Towards an improved limit on the electron electric dipole moment.

Russell StutzLaura SinclairAaron LeanhardtEric Cornell

JILA (CU Physics and NIST) $$: NSF, NIST, Keck Found., Marsico.

Local Theory John Bohn “Q: Who are your influences?”Ed Meyer The Commitments (1991)

JILA A: John Lee Hooker, Aretha FranklinJJ Cale, Ramsey, Commins, Hinds, Demille

Nonlocal TheoryAnatoly TitovA. N. Petrov

Petersburg Nuclear Physics Institute

Towards an improved limit on the electron electric dipole moment.

Russell StutzLaura SinclairAaron LeanhardtEric Cornell

JILA (CU Physics and NIST) $$: NSF, NIST, Keck Found., Marsico.

Local Theory John Bohn “Q: Who are your influences?”Ed Meyer The Commitments (1991)

JILA A: John Lee Hooker, Aretha FranklinJJ Cale, Ramsey, Commins, Hinds, Demille

Nonlocal TheoryAnatoly TitovA. N. Petrov

Petersburg Nuclear Physics Institute

Towards an improved limit on the electron electric dipole moment.

Russell StutzLaura SinclairAaron LeanhardtEric Cornell

JILA (CU Physics and NIST) $$: NSF, NIST, Keck Found., Marsico.

Local Theory John Bohn “Q: Who are your influences?”Ed Meyer The Commitments (1991)

JILA A: John Lee Hooker, Aretha FranklinJJ Cale, Ramsey, Commins, WiemanHinds, Demille

Nonlocal TheoryAnatoly TitovA. N. Petrov

Petersburg Nuclear Physics Institute

1965 1975 1985 1995 2005

10-28

10-29

10-26

10-27

10-24

10-25

10-23

Limit oneEDM(e-cm)

Gould,Sandars,Cs beams

Hunter Cs vapor cell

Commins Tl beam

The Lessons of History: eEDM

2009

1965 1975 1985 1995 2005

10-28

10-29

10-26

10-27

10-24

10-25

10-23

Limit oneEDM(e-cm)

The Lessons of History: eEDM

The smooth marchof progress into the future.... or....

2009

1965 1975 1985 1995 2005

10-28

10-29

10-26

10-27

10-24

10-25

10-23

Limit oneEDM(e-cm)

The Lessons of History: eEDM

...or “ImpulseProgress”?

2009

1965 1975 1985 1995 2005

10-28

10-29

10-26

10-27

10-24

10-25

10-23

Limit oneEDM(e-cm)

The Lessons of History: eEDM

...or “ImpulseProgress”?

2009

Why Use Molecular Ions?

Why use molecules?• Large internal electric fields.• Molecules with Ω>1/2 have closely spaced levels of opposite parity fully polarized with E~10 V/cm. • Can get Eeff/Elab = 109

Why use ions?• Ions are easy to trap.• Potential for long spin coherence times.

Meyer and Bohn “jiffycalc” points in blue. PRA 73, 062108 (2006)Full-on “one-calculation-equals-one-publication”, various authors, in black, arXiv:physics/0506038 and refs. therein

Candidate Molecular IonsHfF+ and ThF+

• 3Δ ground states <1 V/cm to fully polarize• strong atomic 6s character large Eeff

ThF+

3Δ2Π 2Σ 3Σ

Elab

Eeff

-++

Why Use 3Δ1 state of molecule?-1zs ,2 =•=• )))r

zL- ++ )03.0( 0 Bμ=≈g

Thallium: Elab = 105V/cm Eeff = 6x107 V/cm μmag = 1.0 μB

HfF+ or ThF+: Elab = 101 Eeff = 1.5x1010 μmag = 0.03

Figure-of-merit: Eeff/( Elab μmag )

Our experiment is >107 to the good. Probably willnot even need mu-metal shielding.

Why Use 3Δ1 state of molecule?-1zs ,2 =•=• )))r

zL- ++ )03.0( 0 Bμ=≈g

Thallium: Elab = 105V/cm Eeff = 6x107 V/cm μmag = 1.0 μB

HfF+ or ThF+: Elab = 101 Eeff = 1.5x1010 μmag = 0.03

Figure-of-merit: Eeff/( Elab μmag )

Our experiment is >107 to the good.?????But even 10 V/cm is enough to make an ion scoot away????

!!!!!Use rotating E-field bias!!!!!-E-field defines quantization axis

-Excellent rejection of lab-frame residual

B-field.

+

ωrott

E

+

++

ωrot is:BIG enough that radiusof “micromotion” circleis small compared to trap size.

SMALL enough so thatdmol E >> ωrot and the molecule axis stays aligned with E.

One does Zeeman-level spectroscopy thenin the rotating frame.

Experimental ProcedureHfF+ 3Δ1 J=1 ground state

• Ω-doublet splitting ~ 1 MHz

m = -1 m = 0 m = +1

Ω-d

oubl

et s

plitt

ing

~ 1

MH

z

Energies not to scale.Nuclear spin of ½ excluded for clarity.

|p=+>|p=->

Experimental ProcedureHfF+ 3Δ1 J=1 ground state

• Electric field 1 V/cm mixes states of opposite parity.

m = -1 m = 0 m = +1

μ elE

lab

μ elE

lab

μ elE

lab

μ elE

lab

Energies not to scale.

Elab Elab

Experimental ProcedureHfF+ 3Δ1 J=1 ground state

• Magnetic field lifts degeneracy between |m|=1 levels.

m = -1 m = 0 m = +1

μmB

μmBμmB

μmB

Energies not to scale.

B

ss

B

ss

Experimental ProcedureHfH+ 3Δ1 J=1 ground state

• Electron EDM shifts the |m|=1 levels in opposite directions in the two Ω-doublet levels.

m = -1 m = 0 m = +1

deEeff

deEeff

deEeff

deEeff

2μmB + 2deEeff

2μmB - 2deEeff

Energies not to scale.

ss

ss

Science signal = 4deEeff<28mHz,out of “Berry’s offset” of 250 kHz

Experimental ProcedureHfH+ 3Δ1 J=1 ground state

• Perform electron spin resonance (ESR) frequency measurement via the Ramsey Method.• Photodissociate one spin state and count HfH+

and Hf+ ions.

m = -1 m = 0 m = +1

Energies not to scale.

Hf+

F

Hf+F

deEeff

deEeff2μmB - 2deEeff

deEeff

deEeff

2μmB + 2deEeff

He or NeSeed Gas

Pulse valve

Laser Pulse

Ablation target

Make, cool the molecules,

Plus a little SF6

(Hf or Th)

He or NeSeed Gas

Pulse valve

Laser Pulse

Ablation target

Make, cool the molecules,

Plus a little SF6 ion/neutral

(Hf or Th)

Experimental Setup• Laser ablation creates molecular ions.• Expansion cools ions rotation, vibration, translation (T ~ 2 K).

Ablation laser

Experimental Setup

Paul trap

• Linear Paul trap holds ions for measurement.

Trapped Tint=2K,trapped Text = 600K

Experimental progress: We can, make, stop, trap, and store for many seconds many more HfF+ (or ThF+ ions) than we will ever need (or want!) for precision rf spectroscopy of trapped molecular ions.

Experimental Setup

Paul trap

• Linear Paul trap holds ions for measurement.• Rotating E-field and B-field are applied.• Rf applied for ESR via Ramsey Method.• Photodissociation laser pulse to detect spin states.

Trapped Tint=2K,trapped Text = 600K

Experimental Setup• Linear Paul trap holds ions for measurement.• Rotating E-field and B-field are applied.• Rf applied for ESR via Ramsey Method.• Photodissociation laser pulse to detect spin states.• Channeltron counts atomic or molecular ions.

ioncounting

1Σ

3Δ1,2,3

3Π1,2,3

1Π1

1Δ2

Preliminary Calculation of HfF Potential Curves

+

R( )Å

E-E

(cm

)10

0-1

21.951.85 1.91.81.751.71.651.6-50000

-45000

-25000

-40000

-30000

-35000

HfF+ electronic states

• 1Σ ground state?

• 3Δ1 ~ 800 cm-1

above ground state

S. Petrov, K. Mosyagin, T. Isaev, A. Titov

Experimental Procedure, HfF+

m = -1 m = 0 m = +1

Energies not to scale.Nuclear spin of ½ excluded for clarity.

3Δ1

τ ~ 1sec

1Σ

3Π1

1Π1

~ 14000cm-1

~ 800cm-1 Ω-d

oubl

et s

plitt

ing

~ 2

MH

z

SO mixed

m = -1 m = 0 m = +1

Energies not to scale.Nuclear spin of ½ excluded for clarity.

3Δ1

1Σ

3Π1

1Π1

Experimental Procedure, HfF+

SO mixed

2 photon Raman transition to single Zeeman level

m = -1 m = 0 m = +12μmB + 2deE

eff

2μmB - 2deEeff

3Δ1

1Σ

3Π1

1Π1

Experimental Procedure, HfF+

Apply E and B fields to lift degeneracy of |m|=1 levels. Perform electron spin resonance to measure splitting.

Energies not to scale.Nuclear spin of ½ excluded for clarity.

m = -1 m = 0 m = +12μmB + 2deE

eff

2μmB - 2deEeff

3Δ1

1Σ

3Π1

1Π1

Photo-dissociate one spin state for ESR read out

Experimental Procedure, HfF+

Energies not to scale.Nuclear spin of ½ excluded for clarity.

Repeat Experiment in other Ω-doublet level

1Σ

3Δ1,2,3

3Π1,2,3

1Π1

1Δ2

Preliminary Calculation of HfF Potential Curves

+

R( )Å

E-E

(cm

)10

0-1

21.951.85 1.91.81.751.71.651.6-50000

-45000

-25000

-40000

-30000

-35000

HfF+ electronic states

• 1Σ ground state?

• 3Δ1 ~ 800 cm-1

above ground state

S. Petrov, K. Mosyagin, T. Isaev, A. Titov

1Σ

3Δ1,2,3

3Π1,2,3

1Π1

1Δ2

Preliminary Calculation of HfF Potential Curves

+

R( )Å

E-E

(cm

)10

0-1

21.951.85 1.91.81.751.71.651.6-50000

-45000

-25000

-40000

-30000

-35000

HfF+ electronic states

• 1Σ ground state?

• 3Δ1 ~ 800 cm-1

above ground state

S. Petrov, K. Mosyagin, T. Isaev, A. Titov

Uncertainties of 1000 cm-1 !!!(3 x 1013 Hz)

HfF+ Spectroscopy

PMT

• Search for HfF+ excited electronic states• Remove ion lens and perform spectroscopy on ion beam before Paul trap

IR Laser

Experimental “progress”: Laser-induced fluoresencesignal from neutral ( ) HfF

The R, Q, and P branches of a v’=0, Ω’=3/2 v”=0, Ω”=3/2transition in HfF

Current limit, beam of atomic Thallium:B. Regan, E. Commins, C. Schmidt, D. DeMille, Phys. Rev. Lett. 88, 071805 (2002)

|de| < 1.6 x 10-27 e*cm (90% c.l.)

Eeff τCommins Tl beam 6 x 107 V/cm 2 msec 109 s-1

Hinds YbF beam > <DeMille PbO vapor cell > <Weiss trapped Cs < > <Heinzen trapped Cs < > <Gould Cs fountain < > <Shafer-Ray PbF beam > <Cornell trapped HfF+ or ThF+ > > <<

effN

Solid State

Sensitivity Estimate

• N = 150 ions/shot (107 ions/day)• Eeff = 1.5x1010 V/cm• τ = 1 secondNE

hdeff

e τ2<

proj. sensitivity: |de| < 5 x 10-29 e*cm with 1 day of data

Systematic Error Rejection. Key Chops.

Chop: B E E/Eeff v OtherY

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

N

Tl beam N Y

YbF beam N N*

PbO vapor cell Y N*

trapped Cs N Trap

Cs fountain N N

PbF beam N N*

Trapped MF+ Y Rotationsense

Systematic Error Rejection. Key Chops.

Chop: B E E/Eeff v OtherY

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

N

Tl beam N Y

YbF beam N N*

PbO vapor cell Y N*

trapped Cs N Trap

Cs fountain N N

PbF beam N N*

Trapped MF+ Y Y* Rotationsense

We’ve got the chops, and:Key fact: νscience is independent of magnitude of

E, B, and ωrot. Also should be independent ofstrength of ion trap confinement, T, and nion.

-++

-++

-++

-++

M=-1 M=1

Ω=1

Ω=1Ω=-1

Ω=-1

M=-1 M=1

E

ωrt

Rotating electric quantization axis

Stark shift and Berry’s phase:

We are working in a TRAP. Electric field is perforcespatially inhomogenous, and it rotates!Consequences for decoherence? systematics?

-++

-++

-++

-++

M=-1 M=1

Ω=1

Ω=1Ω=-1

Ω=-1

M=-1 M=1

E

ωrt

Rotating electric quantization axis

Stark shift and Berry’s phase:

( )K+

Ω+

Ω++Ω=Ω 2

32

||

|| ||),,,(

EdMA

EdMAMAMEdEMU

mol

r

mol

rrmolr

ωβωαωω

-++

-++

-++

-++

M=-1 M=1

Ω=1

Ω=1Ω=-1

Ω=-1

M=-1 M=1

E

ωrt

Rotating electric quantization axis

Stark shift and Berry’s phase:

( )K+

Ω+

Ω++Ω=Ω 2

32

||

|| ||),,,(

EdMA

EdMAMAMEdEMU

mol

r

mol

rrmolr

ωβωαωω

( ) [ ]32 1 || εβεαε AAAMEdU mol +++Ω=

Ω≡

|| Edmolrotωε

(A, solid angle =2π)

-++

-+

-+

-++

M=-1 M=1

Ω=1

Ω=1Ω=-1

Ω=-1

M=-1 M=1

E

ωrt

g q

Stark shift and Berry’s phase:

( )K+

Ω+

Ω++Ω=Ω 2

32

||

|| ||),,,(

EdMA

EdMAMAMEdEMU

mol

r

mol

rrmolr

ωβωαωω80 MHz

250 kHz 800 Hz 2.5 HzCancelsCancels

The decohering effects of ion-ion collisions:

Ebias+Eion-ion

Ion picks up a little random Berry’s phase with each near miss. 1−∝ ioncohere nτ

Sensitivity to EDM fairly flat with Nion, but Nusable/Nion is critical. (And rather uncertain).

Random issues:

Inhomogeneity in Erot can lead to line-broadeningbut first to problems with ponderomotive potential (an anti-Paul trap.)

Momentum kick associated with optical pumpingto one Omega level or the other can be troublesome if one doesn’t insert a suitable dwell time.

Systematics bottom line:We haven’t thought of a killer systematic atthe 10-28 level yet.We will have a number of powerful techniques for smoking out unforeseen ones.

In the end, we’ve got to try it.

Decoherence Effects

1.02 ×≈=Δ ππϕrot

Bcoll U

TkN

dΩ<2π dΩ=2π dΩ>2π

• Axial electric field tips molecular axis out of radial plane.• Rotating spin picks up spatially varying Berry’s phase.• Net effect cancels out in the absence of ion-ion collisions.• Collisions lead to phase diffusion and decoherence.

Experimental Progress• Laser ablation of Hf or Th targets in the expansion gives

HfF+, ThF+. We can “catch”, trap, 105/shot, hold time >> 1s• Comoving beam temperature measured (in Hf and Hf+) <2K• Photodissociation of CH+ to C+ and H.

1 cm

CH+ → C+ + H

Initial spectroscopy• Must scan over 1000’s of cm-1’s, doppler width of ~50 MHz

– Course scans with pulsed dye laser– Fine scans with cw Ti:Saph laser

• Optimized detection on Hf neutral lines– S/N ~104:1 w/ Ti:Saph laser– Observed cooling of Hf fine structure from Helium collisions

Hf neutral LIF

Dye Laser scan

T~1K Hf+ beam (measured with translatable ion detector

T = 2K, Hf laser fluorescence,crossed-beam doppler width.

Experimental Progress

• Comoving beam temperature measured (in Hf and Hf+) <2 K.• Photodissociation of CH+ to C+ and H.

1 cm

Sensitivity Estimate• N = 150 ions/shot (107 ions/day)• Eeff = 3x1010 V/cm• τ = 1 second

• Flip B-Field bias gradient.• Change Ω-doublet levels.• Change sign, mag., freq of Erot.• Multiple internal mol. states*

NEhd

effe τ2

<

Inverts EDM signal

Constant EDM signal

SUSYMulti-Higgs

Left-RightStd. Mod.

de [e*cm]10-24 10-3810-26 10-28 10-30 10-32 10-34 10-36

|de| < 1.6 x 10-27 e*cmE.D. Commins Tl Exp. Limit [PRL 88, 071805 (2002)]

proj. sensitivity: |de| < 6 x 10-29 e*cm with 1 day of data

Common traits of (AMO) eEDM searches

• Magnetic and dipole moment of electron must be aligned– no other direction to point

• Perform electron spin resonance in the presence of E and B fields

Look for ω1 ≠ ω2 , ћ(ω1-ω2) = 4de·E

Figure of Merit for experiment

Εeff∗τ∗√N

B EE Bħω1 ħω2↑

↓

↑

↓