EDMs of stable atoms and molecules outline Introduction EDM - - PowerPoint PPT Presentation

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
• utline

W.Heil

Our world is composed of matter

... and not antimatter

n  400/cm3 (CMB) nb  0.2 protons/m3

10

10 6



   



 n n n

b b

SM prediction based on observed flavor-changing CP-violation (CKM-matrix)

18

10   



 n n n

b b

SM CP-odd phases

10

10 

QCD



constrained experimentally (dn, dHg ) (strong CP problem)

) 1 ( ~ O

CKM



explains CP in K and B meson mixing and decays

Electric dipole moments (EDMs)

• f elementary particles

(flavor-diagonal CP ) EDM measurement free of SM background

cm e dn

34 32

10 10 ~

 



Khriplovich, Zhitnitsky 86

cm e de

38

10 

fourth order electroweak

p n d

d , He t d

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,..) Fundamental theory Wilson coefficients Low energy parameters Nucleus level Atom/molecule level

TeV QCD

nuclear atomic

Atomic EDM

𝐹𝑓𝑦𝑢 + +

• -

𝐹𝑗𝑜𝑢 𝐹𝑓𝑔𝑔 = 𝐹𝑓𝑦𝑢 + 𝐹𝑗𝑜𝑢 = 𝜁 ⋅ 𝐹𝑓𝑦𝑢 = 0 ⇒ Δ𝐹𝐹𝐸𝑁 = − Ԧ 𝑒𝐹𝐸𝑁 ⋅ 𝐹𝑓𝑔𝑔 = − Ԧ 𝑒𝐹𝐸𝑁 ⋅ 𝜁 ⋅ 𝐹𝑓𝑦𝑢 = 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 : 𝜁 = 0

Ԧ 𝑒𝐹𝐸𝑁 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:

cm e fm e S k d

A A

        

 3 17

10

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

( kHg~ -3 )

(low energy parameters)

 

nuc nuc A N A

d O d R R Z d ) 10 ( ~ / 10 ~

3 2 2 



Nuclear deformation can enhance heavy atom EDMs (e.g., 225Ra, 223Rn )



• Heavy atoms (relativistic treatment) + finite size:   0

 de  0  datom  0 ~ Z32de  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] 𝜃 𝑒𝑜, 𝑒𝑞, ҧ 𝑕0, ҧ 𝑕1, ҧ 𝑕2 ഥ Θ𝑅𝐷𝐸 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:

𝑒(129𝑌𝑓) = 10−3𝑒𝑓 + 5.2𝑦10−21𝐷𝑈 + 5.6𝑦10−23𝐷𝑇 + 6.7𝑦10−26𝜃 ≈ 6.7𝑦10−26𝜃



Xe

EDM precision experiments (upper limits)

EDM search: Ramsey type phase measurements



 

 / 2 2             E d B

E B

EDM sensitivity (FOM)

 

 / ) ( 2 / N E d noise d dS resolution shift

E

           

 

SNR E d

ext

       1

Signal noise

Precession phase

N d dS  

magnetic bias phase (B) EDM phase shift (E)

𝑂

 



x ˆ



𝑭, 𝑪 ො 𝒜



x ˆ

x ˆ



𝑭, 𝑪 ො 𝒜

EDMs of paramagnetic atoms and molecules (Tl, YbF, ThO, …) E

electric field

• de 𝜁E•

𝜁de 

atom containing electron amplification

• 585 for Tl

𝜻  109 for ThO

Interaction energy

(Elab  100 V/cm)

𝜁

• 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

• r molecules

Spin precession B E

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

( )

M = -1 M = 0 M = +1

H

ThO:

metastable state (ground rotational level; J=1), lifetime ~ 2ms

1 ;  J H

M = -1 M = 0 M = +1

H

Elab



eff

E 

eff

E

N = +1 N = -1

M = -1 M = 0 M = +1

H

Elab



eff

E 

eff

E

B   

B   

B   

B   

B

N = +1 N = -1

M = -1 M = 0 M = +1

H

Elab



eff

E 

eff

E

B   

B   

B   

B   

B

eff e E

d  

eff e E

d  

eff e E

d  

eff e E

d  

N = +1 N = -1

M = -1 M = 0 M = +1

H

Elab



eff

E 

eff

E

B   

B   

B   

B   

B

eff e E

d  

eff e E

d  

eff e E

d  

eff e E

d  

Preparation/Readout Lasers

C

P = +1 P = -1 N = +1 N = -1

 

 /        

eff e B

E d B g N

 

 

2 / , 1 , 1 , , ˆ N N N       

 

M e M e x

i i  



Results

 

 / ) ( ] / [ 10 2 . 3 8 . 4 6 . 2

3 S S eff e sys stat

C W E d s rad        



using Eeff = 84 GV/cm , WS (molecule-specific constant)

Phys.Rev. A 84, 052108 (2011)

 

) % 90 ( 10 7 . 8 10 5 . 2 7 . 3 1 . 2

29 29

CL ecm d ecm d

e sys stat e  

       

) % 90 ( 10 9 . 5

9

CL CS



 

CS = 0 de = 0

 

 / ) ( ] / [ 10 2 . 3 8 . 4 6 . 2

3 eff e sys stat

E d s rad      



Science 343 (2014) 269

199Hg EDM experiment

19 cm use of buffer gases: no EDM false effects due to geometric phases

cm kV E / 10 

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)

ecm dHg

30

10 4 . 7



 

Courtesy of B. Santra

Towards long spin-coherence times (T2*)

SQUID detector h 100 

1

T



T B cm R mbar p T Long  ~ , 5 ~ , ~ :

1 * 2

2 4 2 z , 1 2 y , 1 2 x , 1 2 4 field 2, field 2, 1 * 2

2 175 4 1 1 1 1 B p R B B B D R T T T T                       

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

Motional narrowing regime: diff <<1/(B)

 h

T He 1 . 2 . 60

* , 2

 

2 4 6 8 10

• 12
• 8
• 4

4 8 12

BSQUID [pT] time [h]

0,0 0,2 0,4

• 15
• 10
• 5

5 10 15

BSQUID [pT] time [s]

129Xe 3He

(4,7 Hz) (13 Hz)

, ,

    

Xe L Xe He He L

    

. const

Xe Xe He He

        

B [nT] t [h]

5 1 1 5 2

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 / /

Xe He Xe He

T t Xe T t He T t Xe T t He Earth

e b e b e a e a t a c

   

           

) (t

EDM

 

He Xe

• II. Ramsey-Bloch-Siegert shift

cross-talk ~

* 2

/ T t

e S





self shift ~

 

2 /

* 2

T t

e S





Measurement sensitivity: 129Xe electric dipole moment

 

Xe

d E h h          

 

4   

Eo E E Bo E E

Observable: weighted frequency difference

 

Xe He Xe

E h d        4

sensitivity limit:

Rosenberry and Chupp, PRL 86,22 (2001)

 

27

10 1 . 3 . 3 7 .



   

Xe

d

ecm EDM Xe Xe He EDM Xe Xe He EDM He , , ,

) ( ) (

   

                 

EDM Xe Xe He EDM Xe Xe He EDM He , , ,

) ( ) (

   

                 

• 𝑒𝑌𝑓 sensitivity per day estimation from previous run on LV search
• (SNR ≈ 3000, )

+ 2 kV/cm

• 2 kV/cm

𝑈

𝑏, E-Field switching time

Experimental EDM sensitivity estimation

h T T 24 3

* 2 

 

 =

 

t

EDM



* , 2 * , 2 * , 2 * , 2

/ 2 / 2 / /

Xe He Xe He

T t Xe T t He T t Xe T t He Earth

e b e b e a e a t a

   

          

low Tc-SQUID gradiometer(s)

• 5 kV

+5 kV

 

3He 129Xe

CO2 , SF6

 

gas preparation area 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 magnetically shielded room (MSR)

Experimental Setup: EDM-Cell

+4kV

• 4kV

SQUID gradiometer

SF6

(HV protective gas) Glass vessel (conductive coating)

y z x

Bcos= B0 , E Bsolenoid

𝑪𝟏 E

10 cm

Gas inlet

1 2 3 4 5 6

• 8
• 6
• 4
• 2

2 4 6 8 dXe / 10-27 ecm

# EDM-run

ecm d Xe

28

10 ) 2 . 4 5 . 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-field geo~ 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 

    SNR E d

ext 

 

Thank you for your attention.

MIXed-collaboration 2015

EDM5

day rad @ 10    

day pHz f @ 18 86400 2       

Measurement sensitivity

Phase residuals after subtraction of deterministic phase shifts

ASD plot of phase residuals

3He/129Xe clock-comparison experiments

 

* , 2

/ exp

Xe

T t  





* , 2

3

Xe

T T  

 -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:

PM PM magn non

B a V         



 

.

• Search for spin-dependent short-range interactions

Phys.Rev.Lett. 111 111, 100801 (2013)

• Search for a Lorentz violating sidereal modulation
• f the Larmor frequency
• Phys. Rev. Lett. 112, 110801 (2014)
• Search for EDM of Xenon
• …

   / ˆ b ~ / ) (     r V

   / ˆ / ) ( r c r V   

    / d / ) (

Xe

E r V    

3He/129Xe clock-comparison experiments

 

Xe He Xe L Xe He He L

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 Fie

ield ld

• 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

2 4 2 2 2

1 p R B D    

5 . ) (    a

cm pT Bz /  

sensitivity:

cm fT Bz / 30    

( arXiv:1608.01830v1 )

Minimizing magnetic field gradients

2 4 2 2 2

1 p R B D    

5 . ) (    a

( arXiv:1608.01830v1 )

 

2 / 3 2 / 1

1 # 1 1 T T poin data T width Fourier

f

               

# data points Fourier 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

 

3 2 2 2

) 2 ( 12 T f SNR

BW f

     

) , (

* 2

T T C 

example: SNR = 10000:1 , = 1 Hz , T= 1 day 

BW

f

pHz

f  2



2 f



<

x  0.1m /day

D=10 cm

Caveat (pHz)

Test of CRLB via Allan Standard Deviation (ASD)

     

 

1 2 1

1 1 2 1

  



  

N f f

N i i i f

   

i i+1



Features of 3He/129Xe spin-clocks

n

s f

1 1

2 / 3

   

Repetition (n) of short measurements (s) of free spin precession s  60 s Measurement of uninterrupted spin precession (n=sn)

2 / 3

1

n f

  

Gain in sensitivity:

s n

n   

…. systematics (cont.)

• motional magnetic fields

2

2 1 B B B B B

m m EB

     

 

E v c Bm     

2

1

• parameter correlations

B0 E Bm



v 

EB

    v





fm nHz

12

10 3



 

PRA 53 (1996) R3705

• ….



Magnetically shielded room (MSR) at Jülich Research Center

 300 @ 1Hz Inside dimensions: 32.52.4 m3 Shielding factor: