EDMs of stable atoms and molecules

Solvay workshop „Beyond the Standard model with Neutrinos and Nuclear Physics“Brussels, Nov. 29th – Dec. 1st, 2017

• Introduction

• EDM sensitivity

• Recent progress in

-EDMs paramagnetic atoms/molecules

-EDMs diamagnetic atoms

• Conclusion and outlook

outline

W.Heil

Our world is composed of matter... and not antimatter

n 400/cm3 (CMB)

nb 0.2 protons/m3

10106

n

nnbb

SM prediction based on observed

flavor-changing CP-violation (CKM-matrix)

1810

n

nnbb

SM CP-odd phases

1010QCD

constrained experimentally (dn, dHg )

(strong CP problem)

)1(~ OCKM

explains CP in K and B meson

mixing and decays

Electric dipole moments (EDMs) of elementary particles

(flavor-diagonal CP )

EDM measurement free of SM

background

cmedn

3432 1010~

Khriplovich, Zhitnitsky 86

cmede

3810

fourth orderelectroweak

pn dd ,

Hetd 3,,

EDMs of paramagnetic

atoms and molecules

(Tl,YbF,ThO,…)

Atoms in traps (Rb,Cs,Fr)

Solid state

EDMs of

diamagnetic atoms

(Hg,Xe,Ra.Rn,..)

Fundamentaltheory

Wilsoncoefficients

Low energyparameters

Nucleuslevel

Atom/moleculelevel

TeV

QCD

nuclear

atomic

Atomic EDM

𝐸𝑒𝑥𝑡

+ +

- -

𝐸𝑖𝑛𝑡

𝐸𝑒𝑓𝑓 = 𝐸𝑒𝑥𝑡 + 𝐸𝑖𝑛𝑡 = 𝜀 ⋅ 𝐸𝑒𝑥𝑡 = 0

⇒ Δ𝐸𝐸𝐷𝑀 = − Ԧ𝑑𝐸𝐷𝑀 ⋅ 𝐸𝑒𝑓𝑓 = − Ԧ𝑑𝐸𝐷𝑀 ⋅ 𝜀 ⋅ 𝐸𝑒𝑥𝑡 = 0

L.I.Schiff (PR 132 2194,1963):

EDM of a system of non-relativistic charged point particles that

interact electrostatically can not be measured : 𝜀 = 0

Ԧ𝑑𝐸𝐷𝑀

complete shielding:

Relativistic violation of Schiff screening

(requires the use of relativistic electron radial wavefunctions)

Paramagnetic EDMs – „Schiff enhancement“

Polar molecules

Atoms

Finite size violation of Schiff screening

Diamagnetic EDMs – „Schiff suppression“

For a finite nucleus, the charge and EDM have different spatial

distributions

S- Schiff moment:

cmefme

Skd AA

3

1710

Schiff moment is dominant CP-odd N-N interaction for large atoms

( kHg~ -3 )

(low energy parameters)

nucnucANA dOdRRZd )10(~/10~ 322

Nuclear deformation can enhance heavy atom EDMs

(e.g., 225Ra, 223Rn )

Heavy atoms (relativistic treatment) + finite size: 0

de 0 datom 0 ~ Z32de

P,T-odd eN interaction

Tensor-Pseudotensor ~Z2GFCT

Scalar- Pseudoscalar ~Z3GFCS

Nuclear EDM – finite size

Schiff moment induced by P,T-odd N-N interaction ~10-25 [ecm]

𝜂 𝑑𝑛, 𝑑𝑝, ҧ𝑔0, ҧ𝑔1, ҧ𝑔2

ഥΘ𝑄𝐶𝐷

Paramagnetic EDMs:„Schiff enhancement“ ( >> 1)

Diamagnetic EDMs:„Schiff suppression“ ( << 1)

General finding:

Phys. Rep. 397 (04) 63; Phys. Rev. A 66 (02) 012111.

Diamagnetic atoms:

𝑑(129𝑋𝑒) = 10−3𝑑𝑒 + 5.2𝑥10−21𝐶𝑇 + 5.6𝑥10−23𝐶𝑆 + 6.7𝑥10−26𝜂 ≈ 6.7𝑥10−26𝜂

Xe

EDM precision experiments (upper limits)

EDM search: Ramsey type phase measurements

/22 EdBEB

EDM sensitivity (FOM)

/)(2

/NEd

noise

ddS

resolution

shift E

SNREd

ext

1

Sign

al

noise

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0.0

0.2

0.4

0.6

0.8

1.0

B

A

B

Precession phase

Nd

dS

magneticbias phase (B)

EDM phaseshift (E)

𝑁

x̂

𝑬,𝑩 ො𝒛

x̂

x̂

𝑬,𝑩 ො𝒛

EDMs of paramagnetic atoms and molecules

(Tl, YbF, ThO, …)

E

electric field

-de 𝜀E•𝜀de

atom containing electron

amplification-585 for Tl

𝜺 109 for ThO

Interaction energy

(Elab 100 V/cm)

𝜀

2. advantage of YbF , ThO :

No coupling v E to motional magnetic field

and internuclear axis is coupled to E

v E = 0 no motional systematic error

electron spin is coupled to internuclear axis

Experimental setup: general scheme

state preparation state readout

beam of atoms

or molecules

Spin precession

B E

Observable: phase difference = 2 (mBB ± de𝜀E) / ħ( )

M = -1 M = 0 M = +1

HThO:metastable state (ground rotational level; J=1), lifetime ~ 2ms1; JH

M = -1 M = 0 M = +1

H

Elab

0effE

0effE

N = +1

N = -1

M = -1 M = 0 M = +1

H

Elab

0effE

0effE

B

B

B

B

B

N = +1

N = -1

M = -1 M = 0 M = +1

H

Elab

0effE

0effE

B

B

B

B

B

effe Ed

effe Ed effe Ed

effe Ed

N = +1

N = -1

M = -1 M = 0 M = +1

H

Elab

0effE

0effE

B

B

B

B

B

effe Ed

effe Ed effe Ed

effe Ed

Preparation/ReadoutLasers

CP = +1

P = -1

N = +1

N = -1

/ effeB EdBg N

2/,1,1,,ˆ NNN MeMex ii

Results

/)(]/[102.38.46.2 3

SSeffesysstat CWEdsrad

using Eeff = 84 GV/cm , WS (molecule-specific constant)Phys.Rev. A 84, 052108 (2011)

)%90(107.8105.27.31.2 2929 CLecmdecmd esysstate

)%90(109.5 9 CLCS

CS = 0

de = 0

/)(]/[102.38.46.2 3

effesysstat Edsrad

Science 343 (2014) 269

199Hg EDM experiment

19 cm

use of buffer gases:no EDM false effectsdue to geometric phases

cmkVE /10

0,00,51,01,52,0

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

B

A

B

PRL 116, 161601 (2016)

systematic effects in units of 10-32 ecm

Effective data taking: 252 days

Limits on CP-violating observables from 199Hg EDM limit

Results: Hg-EDM

(95% CL)ecmdHg

30104.7

Courtesy of B. Santra

Towards long spin-coherence times (T2*)

SQUIDdetector

h 1001T TBcmRmbarp

TLong

~,5~,~

:

1

*

2

24

2

z ,1

2

y ,1

2

x,1

24

field 2,

field 2,1

*

2

2175

41

111

BpRBBBD

R

T

TTT

(G. D. Cates, et al., Phys. Rev. A 37, 2877)

Motional narrowing regime: diff <<1/(B)

hT He 1.02.60*

,2

0 2 4 6 8 10

-12

-8

-4

0

4

8

12

BS

QU

ID [

pT

]

time [h]

0,0 0,2 0,4-15

-10

-5

0

5

10

15

BS

QU

ID [p

T]

time [s]

129Xe3He(4,7 Hz) (13 Hz)

0,, XeL

Xe

HeHeL

.constXe

Xe

HeHe

B [

nT

]

t [h]0 5 10 15 20

406.68

406.67

406.66

drift ~ 1pT/h

Comagnetometry to get rid of magnetic field drifts

10-5 Hz/h

B0

I. Earth‘s rotation = He- He / Xe Xe

rem = - Earth

Subtraction of deterministic phase shifts

*,2

*,2

*,2

*,2 /2/2// XeHeXeHe Tt

Xe

Tt

He

Tt

Xe

Tt

HeEarth ebebeaeatac

)(tEDM

He

Xe

II. Ramsey-Bloch-Siegert shift

cross-talk ~

*2/

0

TteS

self shift ~

2/

0

*2Tt

eS

Measurement sensitivity: 129Xe electric dipole moment

XedEhh

4

Eo E E

BoE E

Observable: weighted frequency difference

XeHe

XeE

hd

4sensitivity limit:

Rosenberry and Chupp, PRL 86,22 (2001)

27101.03.37.0 Xed ecm

EDMXe

XeHe

EDMXe

XeHe

EDMHe ,,, )()(

EDMXe

XeHe

EDMXe

XeHe

EDMHe ,,, )()(

• 𝑑𝑋𝑒 sensitivity per day estimation from previous run on LV search

• (SNR ≈ 3000, )

+ 2 kV/cm

- 2 kV/cm

𝑇𝑎, E-Field switching time

Experimental EDM sensitivity estimation

hTT 243 *

2

=

tEDM

*,2

*,2

*,2

*,2

/2/2

//

XeHe

XeHe

Tt

Xe

Tt

He

Tt

Xe

Tt

HeEarth

ebeb

eaeata

low Tc-SQUIDgradiometer(s)

-5 kV +5 kV 3He

129Xe

CO2 , SF6

gas preparationarea outside MSR

gas transfer line

l He

dewar

Turbo pump

pneumatic valve

B0(cos-coil) Bv(solenoid)

Btrans

Experimental Setup: Overview

mu-metal cylinder

solenoid

cos-coil

magneticallyshielded room(MSR)

Experimental Setup: EDM-Cell

+4kV -4kV

SQUIDgradiometer

SF6(HV protective gas)

Glass vessel(conductive coating)

y

z

x

Bcos= B0 , E

Bsolenoid

𝑩𝟎

E

10 cm

Gas inlet

1 2 3 4 5 6-8

-6

-4

-2

0

2

4

6

8d

Xe /

10

-27 e

cm

# EDM-run

ecmd Xe

2810)2.45.1(

total data taking time: ~ 45 h SNR~ 1800

SNR ~ 10000

Comparison: Hg-EDM vs Xe-EDM sensitivity

Hg-EDM:

SNR~ 30000 @ fBW = 1 Hz

<E> = 8 kV/cm

dHg = 4.1 x 10-29 ecm/day

Xe-EDM:

SNR~ 10000 @ fBW = 1 Hz

<E> = 0.8 kV/cm

T2,Xe*~ 3 h

dXe = 4 x 10-28 ecm/day

Improvements:

• <E>

• T2,Xe*

• SNR magnetic shield

SNR~1800

SNR~10000

B-fieldgeo~ 10-7 rad/s

Conclusion and outlook

Tremendous advance in complexity and sensitivity for polar molecules

Steady progress in EDMs of diamagnetic atoms (Hg,Xe,…)

EDM measurement FOM

Further improvements to be expected:

- magnetic shielded rooms

- laser sources

- yield of atomic and molecular beam sources

- comagnetometry techniques

- spin coherence times O (h)

- …

Connecting experiment and theory

- theory efforts in particular nuclear theory to sharpen EDM results.

1 SNREd ext

Thank you for your attention.

MIXed-collaboration 2015

EDM5

dayrad @10 daypHzf @18864002

Measurement sensitivity

Phase residuals after subtraction ofdeterministic phase shifts

ASD plot of phase residuals

3He/129Xe clock-comparison experiments

*

,2/exp XeTt

*

,23 XeTT -1/2

The detection of the free precession of co-located 3He/129Xe sample spins can be used as ultra-sensitive probe for

non-magnetic spin interactions of type:

PMPMmagnnon BaV

.

Search for spin-dependent short-range interactionsPhys.Rev.Lett. 111, 100801 (2013)

Search for a Lorentz violating sidereal modulationof the Larmor frequency

Phys. Rev. Lett. 112, 110801 (2014)

Search for EDM of Xenon

…

/ˆ b~

/)( rV

/ˆ /)( rcrV

/ d/)( Xe ErV

3He/129Xe clock-comparison experiments

XeHeXeL

Xe

HeHeL a

/1/,,

Observable:

Current limits on EDMs

129Xe: |dXe|< 3.3 · 10-27 ecm

Rosenberry and Chupp, PRL 86, 22 (2001)

PRL 97, 13 (2006)

• solenoid

Experimental Setup: Magnetic Field

• cos-coil

• cos-gradient coil

• x,y,z – gradient coils

Homogeneity of coil-system + mu-metal shield (@ ~ 600nT):• simulated ~pT/cm• measured (T2*) ~ 10 pT/cm (position of EDM-cell)

z

y

x

Bsolenoid

Bcos=B0 , E

Minimizing magnetic field gradients

242

0

2

2 1

pRB

D

5.0)(0 a

cmpTBz /

sensitivity:

cmfTBz /30

( arXiv:1608.01830v1 )

Minimizing magnetic field gradients

242

0

2

2 1

pRB

D

5.0)(0 a

( arXiv:1608.01830v1 )

2/32/1

1

#

11

TTpoindataTwidthFourierf

# data pointsFourier width

T

Features of 3He/129Xe spin-clocks

Accuracy of frequency estimation:

If the noise w[n] is Gaussian distributed, the Cramer-Rao Lower

Bound (CRLB) sets the lower limit on the variance

322

2

)2(

12

TfSNR BW

f

),( *

2TTC

example: SNR = 10000:1 , = 1 Hz , T= 1 day BWf pHzf 2

2

f<

x 0.1m /day

D=10 cm

Caveat (pHz)

Test of CRLB via Allan Standard Deviation (ASD)

12

1

1

1

2

1

N

ffN

i

ii

f

i i+1

Features of 3He/129Xe spin-clocks

ns

f

112/3

Repetition (n) of shortmeasurements (s) offree spin precession

s 60 s

Measurement ofuninterrupted

spin precession (n=sn)

2/3

1

n

f

Gain in sensitivity: s

nn

…. systematics (cont.)

motional magnetic fields

0

2

02

1

B

BBBB m

mEB

Evc

Bm

2

1

parameter correlations

B0

E

Bm

v

EB0

v

0

fm

nHz12103

PRA 53 (1996) R3705

….

Magnetically shielded room (MSR) at Jülich Research Center

300 @ 1Hz

Inside dimensions:

32.52.4 m3

Shielding factor: