w.heil edms of stable atoms and molecules...edms of stable atoms and molecules solvay workshop...
TRANSCRIPT
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: