Funding sources for preliminary research: National Research Council (US)

The University of Oklahoma

Measuring the Electron’s Electric Dipole Moment usingMeasuring the Electron’s Electric Dipole Moment usingzero-g-factor paramagnetic moleculeszero-g-factor paramagnetic molecules

APS March Meeting, 2006APS March Meeting, 2006

Funding sources for preliminary research:

National Research Council (US)

NATO SfP (for field measurement.)

OU Office of the Vice Presidentfor Research

Neil Shafer-Ray, The University of Oklahoma

Current funding:

National Science Foundation

DOE EPSCoR Laboratory-StatePartnership


I am very sorry that I was not able to deliver this talk. My grandmother has passed away a few hours ago and I must return to the United States.

Sunday, October 8, 11:30pmNeil Shafer-Ray

To all,


CP (time reversal) violation

K-zero-long decay

http://www.bnl.gov/bnlweb/history/nobel/nobel_80.asp


A completely different place to look for CP violationA completely different place to look for CP violationis in the interaction of fundamental particles with external is in the interaction of fundamental particles with external

fields.fields.


The study of the magnetic moment of the electronThe study of the magnetic moment of the electronis an integral part of some of the mostis an integral part of some of the most

compelling experiments of the last 100 years.compelling experiments of the last 100 years.

GHz/ 39962458.1)( BB SBgU

Stern and Gerlach 1922"space quantization"g=1 to 10% (assumed integral spin)Nobel Prize 1943

II Rabi 1938Magnetic Resonanceresonant line widths <10kHzNobel Prize 1944 MAINSTAY of MODERN CHEMISTRY

Norman RamseySeparated Oscillator Beam Resonanceresonant line witdths <100HzNobel Prize 1989 STANDARD OF TIME

Hans G. Dehmeltion trapping, spectroscopy of a single

trapped electron.Nobel Prize 1989

2.002319304361716Gerald GabrielseQuantum nondistructive measurement

of the quantum structure ofa single electron in a magnetic trap

STANDARD OF MASS?


An EDM proportional to spin would also give CPAn EDM proportional to spin would also give CP

g = 2.0023193043617(16)Gabrielse,PRL 2006

gedm = 0.00000000000000000(5)Commins, PRL, 2004

GHz/ 39962458.1

)(

B

edmB SEgSBgU

cme1093080.1 11


Su

per

Sym

.S

td. M

od

.

(Hoo

geve

en 1

990)

(Arn

owitt

200

1)

- Commins & coworkers, Tl, PRL, 2002

- Hinds & coworkers, YbF, DAMOP, 2005

An EDM proportional to spin would also give CPAn EDM proportional to spin would also give CP


I. Introduction

What is the OU group up to?

How was the current experimental limit on the magnitude of the e-EDM obtained?

OutlineOutlineOutline

What are some of the current experiments beingcarried out to measure the e-edm


To search for an e-EDM we will look for

U=U+M –U-M

in a strong E field.

Symmetry leads to a ±M degeneracy of any molecule or atom that is not broken by an electric field along the quantization axis.

The existence of an electron electric dipole moment would break this symmetry.

How the current limit on electron EDM is knownHow the current limit on electron EDM is known

Precision structurecalculations arenot necessary.

Major Difficulty:A backgroundmagnetic field mimics an EDM.


The Commins Experiment withThe Commins Experiment with22PP1/2 1/2 (F=1, M=(F=1, M=±1) ±1) TlTl

.)( zzsysedmzz

syszB FEgFBgU

For an atom or molecule in a strong electric field,

)( SEgSBgU edmB

For an isolated electron,

edmsysedm gg for light atoms/molecules (Schiff's theorem.)

0sysedmg for diamagnetic atoms

edmsysedm gg for relativistic (heavy atoms/molecules.)

We want to use heavy paramagnetic atoms or molecues.


z

Bz

eTl Bh

Eh

d

h

U )34.0()77.0)(585(2

The Commins Experiment withThe Commins Experiment with22PP1/2 1/2 (F=1, M=(F=1, M=±1) ±1) TlTl

pG

B

cmvolt

E

cme

dmHz

h

U zzeTl

24/1010022.0

527

enhancement factor geometric factors


Tl(2P1/2 F=1), incoherent combination of|1,1>, |1,0> and |1,-1> states

P() = probabilityof finding the systemIn the state M=F whenquantization axis isin the direction of .

E

LASER RADIATION

Tl(2P1/2 F=1), |1,1> + |1,-1>

Graphical Description of the Commins e-EDM ExperimentGraphical Description of the Commins e-EDM Experiment


EFFECT OF MAGNETIC FIELDS ONTHE DISTRIBUTION OF ANGULAR MOMENTUM

Tl(2P1/2 F=1),

|1,1> + Exp[i U t /] |1,-1>

B


Bx

A small constant field Bx along an axis perpendicular to Bhas little effect.

B



B

A small field Bx along an axis perpendicular to Bthat rotates with the distribution may have a dramatic effect.


Brot


EFFECT OF A MAGNETIC FIELD ONOF ANGULAR MOMENTUM ORIENTATION

B

A small field Bx along an axis perpendicular to Bthat rotates with the distribution may have a dramatic effect.

The Ramsey beam resonance technique takes advantage of this dependenceof the Rabi rotation on the phase of the rotating field.

B

The Commins experimentCommins et al, PRL 88, 71805, 2002

U/ =RF

LASER LASER


U/ RF

B

LASERLASER


600400200 0 200 400 600Hz

0.2

0.4

0.6

0.8

1

P 1

f

Expected Ramsey resonance signal forT = (2kT/m)1/2 / 2L = 140 Hz

(m=100 amu , T=500K, and interaction length L= 1000mm)

FL

UO

RE

SC

EN

CE

(L

IGH

T S

EE

N)

MISMATCH BETWEEN and RF

B E


LASER

U/ =RF(+)

LASER

LASER

B

U/ =RF(-)

E


LASER


600400200 0 200 400 600Hz

0.2

0.4

0.6

0.8

1

P 1

f

E||BE(-||)B

SHIFT GIVES EDM

SHIFT SHOWN TO BE ~ 10-7 OF THE WIDTH!!!

GREAT STATISTICS!


limiting systematic error

B

E

2/' cEvB

sin)100(of splitting

/sin2|'||'| 2

Hz

cvEBBBB downup

sin ≈10-6


Measurement of the e-EDM using paramagnetic moleculesMeasurement of the e-EDM using paramagnetic molecules

0.024Tl(2P1/2 F=1)

System(state)

E-field(kV/cm)

split @10-27e cm

(mHz)

B @10-27e cm

(nG)

0.02100

tcoherence

(ms)

3

YbF(X2,F=1)

10. 13 5 3

dlimit

(10-27e cm)

1.3

-Hind

s

Commins

1) Effective electric field is the internal field of the molecule.2) Idea by Saunders (Atomic Phys, 14 1975,71).3) Calculation of shift by N.S. Mosyagin, M.G. Kozlov, A.V. Titov,

(J Phys B, 31, L763)


Effect of the large tensorsplit (energy dependence on |M|)

B

E

v

Only the projection of B on the E axiscontributes to the energy between ±M levels:

0)()( ''

,,

downzupzBBBB zz

2/' cEvB

away! goes systematic / 2cEv


Effect of the large tensorsplit (energy dependence on |M|)

B

downE

Only the projection of B on the E axiscontributes to the energy between ±M levels: upE

6

,,

10

sin)1(of splitting

sin2

Gauss

BHz

BBB downzupz

A much less severe problemthen the vxE/c2 effect.


Easy to lose in statistics what one gains in intrinsic sensitivity.

Beam Expected Flux Speed Distribution

Tl(F=1,|M|=1) 8 × 1015/str/sec

YbF(J=1/2, F=1,|M|=1)6 × 1010/str/sec

0 400 800 v(m/s)

(from oven)

(from supersonicexpansion)

0 400 800 v(m/s)

Differences between an atomic beam and a beam of Differences between an atomic beam and a beam of paramagnetic moleculesparamagnetic molecules


0.024Tl(2P1/2 F=1)

System(state)

E-field(kV/cm)

shift @10-27e cm

(mHz)

B @10-27e cm

(nG)

0.02100

tcoherence

(ms)

3

YbF(X2,F=1)

10. 13 5

PbO(a3,F=1)

.01 2.9 1

3

0.1

dlimit

(10-27e cm)

1.3

30(1?)

-

-

Hinds

Cs(2P1/2 F=3)

0.000254 0.00016 15 60Hunter

(DeMille)

Commins

-PbF(X21/2, F=1)

60-100 12 500 to 107 103 to 3(Shafer-

Ray)

(Weiss)

(Gould)

HfF+

(31)(Cornell) ~10 ~200 ~103~1 volt RF

ion trap

2x103

~103 -

-0.0050.0040.0050.004

100??

(Hinds)


Cs Atomic Fountain (Provided by Harvey Gould)Cs Atomic Fountain (Provided by Harvey Gould)


The OU PbF edm experiment


g factor of PbF F=1, |Mg factor of PbF F=1, |MFF|=1, high-field-seeking ground state:|=1, high-field-seeking ground state:

g-factor can be tuned to zero!

11.0)3/2(21 Gg

017.0)( ||21 Gg

Shafer-Ray, PRA,73, 34102


PbF molecular beam source

optical polarization(create M=0 state) high-field region

Raman

-RF p

ump

prob

e +

prob

e -

Schematic of PbF g=0 measurementSchematic of PbF g=0 measurement

LIF or REMPI detection region

(probe M=0 state)




Raman

-RF p

ump

prob

e +

prob

e -



(probe M=0 state)


First things first: Production and detection of PbFFirst things first: Production and detection of PbF

Pb / F2 flow reactor: Operational Temperature 1200K

Pb +MgF2 reactor: Operational Temperature 1200K

Pb +PbF2 reactor: Operational Temperature 1200K




Raman

-RF p

ump

prob

e +

prob

e -


REMPI detection region

(probe M=0 state)


Current Apparatus for Exploring PbF SpectroscopyCurrent Apparatus for Exploring PbF Spectroscopy

Nd:YAG 10ns, 10Hz

tunable dye laser0.1 cm-1 resolutiontunable dye laser

0.1 cm-1 resolution

PbF Source Chamberionization chamber

detection chamber

Not an ideal detection scheme:PbF molecules stay in probe region ~5s

Time between laser shots: 100msDuty cycle: 1/(20,000)



det

ect

ion

cha

mb

er

PbF

PbF

+




det

ect

ion

cha

mb

er

PbF

PbF

+



(0,0) band

5.0

4.0

0.0

-2.0

-1.0

-3.0

3.0

2.0

1.0

ener

gy (

eV)

X21/2

A21/2

B21/2

PbF+

3.0 5.0 7.0R(Bohr)

1+1 X1+1 X11221/21/2 →→BB221/21/2 REMPI of PbF REMPI of PbF

OU data, 2005

McRaven, Poopalasingam, Shafer-Ray,Chemical Physics Letters, In Progress.

355-397nm

280 nm


Observation of an ionization threshold for PbFObservation of an ionization threshold for PbF

McRaven, Poopalasingam, Shafer-Ray,Chemical Physics Letters, In Progress.

I.P. 7.55eV


R(Bohr)

5.0

4.0

0.0

-2.0

-1.0

-3.0

3.0

2.0

1.0

ener

gy (

eV)

E' 43/2?

PbF+

3.0 5.0 7.0

State selective ionization of PbF+ via 1+1+1 doubly-resonant multi-photonionization.

X21/2

A21/2

(A→E') / nm442.4 440.8

(X

→A

) / n

m

436.612

436.320

WE HAVE DISCOVERED A NEW ELECTRONIC

STATE OF PbF(tentative assignment: E'43/2)


f (A→E') / cm-1

226

12.1 f (A→E') / cm-1

226

12.1

226

41.8

226

41.8

f (X

→A

) /

cm-1

22889.9

22900.6

SIMULATION EXPERIMENT

Double Resonant Ionization of PbF


R2-R21

JX1 1/2 3/2 5/2 7/2

3/2

P1-R21

R2-Q1

1/2 3/2 5/2

9/2

R2-P21

3/2 5/2

A→E' photon energy (cm-1)

We have used our0.1cm-1 lasers to

almost isolatethe J=1/2 state!

(Impossible with 1 resonant step.)

We now have a bluediode laser and will start scanningwith 10 MHz resolutionin the next few weeks

We have yet torotationally cool.(Bigger pumps

await promised DOEmoney. Program in

limbo untilCongress approves

the Energy and Waterappropriations bill.)


Saturation of X->A transition in high J, X->A->E' ionization (probe laser power at 0.12 fluence J/cm^2 )

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

3.50E-02

4.00E-02

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0

pump energy (fluence-mJ/cm 2̂)

signa

l inten

sity (

mV)

X→A Saturation Curve(A→E' fluence at 0.12 J/cm2)

Sig

nal

In

ten

sity

(a.

u.)

0

5

fluence of X→A laser radiaion (mJ/cm2)

~40mJ/cm2 of 0.1cm-1 light to saturateX→A

ionization step at 437nm. A-state lifetime 3S

X→A transition may be saturatuatedwith ~15mW/mm2 diode laser radiation


Saturation of E'->A transition in high J, X->A->E' ionization (pump laser power a 42.6 fluence mJ/cm2 )

0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

3.00E-01

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

Probe energy(fluence J/cm2)

Sign

al int

ensit

y(m

v)A→E' Saturation Curve

(X→A fluence at 43 mJ/cm2)

fluence of A→E' laser radiaion (J/cm2)

Sig

nal

In

ten

sity

(a.

u.)

0

5

radiation drivingboth A→E' andE'→PbF+

ionization stepsaturated

A→E' step saturated

12J/cm2 to saturateA→E'→PbF+

ionization step at441nm.

E' lifetime <5ns

can not be ionized with cw laser radiation


TIMING FOR OPTIMIZED PbF DETECTION

0 2usec

437nm X→A diode laser radiation.

6usec

10mW/mm2 cw

442nm A→E'→PbF+ pulse laser radiation 10 mJ/mm2, 10-100ns

208PbF ion signal

100-1000Hz


2mm (x 0.1mm)

lase

r ra

dia

tion

PbF beam

re

p ra

te 1

0 H

z

Current set up.


100 mm (x 0.1mm)

re

p ra

te 1

000

Hz

50,000 to50010

000,1 to10

/1

/10

2

1002

2

Hz

HzHz

cmmJ

cmmJ

mm

mm

PbF beam

Improvement over current spectra:

OPTIMIZED DETECTION OF PbF


optic

al p

olar

izatio

n

(cre

ate

M=0

sta

te) high-field region

Raman

-RF p

ump

prob

e +

prob

e -


(probe M=0 state)

X1 21/2 (F=1)

A 21/2 (F=1)

|M|=1

|M|=1M=0

M=0


optic

al p

olar

izatio

n

(cre

ate

M=0

sta


Raman

-RF p

ump

prob

e +

prob

e -


(probe M=0 state)

X1 21/2 (F=1)

A 21/2 (F=1)

|M|=1

|M|=1M=0

M=0


optic

al p

olar

izatio

n

(cre

ate

M=0

sta


Raman

-RF p

ump

prob

e +

prob

e -


(probe M=0 state)

M=0400MHz|M|=1


optic

al p

olar

izatio

n

(cre

ate

M=0

sta


Raman

-RF p

ump

prob

e +

prob

e -


(probe M=0 state)

M=0400MHz|M|=1


Requirements for large Rabi populationamplitude in Raman pumping

from a state A to a state B

(1) of lasers on resonance.

A B

C

(2) At least 1 state C that couples to both A and B.

(3) A finely tuned ratio of A-C to B-C coupling.


0 20 40 60 80 100 120 140ts0

0.2

0.4

0.6

0.8

1

P

Simulation of RF Raman .02

PM=0

P|M|=1

M=0 |M|=1X1 2

A 2

EDC

k = BRF,effective

^

^ ^

0 20 40 60 80 100 120 140ts0

0.2

0.4

0.6

0.8

1

P

Simulation of RF Raman .20

PM=0

P|M|=1

= 0= /2


optic

al p

olar

izatio

n

(cre

ate

M=0

sta


Raman

-RF p

ump

prob

e +

prob

e -


(probe M=0 state)


optic

al p

olar

izatio

n

(cre

ate

M=0

sta


Raman

-RF p

ump

prob

e +

prob

e -


(probe M=0 state)


optic

al p

olar

izatio

n

(cre

ate

M=0

sta


Raman

-RF p

ump

prob

e +

prob

e -


(probe M=0 state)

PROBE+


optic

al p

olar

izatio

n

(cre

ate

M=0

sta


Raman

-RF p

ump

prob

e +

prob

e -


(probe M=0 state)

PROBE+


optic

al p

olar

izatio

n

(cre

ate

M=0

sta


Raman

-RF p

ump

prob

e +

prob

e -


(probe M=0 state)

PROBE+


PROBE-

QQ

QQpgBedm ..

optic

al p

olar

izatio

n

(cre

ate

M=0

sta


Raman

-RF p

ump

prob

e +

prob

e -


(probe M=0 state)

reverse sign with changing E.^

small, E even^


Using Ramsey fringes to lock the electric field: Using Ramsey fringes to lock the electric field:

/2

0

4214/2

02

)()sin(

))sin1(sin(cos)(

dttSignaltS

NdttSignalQ

4 2 0 2 4EEovoltcm1

0.5

0

0.5

1

RF1

RF2

RF1 fixed to a frequency standard.

RF2=RF1+

40 20 0 20 40EEovoltcm1

0.5

0

0.5

1

Q

S

S

zero crossing independent of ±M phase


A totally different idea: Guided PbF molecules in a Coaxial cable A totally different idea: Guided PbF molecules in a Coaxial cable

Ra

ma

n-R

F

LIF

imag

ing

dete

ctor

polarizatiing laser radiation

Raman-RF

LIF image

EDM

1 to 100 meters

Disadvantages: Must use LIF detection g=0.017 (not zero)Advantage: long (~1second) coherence time


Conclusions

• We have found a system for which the effect of background magnetic fields may be suppressed by seven orders of magnitude.

• We have developed a source of PbF as well as sensitive state selective REMPI of the molecule.

• We are designing a beam machine to take advantage of this new system.


THANKS TO:

Chris McRaven , Sivakumar Poopalasingam,Milinda Rupasinghe

Graduate Students:

Chris Crowe, Dustin Combs, Chris BaresUndergraduate Students:

Professor George Kalbfleisch:

March 14, 1931 - September 12 2006


The University of OklahomaNeil Shafer-Ray Kim MiltonJohn Furneaux

Petersburg

Nuclear Physics

Institute

Victor Ezhov

Mikhail Kozlov

University of Latvia

Marcis Auzinsch

BNL Chemistry

Greg Hall

Trevor Sears

U Cal Berkeley

Dmitry Budker

And thanks to the e-EDM COLLABORATION

Documents

Funding sources for preliminary research: National Research Council (US)