progress towards measurement of the electron’s electric...

The University of Oklahoma

Progress Towards Measurement of the ElectronProgress Towards Measurement of the Electron’’s Electric s Electric Dipole Moment using the Dipole Moment using the PbFPbF MoleculeMolecule

ucnucn 20072007

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

NATO SfP

OU Office of the Vice Presidentfor Research

Neil Shafer-Ray, The University of Oklahoma

Current funding:National Science Foundation

DOE EPSCoR Laboratory-StatePartnership


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

MHz/G 39962458.1=Bμ)( SEgSBgU edmBrrrr

⋅+⋅=Δ μ

cm1093080.1 11 ⋅×= − e

Pur

cell,

Ram

sey

PR

A 7

8 80

7 (1

950.

)


Sup

er S

ym.

Std

. Mod

.

(Hoo

geve

en 1

990)

(Arn

owitt

2001

)

- 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

5

5 x 10-5

5 x 10-10

5 x 10-15

5 x 10-20

5 x 10-25

g ED

M


What is the OU group up to?

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

ΔU=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 The ComminsCommins Experiment withExperiment with22PP1/2 1/2 (F=1, M=(F=1, M=±±1) 1) TlTl

For an atom or molecule in a strong electric field,

)( SEgSBgU edmBrrrr

⋅+⋅= μFor an isolated electron,

0=effE for light atoms/molecules (Schiff's theorem.)0=sysedmg for diamagnetic atoms

labeff EE >> for relativistic (heavy) atoms/molecules.Heavy paramagnetic atoms or molecules are sensitive to an e-edm.

)( SEgSBgU effsysedm

sysB

rrrr⋅+⋅≈ μ


⎥⎦⎤

⎢⎣⎡ −−−=Δ zBzeTl Bh

Ehp

hU μ)34.0()77.0)(585(2

The The ComminsCommins Experiment withExperiment with22PP1/2 1/2 (F=1, M=(F=1, M=±±1) 1) TlTl

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎠⎞

⎜⎝⎛

⋅=Δ − pG

Bcmvolt

Ecme

pmHzhU zzeTl

24/1010022.0 527

enhancement factor geometric factors


Measurement of the eMeasurement of the e--EDM using paramagnetic moleculesEDM 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(X2Σ,F=1)

10. 13 5 3

dlimit(10-27e cm)

1.3

30(1?)H

inds

Comm

ins

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)


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(X2Σ,F=1)

10. 13 5

PbO(a3Σ,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(X2Π1/2, F=1)

60 12 500 to 107 3(Shafer-

Ray)

(Weiss)

(Gould)

HfF+

(3Δ1)(Cornell) ~10 ~200 ~103

~1 volt RFion trap

2,000

~103 -

-0.0050.0040.0050.004

100??

(Hinds)


The OU PbF edm experiment

System(state)

E-field(kV/cm)

shift @10-27e cm

(mHz)

B @10-27e cm

(nG)tcoherence

(ms)dlimit

(10-27e cm)

-PbF(X2Π1/2, F=1)

60 12 500 to 107 3(Shafer-

Ray)


g factor of the Xg factor of the X11 ((22ΠΠ1/21/2) J=1/2, ) J=1/2, ΩΩ++ F=1, |MF=1, |MFF|=1 |=1 state of state of PbFPbF

g-factor can be tuned to zero!

11.0)3/2(21 −≈−≈ ⊥Gg

017.0)( ||21 ≈≈ GgShafer-Ray, PRA,73, 34102

prob

e +

Schematic of PbF e EDM measurementSchematic of PbF e EDM measurement

PbF molecular beam source

optical polarization(create M=0 state)

high-field region

REMPI detection region

(probe M=0 state)

RF

RF



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

prob

e +




high-field region


(probe M=0 state)

RF

RF



0 10 20 30 40 50 60E HkVêcmL

−2

0

2

4

6

UHmc−1L

Stark Effect in PbF HX2Π1ê2L

J=1/2J=3/2

J=5/2

J=7/2

Ω+

Ω-

F≈1, M=0F≈1, |M|=1

M=0

F = I+J(I=IFluorine=1/2)

Basic of Energy Level Structure of Basic of Energy Level Structure of PbFPbF

~0.1-100MHz

10-100mHz

Our experiment probes these three states.

optical polarization

RF mixing


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

Graphical Description of the Graphical Description of the ComminsCommins ee--EDM ExperimentEDM Experiment

PbF(2Π1/2 F=1), incoherent combination of|1,1>, |1,0> and |1,-1> states

E

STATE SELECTIVE

LASER RADIATION

PbF(2Π1/2 F=1), |1,0>

Appendix of Shafer-Ray,Orr-Ewing, Zare,J. Phys. Chem. 99, 7591, (1995.)


(0,0) band

5.0

4.0

0.0

-2.0

-1.0

-3.0

3.0

2.0

1.0

ener

gy (

eV)

X2Π1/2

A2Σ1/2B2Σ1/2

PbF+

3.0 5.0 7.0R(Bohr)

1+1 X1+1 X1122ΠΠ1/21/2 →→BB22ΣΣ1/21/2 REMPI of PbFREMPI of PbF

OU data, 2005

McRaven, Poopalasingam, Shafer-Ray,PRA. 75, 024502 (2007.)

355-397nm

279-281 nm

νX->A/c (cm-1)35700 35900


I.P. 7.55eV

1+1 X1+1 X1122ΠΠ1/21/2 →→BB22ΣΣ1/21/2 REMPI of PbFREMPI of PbF

McRaven, Poopalasingam, Shafer-Ray,PRA. 75, 024502 (2007.)


SIVA

f1≈c/436.8nm+f2≈c/476.7nm+f3≈c/532nm

PbF+

Chris

206Pb19F 207Pb19F 208Pb19F

PbF

The University of OklahomaR(Bohr)

5.0

4.0

0.0

-2.0

-1.0

-3.0

3.0

2.0

1.0

ener

gy (

eV)

E' 2Σ1/2

PbF+

3.0 5.0 7.0

X2Π1/2A2Σ1/2

532nm

LASER X-A

LASER A-E'

A-E' FREQUENCY

X-A

FR

EQ

UE

NC

Y

Stateof PbFuniquelysensitive to the e-edm.

J=1/2, Ω+

J=3/2, Ω-J=5/2, Ω+

RAW DATA TAKEN, DECEMBER 2006

REMPI Detection /Polarization of REMPI Detection /Polarization of PbFPbF

[R-R]e

[R-Q]e[R-P]e

prob

e +




high-field region


(probe M=0 state)

RF

RF


X1 2Π1/2 (F=1)

A 2Σ1/2 (F=1)

|M|=1

|M|=1M=0

M=0

prob

e +




high-field region


(probe M=0 state)

RF

RF



First RF CavityFirst RF Cavity

BRF

M=0

|M|=1

BRF

prob

e +




high-field region


(probe M=0 state)

RF

RF


X1 2Π1/2 (F=1)

M=0

|M|=1

BRF1

prob

e +




high-field region


(probe M=0 state)

RF

RF


0,12

1,11,1 //

hh

iUtUti

ee −

Δ−

+−+

= αψ


Evolution of Evolution of PbFPbF in Measurement Regionin Measurement Region

E,B0,12

1,11,1 //

hh

iUtUti

ee −

Δ−

+−+

= αψ

MHzU

mHzEggBU effEDMBB50

22

≈

≈+=Δ μμ

M=0

|M|=1 ΔU (rotation)

U (shake)

prob

e +




high-field region


(probe M=0 state)

RF

RF


))cos((]€sin€[cos

cos]€[

2

1

tjiBB

tiBB

oRF

oRF

ωωφφω

Δ++=

=

X1 2Π1/2 (F=1)

M=0

|M|=1BRF2

Measure I(t)~Io+ I1cos2Δωt


time ave signal

demodulatederror signal

1+cos(2θ)

1||0 =↔=− MMRF νν

t/tRF≈100

Second RF CavitySecond RF Cavity

BRF2

θφμθ ++= )(2 effEDMB EggB

th

Probability of population transfer to M=0 dependson both

and phase of RF modulation wrt phase of shake.

))(4sin(12cos1

: EggB y tosensitivit order-firstobtain to)4/(between B and Bbetween angle Alternate

signal.error narrow tofield ELock

4/

effEDM

RF2RF1

effEDMB EggBt +±=+

+=

=h

m

m

μθ

πφ

πφ

h/th/tRF

prob

e +




high-field region


(probe M=0 state)

RF

RF


))cos((]€sin€[cos

cos]€[

2

1

tjiBB

tiBB

oRF

oRF

ωωφφω

Δ++=

=

lock electricfield to a clockstandard

sensitivity togEDME+gB ∫ dttI )(

∫ Δ dttIt )()2sin( ωMeasure I(t)~Io+ I1cos2Δωt


Estimated Sensitivity

Eeff = effective field = 60GV/cm (Kozlov)τ=Coherence time ~ 3msT=collection time ~ 1 dayR=Expected Count Rate: ~1MHz

pe≈(h/τ)(RT)-1/2 (Eeff-1) ≈ 3x10-30 e cm

We expect a 1-day sensitivity that is 10-500 times smaller than the current limit of 10-27e cm in an

experiment designed to dramatically reduce systematic errors.

optimistic estimate:


Status of the eEDM experiment• 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 an extraordinarily sensitive state selective REMPI detection scheme.

• We have designed a Ramsey resonance experiment to take advantage of the small and tunable g factor of PbF.


THANKS TO:

Chris McRaven , Sivakumar Poopalasingam,Milinda Rupasinghe

Graduate Students:

Chris Crowe, Dustin Combs, Chris Bares, Leah Trafford,Erik Villenti

Undergraduate Students:

Professor George Kalbfleisch:

March 14, 1931 - September 12, 2006


The University of OklahomaNeil Shafer-Ray Kim MiltonJohn Furneaux

PetersburgNuclear PhysicsInstituteVictor EzhovMikhail Kozlov

University of Latvia

Marcis Auzinsch

BNL ChemistryGreg HallTrevor Sears

U Cal BerkeleyDmitry Budker

And thanks to the e-EDM COLLABORATION

progress towards measurement of the electron’s electric...

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