1. Parity Violation in Heavy Atoms &
International Conference on Warsaw, May ‘17
\ Precision Physics and Fundamental Physical Constants
FFK-2017
Parity Violation in Heavy Atoms
&
Searches for Permanent Electric Dipole Moments
Klaus Jungmann, Van Swinderen Institute, University of Groningen

2. Parity Violation in Heavy Atoms & Searches for Permanent Electric Dipole Moments
Testing the Standard Model with Atoms
Discrete Symmetries
Parity: Few Valence Electron Systems Privileged
Unique Possibilities for sin2 W at Low Energies
EDM: Searches in Atoms and Molecules
Perspectives in the Period to Come

3.  Standard Model Tests Best Theory we have
Standard Model (SM) of particle physics is
Best Theory we have
Still large number of open questions
e.g. particle masses, origin of parity violation, ....
Direct:
Searches for New Particles
Indirect:
High Precision Measurements 
Equivalent
Approaches
CERN e.g. LHC
Van Swinderen Institute
also: Difference Matter-Antimatter …
e.g. Discovery of Higgs boson,..
e.g. Atomic Parity Violation,
EDM searches, …..

4. Discrete Symmetries
C,P,T,CP,CPT

5. Parity → relatively large effects in some atoms and molecules
→ one valence electron atoms to extract precise constants
→ more complex systems to study e.g. anapole moments

6. Extraction of Weinberg Angle
Atomic Parity Violation
Extraction of Weinberg Angle
72P3/2
APV effect
Ψe Ψn overlap
72P1/2
62D5/2
62D3/2
+ ε' n' 2P3/2
Ra+ E2
E1APV
Weak charge
72S1/2
+ ε n2P1/2
How does the weak interaction show up in an atomic system?
Here are the lowest energy levels of the radium ion.
Effect of weak interaction is to mix opposite-parity states: now a parity-violating dipole transition amplitude arises
E1 (APV) scales as weak charge (related to Weinberg angle) times overlap between electronic and nuclear wavefunction
E1 is 11 orders of magnitude smaller than E2
Experimental trick to make it measurable: use interference (weak part too weak for actual transitions)
→ Trapped single ion
Fortson, Phys. Rev. Lett. 70, 2383 (1993)

7. Atomic Parity Violation (APV)
Physics beyond the SM
QW = –N+(1–4 sin2θW)Z + rad. corr. + “new physics”
Extra Z’ boson in SO(10) GUTs:
Additional U(1)’ gauge symmetry
Known Z and W unaffected
No Z-Z’ mixing
Londen en Rosner (1986), Marciano en Rosner (1990), Altarelli et al. (1991) q e V A Z0
Z0’
Bound on MZ’ from cesium APV
(68% confidence level, ξ= 52°) Wansbeek et al.. PRA,(2010)
Mz’> 1.2 TeV/c2
(Tevatron MZ’> 0.9 TeV/c2)
Bound (possible) on MZ’ from Ra+ APV
Mz’> 6 TeV/c2
(full LHC MZ’ ~4.5 TeV/c2)
The way to go!

8. Test of Standard Model Electroweak Interaction

9. Test of Standard Model Electroweak Interaction

10. Test of Standard Model Electroweak Interaction

11. Test of Standard Model Electroweak Interaction
S. Kumar, W. Marciano, Annu. Rev. of Nucl. Part. Sci. 63, 237 (2013)
H. Davoudiasl, Hye-Sung Lee, W. Marciano, arxiv (2014)

12. Test of Standard Model Electroweak Interaction
Work in progress
S. Kumar, W. Marciano, Annu. Rev. of Nucl. Part. Sci. 63, 237 (2013)
H. Davoudiasl, Hye-Sung Lee, W. Marciano, arxiv (2014)

13. Atomic Parity Violation
Ba+ and Ra+
S-S
S-D Cs
0.9
Ba+
2.2 Fr
14.2
Ra+
46.4
6D5/2
7P1/2
7P3/2
7S1/2 E2
6D3/2
E1APV
Calculated from
atomic wavefunctions
Detailed calculations → stronger than Z3
Ra+ superior to measure APV …
50x more sensitive to APV than current best measurement in Cs
Theory Calculations:
kRa = 46.4(1.4) · iea0 /N *
kCs = (26) · iea0 /N **
*L.W. Wansbeek et al., Phys. Rev. A 78, (2008)
**A. Derevianko et al., Phys. Rev. A 79, (2009)

14. Laser Spectroscopy in Ra+ Ions
Probe of atomic theory & size and
shape of the nucleus
Probe of atomic wave functions
at the origin
Good agreement with theory at few % level
Theory improvement is in pipeline.
O.O. Versolato et al., Phys. Lett. A 375, 3130 (2012)
O.O. Versolato et al., Phys. Rev. A 82, (R) (2010)
G.S. Giri et al., Phys. Rev. A 84, (R) (2011)
M. Nuñez Portela, et al., Appl. Phys. B (2013)

15. available δ(r2) values: 1.486(75) fm2 vs. 1.277(129) fm2
L.W. Wansbeek et al, Phys. Rev. C 86, (2012)
available δ(r2) values:
1.486(75) fm2
vs.
1.277(129) fm2

16. Relative Ra Charge radii
L.W. Wansbeek et al, Phys. Rev. C 86, (2012)
Radius 226Ra ≈ 5.7 fm
Significant spread between models (up to few 10%)
Need at least one calibration point, best 226Ra

17. Status of Theory 1 PhD student away from necessary sub-% precision
Atomic calculations:
1 PhD student away from necessary sub-% precision
Parity effect calculations:
- nuclear charge radius needed at few-% accuracy
- possibility at PSI opens up

18. Ra+ measurements to test Atomic Theory
Hyperfine Structure:
Probe of atomic wave functions at the origin
Isotope Shifts:
Probe of atomic theory & size and shape
of the nucleus
Excited State Lifetimes:
Probe of S-D E2 matrix element
% level agreement with theory
(Safronova, Sahoo, Timmermans et al.)

19. Single Ba+ Ion Ba+ : Precursor to Ra+ Ra+ Ba+ Hyperbolic Paul Trap
7p2P3/2
7p2P1/2
6d2D3/2
7s2S1/2
λ0=828 nm
λ1=468 nm
λ2=1079 nm
λ4=382 nm
To be measured
λ5=802 nm
6d2D5/2
Ba+
5mm
6p2P3/2
6p2P1/2
5d2D3/2
6s2S1/2
λ0=2050 nm
λ1=493 nm
λ2=649 nm
6.4 ns
8 ns
λ4=455 nm
5d2D5/2
λ5=615 nm
Hyperbolic Paul Trap
localize one ion within one wavelength
electron shelving
large volume
Ba+ : Precursor to Ra+

20. Hyperbolic Paul trap VRF Ba+ 2P3/2 2P1/2 494 nm 2D5/2 2D3/2 5 mm 2S1/2
NNV subatomic Lunteren
Hyperbolic Paul trap
Ba+
494 nm
650 nm
2S1/2
2D3/2
2D5/2
2P1/2
2P3/2
Ion trap
VRF
5 mm 23 23 23

21. Detection Methods & PMT EMCCD camera 10 µm
The usual detection methods: PMT on one side and EMCCD camera on the other
& PMT

22. Ba+ Experiment : Lifetime D5/2
6p2P3/2
6p2P1/2
5d2D3/2
6s2S1/2
λ0=2050 nm
λ1=493 nm
λ2=649 nm
6.4 ns
8 ns
λ4=455 nm
5d2D5/2
λ5=615 nm
Ba+

23. Ba+ Experiment : Lifetime D5/2
6p2P3/2
6p2P1/2
5d2D3/2
6s2S1/2
λ0=2050 nm
λ1=493 nm
λ2=649 nm
6.4 ns
8 ns
λ4=455 nm
5d2D5/2
λ5=615 nm
Ba+

24. Ba+ Experiment : Lifetime D5/2
6p2P3/2
6p2P1/2
5d2D3/2
6s2S1/2
λ0=2050 nm
λ1=493 nm
λ2=649 nm
6.4 ns
8 ns
λ4=455 nm
5d2D5/2
λ5=615 nm
Ba+
1mm
τ≈27.6(8)s
Determine
matrix elements

25. Ba+ 5 2D5/2 Level Lifetime Ba+ EMCCD camera PMT signal
PMT count rate (cnt/s)
PMT signal
Time (s)

26. Ba+ 5 2D5/2 Level Lifetime
2D5/2
τ ≈ 30 s
Ba+
2P3/2
2P1/2
2D3/2
2S1/2
Fitted 2D5/2 level lifetime and shelving rate
No prominent difference with single ion runs
Investigating systematics
1 ion shelved
2 ions shelved
all ions shelved
Diagnostic: 30 s lifetime sensitive to perturbations of ion
Determine D-state lifetime: matrix element
Mohanty et al. (in preparation)

27. Ba+ Experiment : Lifetime D5/2
6p2P3/2
6p2P1/2
5d2D3/2
6s2S1/2
λ0=2050 nm
λ1=493 nm
λ2=649 nm
6.4 ns
8 ns
λ4=455 nm
5d2D5/2
λ5=615 nm
Ba+
Ba+ D5/2 state lifetime
D5/2 = 27.6(8) s

28. Two-photonTransitions in single Ba+
Ba+ level scheme : 8 Zeeman sublevels.
Two photon transition : Raman resonance (δR)
Strongly dependent on:
Mangetic field strength and direction
Laser light polarization
B  E
Offset Frequency of 650nm (MHz)
PMT count rate (counts/sec)
B ll E
Offset Frequency of 650nm (MHz)
PMT count rate (counts/sec)
→ Signals also with blue detuning!
→ Due to rapid cooling laser frequency switching

29. Ba+ spectroscopy 2D5/2 level lifetime Electron shelving
Transition frequencies
Line shape analysis
650 nm
52D5/2
494 nm
52D3/2
Introduce the Ba+ level scheme
Extract these two transition frequencies
2052 nm
62S1/2
138Ba+

30. Modeling of Line Shape |2P1/2⟩ Γ1 Γ2 Optical Bloch equation
|1⟩
|2⟩
|3⟩
|4⟩
|5⟩
|6⟩
|7⟩
|8⟩
Optical Bloch equation
3 level example Δ1 Δ2 γ Ω2 Ω1
|2D3/2⟩ γc
|2S1/2⟩
We use the optical Bloch equations
It uses the density matrix formalism and the time-dependence of the system is given by this Hamiltonian describing the interaction of the ion with the laser light and a damping matrix describing the decoherence effects.
I’m not going to go through all the math, but I just want to describe the ingredients going into this calculations:
Then there’s the spontaneous decay from the excited state which leads to relaxation of the populations, and the associated decoherence effect and finally the finite linewidth of the lasers also causes a decoherence effect.
Ba+
Ω1, Ω2
Rabi frequencies (laser power)
Γ = Γ1 + Γ2
relaxation rate
γ = Γ/2
decoherence rate
Δ1, Δ2
laser detunings γc
laser linewidth

31. Line Shapes and Polarization
494 nm linear polarized B
650 nm circularly polarized
Zeeman sublevels: 8 level system
Magnetic field B
Laser polarization
pmt signal
|1⟩⟨5|
|2⟩⟨8|
|2P1/2⟩
650 nm laser frequency offset
|4⟩
|3⟩
494 nm linear polarized B
650 nm circularly polarized
Including the Zeeman sublevels, there are now two additional parameters playing a role: the magnetic field causing Zeeman splitting and the polarization of the two laser fields with respect to this.
To illustrate that, I have two sets of data here that we collected by keeping the blue laser at a fixed frequency and varying the frequency of the red laser across its corresponding resonance. The two data sets were taken with different polarizations of the lasers.
The wide overall shape is the same, this is the one-photon peak of the transition to the excited state. But depending on polarization and magnetic field, also several dark resonance can appear. These are coherent two-photon effects that occur at frequencies where the sum of a red and a blue photon exactly matches a transition from the ground state to the D level.
So does the optical Bloch model work for fitting these line shapes? YES
|8⟩
|7⟩
|2D3/2⟩
|6⟩
pmt signal
|2⟩
|2S1/2⟩
|5⟩
|1⟩⟨8|
|2⟩⟨5|
|1⟩
650 nm laser frequency offset

32. Transition Frequencies
494 nm
650 nm
Ba+
2P3/2
2P1/2
2D3/2
2S1/2
494 nm
650 nm
2D5/2
Light shift?
Frequency 650 nm laser − 461 311 000 MHz
494 nm laser detuning varied
No, correction in transition frequencies for Ω2 dependent shift consistent with 2° rotation of B-field
138Ba+ Transition
Frequency [MHz]
[Karlsson & Litzén 1999]
This work
6s 2S1/2 – 6p 2P1/2
607 426 290 (100)
607 426 262.5 (0.2)
5d 2D3/2 – 6p 2P1/2
6d 2S1/2 – 5p 2D3/2
461 311 880 (100)
---
461 311 878.5 (0.1)
(0.1)
650 nm laser intensity varied
B-field rotated 2°
Frequency 650 nm laser − 461 311 000 MHz 1 2
One-photon peak frequency (MHz) 3 4 5
461 311 878.0
878.5
879.0
879.5
Expected
Power 650 nm laser (Ω2 / Ω2,sat)
We aim to extract transition frequencies, so we need to know the frequencies of our lasers
Data fit to optical Bloch equation model
Extract transition frequencies with 100 kHz accuracy
Dijck et al., Phys. Rev. A 91, (R) (2015)

33. Atomic Parity Violation
62D5/2
62D3/2
+ ε' n' 2P3/2
Ba+/Ra+
Interference: differential light shift E2
E1APV B0
mF = +1/2
E2 . E1APV
|E2|2 ω0
72S1/2
+ ε n2P1/2 ω0
mF = –1/2
ω0 + Δdiff B0
RF spectroscopy
2D5/2 lifetime → matrix elements
Bloch equations → light shift
N. Fortson, Phys. Rev. Lett. 70, 2383 (1993)
J. A. Sherman arXiv: v1 ( 2009)

34. Radium for APV → 10 days for 5 fold improvement over Cs
Accuracy of single ion Experiment
Coherence
Time
Projected Accuracy
Measurement
Ba+
80 sec
0.2%
1.1 day
Ra+
0.6 sec
1.4 day
→ 10 days for 5 fold improvement over Cs

35. Light Shifts measured in Ba+ ion
Measured Raman dip spectrum for 5d2D3/2 - 6p2P1/2 transition
494nm light linearly polarised in vertical direction along z-axis
650nm light circularly polarised
light shift laser polarised in the horizontal direction
magnetic field of 510 μT along Bz-direction
Detunings were large compared to power broadened linewidth

36. Light Shifts measured in Ba+ ion
Measured Raman dip spectrum for 5d2D3/2 - 6p2P1/2 transition
494nm light linearly polarised in vertical direction along z-axis
650nm light circularly polarised
light shift laser polarised in the horizontal direction
magnetic field of 510 μT along Bz-direction
Detunings were large compared to power broadened linewidth

37. Light Shifts measured in Ba+ ion
Scaling of light shift with detunings of light shifting light
Δ νLS= 0.16(3)GHz2.1/ΔLS , ΔLS is detuning of light shifting light
Polarisation with respect to quantization axes (magnetic field) is important
blue shift
red shift

38. Status Atomic Parity Violation in Ba+/Ra+
Developing Ba+ single ion trapping setup & techniques
Towards measuring atomic parity violation and atomic clocks
Lifetime of 2D5/2 level measured, analysis in progress
Response Λ-system to two lasers described by optical Bloch Model
Improved measurement of transition frequencies
Light shift measurements starting …
And together with my colleagues I’d like to thank you for your attention
Ion Trapping
Van Swinderen Institute, University of Groningen
Mayerlin Nuñez Portela
Nivedya Valappol
Amita Mohanty
Lorenz Willmann
Klaus Jungmann
Olivier Grasdijk
Andrew Grier
Oliver Böll
Elwin Dijck

39. Electric Dipole Moments
Permanent
Electric Dipole Moments z S X sz + -
→ Electron: clean and ready for New Physics
→ Hadrons: depend on θQCD in Standard Model

40. - Spin of Fundamental Particles S + mx= 2(1+ax) S dx =  m0x c-1 S X
S is the only vector characterizing a
non-degenerate quantum state
magnetic moment:
mx= 2(1+ax) S
electric dipole moment:
dx =  m0x c-1 S
magneton:
m0x= eħ / (2mx) m0x c-1 z S X sz + -
m0x c-1 S = {
9.7•10-12 e cm (electron)
4.6•10-14 e cm (muon)
5.3•10-15 e cm (nucleon)

41. Electric Dipole Moment
Lines of attack towards an EDM
Electric
Dipole
Moment
goal:
new source of CP
Hg Xe Tl
Cs Rb
Ra Rn
Fr …
Free Particles
Atoms
Molecules
Condensed State
neutron
muon
deuteron
bare nuclei ? …
electron EDM
nuclear EDM
enhancements
challenging
technology
particle EDM
unique information
new insights
new techniques
challenging
technology
* Since θQCD limited by hadronic EDMs
→ only leptons have direct transformative potential
electron EDM
strong enhancements
new techniques
poor spectroscopic
data
electron EDM
strong enhancements
systematics ??
BaF , YbF
PbO ,WC
PbF ,ThO
HfF+,ThF+ …
garnets
(Gd3Ga5O12)
(Gd3Fe2Fe3O12)
solid He ?
liquid Xe

42. Th+ O– Eext Eeff Eeff  80 GV/cm
Highlight: ThO electron EDM experiment
Eext
Eeff
Th+ O–
Eeff ~ P 2Z 3e/a02
due to relativity
(P.G.H. Sandars)
Jan 2014
Eeff  80 GV/cm
(depending on theorist)
Eext ~ 1 V/cm enough for ThO d
New limit for e-
de < 8.7* e cm
(90% c.l.)
Doyle, Gabrielse , DeMille

43. Atomic/Molecular Enhancement Factors
for Electron EDM
Particle Rb Cs Th Fr Ra
PbO
YbF
Enhancement 24
125
585
1 150
40 000
60 000
Flambaum, Dzuba, 2012
Particle
ThO
BaF
YbF
Enhancement
109
5x105
2 x 106
watch out:
Saturation
→ different theorists agree, typically at 30% level

44. Preferred Systems 199Hg 1014 2x10 2 8x10 -3 10 5x10 13 129Xe 1022 10 4
Particle
Number
Particles
Coherence
Time
[s]
Efficiency
Electric Field
[kV/cm]
Figure of Merrit
199Hg
1014
2x10 2
8x10 -3 10
5x10 13
129Xe
1022
10 4
9x10 -9
3.6
1x10 14
ThO
1011
1.1x10 -3
2x10 -2
<0.1
2x10 13
YbF
105
1.5x10 -3
3x10 -2
1x10 12
BaF
10 -1
10 -2
225Ra
103
4x101
7x10 -5 67
3x10 6

45. EDM Limits vs. Time
HfF+

46. Intermezzo
Search for
Lorentz Invariance Violation

47. Sketch of 129Xe/3He Setup  129Xe SF6 3He -metal cylinder typically:
4 mbar He
8 mbar Xe
40 mbar SF6
l He
dewar
solenoid
3He
129Xe
SF6 
gas preparation
area outside MSR
low Tc-SQUID
gradiometer(s)
cos-coil
glassfibre-reinforced plastic
pneumatic valve
B0(cos-coil)
Bv(solenoid)
gas transfer line
Turbo pump
Btrans
Modified from W. Heil Lepton Moments 2014

48. Dewar housing the LTc-SQUIDs
Pb-glass cylinder
3He/129Xe cell

49. 3He / 129Xe clock comparison to get rid of magnetic field drifts
B [nT]
t [h] 5 1 2
406.68
406.67
406.66
drift ~ 1pT/h
  10-5 Hz/h
129Xe
(4,7 Hz)
3He
(13 Hz)  !
slide from W. Heil

50.  limit on the bound neutron
3He , 129Xe clocks based on free spin precession
yield best limit due to long spin coherence times
in Lorentz violating Standard Model extension
(Kostelecky)
limiting parameter
for experiment
W. Heil et al.
 limit on the bound neutron

51. Electric Dipole Moments
permanent
Electric Dipole Moments z S X sz + -
→ Electron: clean and ready for New Physics
→ Hadrons: depend on θQCD in Standard Model

54. EDM Search from 3He/129Xe Clock Comparison
present limit dXe < 310-27 ecm
goal gain > 3-4 orders o.m.
note dHg < 7 ecm (recent)
W.Heil, U. Schimdt, L. Willmann et al.

57. Sketch of 129Xe/3He Setup  129Xe SF6 3He -metal cylinder  l He
low Tc-SQUID
gradiometer(s)
-5 kV
+5 kV 
gas transfer line
l He
dewar
pneumatic valve
B0(cos-coil)
Bv(solenoid)
Btrans
typically:
4 mbar He
8 mbar Xe
40 mbar SF6
solenoid
3He
129Xe
SF6 
gas preparation
area outside MSR
cos-coil
glassfibre-reinforced plastic
Turbo pump

60. Transport of Hyper-Polarized Xe
3He +CO2
M. Repetto et al., J. Magn. Resonace (2016)

64. Progress
|d |dXe | < ~ X ▪ e cm in a few hours
2016 →

65. Some EDM Limits (in e cm)
ThO Harvard-Yale 8.7x (3.7)(2.5) x e n m
JoGU/HD/RUG ~< X x (first few hours)
atom
7.4 x (2.75)(1.48)
Stay tuned
EDM limits probe TeV scale physics  about LHC
next generation → beyond LHC
SUSY → in trouble ?

66. EDM Limits vs. Time
HfF+

67. Cold Molecules
for
Parity & EDMs
SrF
BaF

68. Atomic/Molecular Enhancement Factors
for Electron EDM
Particle Rb Cs Th Fr Ra
PbO
YbF
Enhancement 24
125
585
1 150
40 000
60 000
Flambaum, Dzuba, 2012
Particle
ThO
BaF
YbF
Enhancement
109
5x105
2 x 106
watch out:
Saturation
→ different theorists agree, typically at 30% level

69. Traveling wave decelerator
SrF
C. Meinema, J. v/d Berg, S. Hoekstra

70. Traveling wave decelerator
5 m of decelerator
10 modules of 50 cm
3360 ring electrodes
diameter electrode: 4 mm
C. Meinema, J. v/d Berg, S. Hoekstra

71. SrF Slowed Down and Guided
Signal
8 of 8 amplifiers
4 m machine
S. Hoekstra et al.
S. Hoekstra, S. Mathavan, A. Zapara, Q. Esajas, VSI
The way to go for eEDM below ecm

72. BaF eEDM → eEDM Collaboration Goal: Best EDM Limit on Electron
machine in statu nascendi
S.Hoekstra, A. Borschevsky, K. Jungmann, R.G.E. Timmermans, L. Willmann,
H. Bethlem, W. Ubachs et al. (FOM/NWO programme )
8 of 8 amplifiers
4 m machine
S. Hoekstra, S. Mathavan, A. Zapara, Q. Esajas, VSI
→ eEDM Collaboration Goal: Best EDM Limit on Electron

73. Precision Tests of Discrete symmetries at Low Energies
SUMMARY
Precision Tests of Discrete symmetries at Low Energies
A few selected Topics
→ Focus on Transformativity
C, P, CP, CPT & Lorentz Invariance
→ Precision Test of Standard Model
Experiment & Theory Hand in Hand
→ Atomic Parity Violation for New Physics Search
Search for permanent Electric Dipole Moments
→ Atoms & Molecules with Enhancement
→ electron and nucleon EDMs
→ Challenge New Physics Models
THANK YOU !