skimmer (2 apertures)

Filament light background reduced by a factor of 1000,

while the LIF signal decreased only by a factor of 5

Signal to Noise

Increase by factor of 6

Continuous WC molecular beam apparatus Tungsten LIF spectrum

- 1 Torr Argon, 1.5mm Nozzle, 3mm Skimmer

1.8 GHz

(vaxial~681m/s)

260 MHz

(~40K) 90 MHz

(~0.05 rad)

10/67

/681

2

5 sm

sm

m

Tk

v

a

vM

tungsten

transB

axialaxial at supersonic regime

LIF signal of WC molecules was not detected from the continuous beam.

=> 2nd generation pulsed supersonic beam source was developed.

Tungsten

Signal to Noise

~1200

Tungsten Carbide

Ground State

(estimated) Signal to Noise

Tungsten Carbide

Molecular Formation

~1% X X

Tungsten Carbide

In Rovibrational

Ground State

at 40K,

~5% ~0.6

Advantage of pulsed beam

- Diagram of Ideal Case

Atomic

Flux

(Signal)

Photon

Counter

gate

Radiated

Light Flux

(Noise)

Time Delay (= time of flight)

Pulse Valve

485nm diode laser

Tungsten Rod

Nd:YAG Laser

PMT

Vacuum Pump

350psi

90% Argon

+ 10% CH4

W + CH4 WC + 2H2

Detect Laser Induced Fluorescence of WC,

75 cm away from the source

2nd generation experiment:

Pulse WC molecular beam apparatus

LIF Spectroscopy

First detected signal !

WC Molecular Spectrum

Ro-vibrational ground state => EDM state

1110 sN

~10MHz

X 3 1

[20.6] =2

R(1) line

3. Uncertainty Analysis

Contents

Elab~10V/cm

X3 1 ground state of WC molecules

0effE

0effE

1m 0m 1m

elElab elElab

elElab elElab

Advantages of X3 1 State WC Molecules for eEDM experiments

B

Large Effective Electric Field Zeeman Shift Cancellation with doublet

calculated

Eeff~-36GV/cm

[1] A.N. Petrov & A.V. Titov, private communication

[1]

Other eEDM experiments with 3 1 State Molecules: JILA (HfF+ , ThF + ), Harvard/Yale (ThO)

Elab~10V/cm

Uncertainties of the Measurement Scheme

0effE

0effE

1m 0m 1m

elElab elElab

elElab elElab

Uncertainties of the eEDM measurement scheme with WC

B

Large Effective Electric Field

=> how accurate is the calculation?

Zeeman Shift Cancellation with doublet

How close are the g factors?

(ge and gf)

calculated

Eeff~-36GV/cm ge

gf

WC|

Uncertainty in

Uncertainty in

Hyperfine constant

measurement

Uncertainty in

Eeff field

2/12/1|

| where

2

2

02

0

psrelreleffr

ra

a

ZeE

[1]

[1] I.B. Khriplovich & S.K. Lamoreaux, CP violation without Strangeness (1997)

Uncertainty Analysis 1

- Effective electric field

WCWCr

|1

|2 WChyperfineWC

H ||

Near the heavy nucleus, electric field seen by the electron ( ) can be written as, effE

Tungsten Carbide R lines

LIF spectroscopy of R branches of [20.6] =2 Lower J lines have larger splittings

Hyperfine Structure of 183W12C

( I = )

183W12C

R(1)

183W12C

R(2)

a b

c

c a

)1(2

)1()1()1(

JJ

IIJJFFhSplittingHyperfine

(excited) 131258

(ground) 121171

2

1

MHzh

MHzh


[2] A.N. Petrov & A.V. Titov, private communication


- Effective electric field

Hyperfine measurement as the test of electronic wavefunction near the nucleus

MHz 121171

Our expt. Previous expt. Calculated

MHz 6011MHz 511363

[2] [1]

WC|

Uncertainty in

Uncertainty in

Hyperfine constant

measurement

Uncertainty in

Eeff field

WCWCr

|1

|2 WChyperfineWC

H ||

0effE

0effE

1m 0m 1m

elElab elElab

elElab elElab

There is a small difference in g factors ( between top and bottom doublet.

effeefBef EdggB 4)(2

gBSystematic B2ty Uncertain


- Difference in g factors

Summary of relation between

-doublet and

Smaller -doublet Smaller Elab to

fully polarized WC Smaller

g

)g(

rotation

labelab

B

EE

labedoublet EH

Polarization condition

Change in Experimental Settings

)1(~ JJoHdoublet)1(2

)1()1()1(

JJ

IIJJFFhHHyperfine

Low Trot Preferred High Trot Preferred Under-expansion & Higher YAG power

Change in Experimental Settings

- Axial Velocity Distribution

)1(~ JJoHdoublet)1(2

)1()1()1(

JJ

IIJJFFhHHyperfine

Low Trot Preferred High Trot Preferred

Under-expansion &

Higher YAG power

Doublet

- Experimental Data

)2)(1()1(~2)1(~2

21 JJJJoJJo

SplittingDoublet

e/f

f/e

f/e

e/f

For R

branch )2)(1()1(~2 2 JJJJo

)1(~2 1 JJo

kHzo

kHz

kHzo

1.1~)13400 : (previous

18418~

2

1

182W12C

184W12C

186W12C

R(4) R(5)

Based on fitting,

[1]


Systematic Uncertainty from

Smaller -doublet Smaller Elab to

fully polarized WC Smaller

-5103g(10V/cm)kHzo 18418~1

Smaller

systematic

uncertainty

10V/cmlabE

)/36~E(when level 10dat y sensitivit thelimits

G)~B(when 1002ty Uncertain

eff

29-

e cmGVcme

HzgBSystematic B

* J. Lee, J. Chen, L. Skripnikov, A. Petrov, A. Titov, A. Leanhardt, full manuscript in preparation

Further Suppression of


Detailed calculation revealed a g-factor crossing point => suppression of systematics as

* J. Lee, J. Chen, L. Skripnikov, A. Petrov, A. Titov, A. Leanhardt, full manuscript in preparation

Further Suppression of


g-factor crossing point results at Elab = 2V/cm

Need to check whether the molecule is fully polarized

=> Eeff = 0.85 * 36GV/cm when Elab = 2V/cm

++++++++++++++++

- - - - - - - - - - - - - - -

sin2( )

cos2( )

E E B B

/2 /2

L ~ 1 m, v ~ 300 m/s, ~ 3 ms populations

oscillate

Chop relative direction of E and B and measure frequency difference.

ei

TN2

1

Frequency Resolution :

Statistical Uncertainty of

Ramsey Spectroscopy


eEDM measurement

TN2

1

Frequency Resolution :

Rate of EDM state

measurement

Increase of

molecular density

Stronger transition

Coherence time

(= time of flight)

Beam line extension

Integration time

Taking more

measurements

at a fixed rate


eEDM measurement

From beam line extension

h

Ed effe2

TN2

1EDM Shift :

Frequency

Resolution :

VS.

Current Status Future Plan

Eeff -36GV/cm -36GV/cm

~1ms ~2ms

~10 Hz ~104 Hz

T 1day (~105s) 1day (~105s)

|de| detection limit < 10-27 e-cm < 10-29 e-cm

N From probing 545nm transition with higher

Frank-Condon factor*

* M. Morse, private communication

* Dispersed Fluorescence data, courtesy of M. Morse group

Improvement in Frank Condon Factor

FC factors

calculated from

RKR method

(R. Le Roy group)

Conclusion & Summary

Motivation

Search of Time symmetry violation

Measurements

Hyperfine Sys. Uncertainty

of Eeff field

Doublet Sys. Uncertainty

of g

WC Beam Stat. Uncertainty

Methods

3 1 ground state of WC molecules

Conclusion

Identified 3 1 state of WC as candidate system for eEDM expt.

Analyzed systematic & statistical

uncertainties for eEDM expt.

with projected sensitivity of

|de| < 10-27 e-cm

Thank You

Top Row: Jinhai Chen, Aaron Leanhardt, Emily Alden

Bottom Row: Kaitlin Moore, Yisa Rumala, Chris Lee, Erika Etnyre

Documents

JLee PhD Defense Presentation 2012