Post on 03-Sep-2018
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