1. Fundamental Symmetry Tests with Atoms
Michael Romalis
Princeton University

2. Atomic Parity Violation
Limits on CP violation from Electric Dipole Moments
Tests of CPT and Lorentz symmetries

3. Atomic parity violation
4/15/2017
Atomic parity violation
Parity transformation:
Electromagnetic forces in an atom conserve parity
[Hatomic, P]=0
Atomic stationary states are eigenstates of Parity
But weak interactions maximally violate Parity!
Electromagnetic
Weak
Tiny virtual contribution of Z-boson exchange can be measured! 3

4. Atomic Parity Violation Experiments
Early work:
M.-A. Bouchiat, C. Bouchiat (Paris)
Sandars (Oxford)
Khriplovich, Barkov, Zolotorev (Novosibirsk)
Fortson (Seattle)
Current Best Measurement – Wieman (Bolder, 1999)
Parity mixing on M1 transition 6S1/2  7S1/2 transition in Cs
Experimental
accuracy on
PV amplitude EPV:
0.35%

5. Relation to Standard Model Parameters
4/15/2017
Relation to Standard Model Parameters
Exchange of virtual Z0 boson:
Weak charge Qw
Nuclear (neutron) distribution
Axial-vector electron current and vector current, the other way leads to a non-scalar contribution to Hw
In electronic sector the operator reduces to
gamma_5 provides parity violation, GF is a Fermi constant and rho_n is a neutron distribution
One of the most accurate tests of the SM below Z-pole
Best Atomic Calculation in Cs: 0.27% error - Derevianko (Reno, 2009)
Phys. Rev. Lett. 102,  (2009) 5

6. K. Tsigutkin et al, Phys. Rev. Lett. 103, 071601 (2009)
Parity violation in Yb
Parity violation is enhanced 100 times in Yb because of close opposite-parity states (DeMille, 1995)
Atomic calculations will not be as accurate, but one can compare a string of isotopes and measure the anapole moment
First observation by Budker with 14 % accuracy (2009)
The experiment is improving, needs to reach ~ 1%
K. Tsigutkin et al, Phys. Rev. Lett. 103, (2009) 

7. Impact on Electroweak Physics

8. T and CP violation by a permanent EDM
Time Reversal: t – I d d = I
Vector:
d  0  violation of time reversal symmetry
CPT theorem also implies violation of CP symmetry
EDM  T violation  CP violation
Relativistic form of interaction:
Requires a complex phase

9. Fundamental Theory - Supersymmetry, Strings
EDM Searches
Experiments
Nuclear
Atomic
Molecular
Neutron n
Diamagnetic
Atoms
Hg, Xe, Rn
Paramagnetic
Atoms
Tl,Cs, Fr
Molecules
PbO, YbF, TlF
Atomic
Theory
Atomic
Theory
Atomic
Theory
Atomic
Nuclear
Theory
Nuclear
QCD
QCD
Quark
EDM
Quark
Chromo-EDM
Electron
EDM
High Energy
Theory
Fundamental Theory - Supersymmetry, Strings

10. Discovery potential of EDMs
In SM the only source of CP violation is a phase in CKM matrix
The EDMs are extremely small, require high-order diagrams with all 3 generations of quarks
Almost any extension of the Standard Model contains additional CP-violating phases that generally produce large EDMs.
Raw energy sensitivity:
Current experiments are already sensitive enough to constrain EDMs from Supersymmetry by a factor of 100 or more
Baryogenesis scenarios:
Electroweak baryogenesis: EDMs around the corner, somewhat unfavorable based on existing constraints
Leptogenesis: No observable EDMs
Other (GUT scale, CPT violation): No observable EDMs d ~ em 2 , 10 – 27 e cm
=100 TeV

11. Experimental Detection of an EDM
Measure spin-precession frequencies B E d m w1 B E d m w1 H = – m × B d E w 1 = 2
m B + dE h w 2 = m B - dE h w 1 – 2 = 4 dE h
Statistical Sensitivity:
Single atom with coherence time t:
N uncorrelated atoms measured for time T >> : dw = 1 t d = h 2 E 1 t TN

12. Search for EDM of the neutron
Historically, nEDM experiments eliminated many proposals for CP violation

13. ILL neutron EDM Experiment
n, 199Hg
40 mHz

14. Recent nEDM result
Complicated effects of motional magnetic field Bm = E  v/c
Random motion results in persistent rotating magnetic field
Dependance on field gradient dBz/dz  dBr/dr  r V
Rotating field causes frequency shift
dBz/dz
E and B0 into page
dn = 0.61.5(stat)0.8(syst) ecm |dn| < 3.0  ecm (90% CL)
Factor of 2 improvement
C.A. Baker et al
Phys. Rev. Lett. 97,  (2006)

15. Cryogenic nEDM experiments
Superthermal production in superfluid 4He
N increased by 100 – 10000
He-4 good isolator, low temperature
E increased by 5
Superconducting magnetic shields
SQUID magnetometers 1m

16. Electron EDM Sandars, 1965 Thallium:
Electron has a finite charge, cannot be at rest in an electric field
For purely electrostatic interactions
F = eE = 0
— Schiff shielding, 1963
Can be circumvented by magnetic interactions, extended nucleus
F = eE+mB = 0, E  0
Enhanced in heavy atoms:
Strong spin-orbit magnetic interaction
Large Nuclear Coulomb field
Relativistic electrons near the nucleus E =
Sandars, 1965
Thallium:
Cs: 114, Fr: 1150

17. Berkeley Tl EDM Experiment
Mixing chamber
Na detectors
590 nm laser beams
RF 1
RF 2
Tl detectors
Light pipe
photodiodes
Beam stop
Collimating slits
E-field
(120 kV/cm)
State Selector
Analyzer
378 nm laser beams B
Atomic beams
Na (~350 C)
Tl (~700 C)
1 m
70 Hz
Na atoms used as a co-magnetometer
de = (6.9 7.4)10-28 ecm
|de| < 1.610-27 ecm (90% C.L.)
B. Regan, E. Commins, C. Schmidt, D. DeMille, Phys. Rev. Lett. 88, (2002)

18. Only 20% better than Thallium
YbF Experiment
Polarized polar molecules have very high internal electric field
It is hard to generate paramagnetic molecules
New Result !!!
de= (−2.4 ± 5.7 ± 1.5) × 10−28e cm
Only 20% better than Thallium
J. J. Hudson, D. M. Kara, I. J. Smallman, B. E. Sauer, M. R. Tarbutt, E. A. Hinds, Nature 473, 493, (2011)

19. 199Hg EDM Experiment 100,000 hours of operation
Solid-state Quadrupled UV laser
100,000 hours of operation
High purity non-magnetic vessel
Hg Vapor cells
All materials tested with SQUID
Spin coherence time: sec
Electrical Resistance: 21016 W 19

20. Recent improvements in 199Hg Experiment
Use four 199Hg cells instead of two to reduce magnetic field noise and have better systematic checks
Larger signal due to cell improvements
Frequency uncertainty 0.1 nHz w1 w2
inner
cells E
outer
cells w3 E w4
Magnetic Gradient Noise Cancellation
Leakage Current Diagnostic
S = (w2 - w3) - 1/3 (w1 - w4)
L = (w2 + w3) - (w1 + w4) 20

21. New 199Hg EDM Result d(199Hg) = (0.49±1.29stat±0.76syst)×10−29 e cm
About 1 year of data
Changed all components of the system:
d(199Hg) = (0.49±1.29stat±0.76syst)×10−29 e cm
|d(199Hg)| < 3.1×10−29 e cm (95% C.L.)
Factor of 7 improvement
W. C. Griffith, M. D. Swallows, T. H. Loftus, M. V. Romalis, B. R. Heckel, E. N. Fortson
Phys. Rev. Lett. 102, (2009)

22. Continued work on 199Hg
Still a factor of away from shot noise limit
Limited by light shift noise, magnetic shield noise
Need to find more precisely path of leakage currents
Practical cell fabrication issues
Steady improvement – factor of 3-5 improvement in ~3 years

23. Interpretation of nuclear EDM Limits
No atomic EDM due to EDM of the nucleus - Schiff’s Theorem
Electrons screen applied electric field
d(Hg) is due to finite nuclear size
nuclear Schiff moment S - Difference between mean square radius of the charge distribution and electric dipole moment distribution
Schiff moment induces parity mixing of atomic states, giving an atomic EDM:
RA - from atomic wavefunction calculations, uncertainty 50% E I
Recent work by Haxton, Flambaum on form of Schiff moment operator
B. P. Das et al,
V. Dzuba et al. 23

24. Interpretation of nuclear EDMs
gpNN p n
The Schiff moment is induced by CP nucleon-nucleon interaction:
Due to coherent interactions between the valence nucleon and the core
Large uncertainties due to collective effects
CP-odd pion exchange dominated by chromo-EDMs of quarks
Factor of 2 uncertainty in overall coefficient due to approximate cancellation
Other effects: nucleon EDMs, electron EDM, CP-violating nuclear-electron exchange NN N g R S p =
Engel, Flambaum g q ) ~ ( 1 d u
QCD NN R g - = p
Pospelov et al.
Sen’kov
Oshima
Flambaum 24

25. Jon Engel calculations for 199Hg(2010)
isovector

26. Octupole Enhancement I I Slab ~ e Z A2/3 b2 b32/DE b2 , b3 ~0.1 |+
+ = ((1+a)|+ +(1-a)|-)/2
- = ((1-a)|+ +(1+a)|-)/2
|+
+ = (|+ + |-)/2
- = (|+ - |-)/2
P, T DE I
|-
Sintr ~ eZAb2b3
Slab ~ e Z A2/3 b2 b32/DE
b2 , b3 ~0.1
Haxton & Henley; Auerbach, Flambaum & Spevak; Hayes, Friar & Engel; Dobaczewski & Engel
223Rn 223Ra 225Ra 223Fr 225Ac 229Pa 199Hg 129Xe
t1/ m d d 22 m d d
I 7/2 3/2 1/2 3/2 3/2 5/2 1/2 1/2
Deth (keV)
DEexp (keV)
105 S (efm3)
1028 dA (e cm)

27. EDM measurement with 225Ra
Transverse
cooling
Oven:
225Ra
Zeeman
Slower
Magneto-optical
trap
Optical
dipole trap
EDM
measurement
EDM measurement with 225Ra
Statistical uncertainty:
100 kV/cm
10 s
104
10%
10 days
dd = 3 x e cm
100 s
106
100 days
dd = 3 x e cm Phase II
225Ra / 199Hg enhance factor ~ 1,000
dd(199Hg) = 1.5 x e cm 27

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29. Limits on EDMs of fundamental particles
199Hg Atom EDM:
Neutron EDM:
Electron EDM: 27 e d – d
< 6 10 – e cm d u e ( d + . 5 d )+ 1 . 3 d – . 32 d
< 3 1 – 26 e cm d u d u m
d ~ m d
< 3 10 – 26 e e cm e m d
CMSSM
m1/2 = 250 GeV
m0 = 75 GeV
tanb = 10
New 199Hg
Limit
New limits on qm,qA
K.A. Olive, M. Pospelov, A. Ritz, and Y. Santoso, PRD 72, (2005)

30. More recent EDM Analysis
Electron, neutron and Hg limits provide complimentary constraints for some, but not all, possible CP-violating phases
Y. Li, S. Profumo, and M. Ramsey-Musolf,
JHEP08(2010)062

31. On to breaking more symmetries …
Started with P, C, T symmetries
Each symmetry violation came as a surprise
Parity violation  weak interactions
CP violation  Three generations of quarks
CPT symmetry is a unique signature of physics beyond quantum field theory.
Provides one of few possible ways to access Quantum Gravity effects experimentally.
In each case symmetry violations were found before corresponding particles could be produced directly

32. A theoretical framework for CPT and Lorentz violation
Introduce an effective field theory with explicit Lorentz violation
am,bm,cmn,dmn are vector fields in space with non-zero expectation value
Vector and tensor analogues to the scalar Higgs vacuum expectation value
Surprising bonus: incorporates CPT violation effects within field theory
Greenberg: Cannot have CPT violation without Lorentz violation (PRL 89, (2002)
CPT-violating interactions break Lorentz symmetry, give anisotropy signals
Can search for CPT violation without the use of anti-particles
In contrast, scalar properties of anti-particles (masses, magnetic moments) are likely to be the same L = – y ( m + a g b 5 ) i 2 n c mn d
a,b - CPT-odd
c,d - CPT-even
Fermions:
Alan Kostelecky
Although see arXiv:

33. Phenomenology of Lorentz/CPT violation
Modified dispersion relations: E2 = m2 + p2 + h p Jacobson
Amelino-Cameli
nm - preferred direction, k ~ h/Mpl
Applied to fermions: H = h m2/MPl S·n
Non-commutativity of space-time: [xm,xn] = qmn Witten, Schwartz
qmn - a tensor field in space, [q] = 1/E2
Interaction inside nucleus: NqmnsmnN  eijkqjkSi Pospelov,Carroll y k g = m 2 5 ) ( n L
Dimention-5 operator:
Myers, Pospelov, Sudarsky
Spin coupling to preferred direction ) )( ( ab mn q = F L

34. Experimental Signatures
Spin Lorentz violation
Spin coupling: S B × - = m ge A e 2 y g L L = – b m y g 5
2b · S
c.f.
CPT-violating interaction
Magnetic moment interaction
b is a (four-)vector field permeating all space
Experimental Signatures
Vector interaction gives a sidereal signal in the lab frame
Don’t need anti-particles to search for CPT violation
Need a co-magnetometer to distinguish from regular magnetic fields
Assume coupling is not in proportion to the magnetic moment bm
hn1= 2m1 B + 2b1 (b·nS)
hn2= 2m2 B + 2b2 (b·nS) ) ( 2 1 S h n b × ÷ ø ö ç è æ m - =
nS – direction of spin sensitivity in the lab

35. Turn most-sensitive atomic magnetometer into a co-magnetometer!
K-3He Co-magnetometer
Optically pump potassium atoms at high density ( /cm3)
2. 3He nuclear spins are polarized by spin-exchange collisions with K vapor
3. Polarized 3He creates a magnetic field felt by K atoms
4. Apply external magnetic field Bz to cancel field BK
K magnetometer operates near zero magnetic field
5. At zero field and high alkali density K-K spin-exchange relaxation is suppressed
6. Obtain high sensitivity of K to magnetic fields in spin-exchange relaxation free (SERF) regime
Turn most-sensitive atomic magnetometer into a co-magnetometer! B K = 8 p 3 k M He
J. C. Allred, R. N. Lyman, T. W. Kornack, and MVR, PRL 89, (2002)
I. K. Kominis, T. W. Kornack, J. C. Allred and MVR, Nature 422, 596 (2003)
T.W. Kornack and MVR, PRL 89, (2002)
T. W. Kornack, R. K. Ghosh and MVR, PRL 95, (2005)

36. Magnetic field self-compensation

37. Co-magnetometer Setup
Simple pump-probe arrangement
Measure Faraday rotation of far-detuned probe beam
Sensitive to spin coupling orthogonal to pump and probe
Details:
Ferrite inner-most shield
3 layers of m-metal
Cell and beams in mtorr vacuum
Polarization modulation of probe beam for polarimetry at 10-7rad/Hz1/2
Whole apparatus in vacuum at 1 Torr

38. Have we found Lorentz violation?
Rotating K-3He co-magnetometer
Rotate – stop – measure – rotate
Fast transient response crucial
Record signal as a function of magnetometer orientation
Have we found Lorentz violation?

39. Recording Sidereal Signal
Measure in North - South and East - West positions
Rotation-correlated signal found from several 180° reversals
Different systematic errors
Any sidereal signal would appear out of phase in the two signals

40. Long-term operation of the experiment
N-S signal riding on top of Earth rotation signal,
Sensitive to calibration
E-W signal is nominally zero
Sensitive to alignment
Fit to sine and cosine waves at the sidereal frequency
Two independent determinations of b components in the equatorial plane
20 days of non-stop running with minimal intervention

41. Final results Previous limit |bnxy| = (6.4 ± 5.4) 10-32 GeV
Anamolous magnetic field constrained:
bxHe-bxe = fT ± fTstat ± fTsys
byHe-bye = fT ± fTstat ± fTsys
Systematic error determined from scatter under various fitting and data selection procedures
Frequency resolution is 0.7 nHz
Anamalous electron couplings be are constrained at the level of fT by torsion pendulum experiments (B.R. Heckel et al, PRD 78, (2008).)
3He nuclear spin mostly comes from the neutron (87%) and some from proton (-5%) Friar et al, Phys. Rev. C 42, 2310 (1990) and V. Flambaum et al, Phys. Rev. D 80, (2009).
bxn = (0.1 ± 1.6)10-33 GeV
byn = (2.5 ± 1.6)10-33 GeV
|bnxy| < 3.7 10-33 GeV at 68% CL
J. M. Brown, S. J. Smullin,
T. W. Kornack, and M. V. R., Phys. Rev. Lett. 105, (2010)
Previous limit
|bnxy| = (6.4 ± 5.4) 10-32 GeV
D. Bear et al, PRL 85, 5038 (2000)

42. Improvement in spin anisotropy limits
199

43. Recent compilation of Lorentz-violation limits
Many new limits in last 10 years
10-33 GeV pl M m b 2 ~ h
m - fermion mass or SUSY breaking scale
Existing limits: h ~
1/Mpl effects are already quite excluded
Natural size for CPT violation ?
Fine-tuning ?
V.A. Kostelecky and N. Russell
arXiv: v4

44. Possible explanation for lack Lorentz violation
With Supersymmetry, dimension 3 and 4 Lorentz violating operators are not allowed
Higher dimension operators are allowed
Dimention-5 operators (e.g ) are CPT- violating, suppressed by MSUSY/MPlanck and are already quite constrained
If CPT is a good symmetry, then the dimention-6 operators are the lowest order allowed
Dimention-6 operators suppressed by (MSUSY/MPlank)2 ~ , still not significantly constrained, could be the lowest order at which Lorentz violation appears y h g = m 2 5 ) ( n L
Pospelov, Mattingly

45. CPT-even Lorentz violation= – y ( m + a g b 5 ) i 2 n c mn d
a,b - CPT-odd
c,d - CPT-even
Maximum attainable particle velocity
Implications for ultra-high energy cosmic rays, Cherenkov radiation, etc
Many laboratory limits (optical cavities, cold atoms, etc)
Models of Lorentz violation without breaking CPT:
Doubly-special relativity
Horava-Lifshitz gravity
Coleman and Glashow
Jacobson ) ˆ 1 ( 00 k j jk
MAX v c - =
Something special needs to happen when particle momentum reaches Plank scale!

46. Astrophysical Limits on Lorentz Violation
Spectrum of Ultra-high energy cosmic rays at Auger:
cp-cp < 6 ×10-23
Scully and Stecker
Synchrotron radiation in the Crab Nebula:
ce < 6 ×10-20
Brett Altschul
Spin limits can do better….!

47. Search for CPT-even Lorentz violation with nuclear spin
Need nuclei with orbital angular momentum and total spin >1/2
Quadrupole energy shift due to angular momentum of the valence nucleon:
Previously has been searched for in two experiments using 201Hg and 21Ne with sensitivity of about 0.5 mHz
Bounds on neutron cn<10-27 – already most stringent bound on c coefficient!
I,L pn
Suppressed by vEarth

48. 21Ne-Rb-K co-magnetometer
Replace 3He with 21Ne
A factor of 10 smaller gyromagnetic ratio of 21Ne gives the co-magnetometer 10 times better energy resolution for anomalous interactions
Use hybrid optical pumping KRb21Ne
Allows control of optical absorption of pump beam, operation with 10 times higher Rb density, lower 21Ne pressure.
Overcomes faster quadrupole spin relaxation of 21Ne
Eventually expect a factor of 100 gain in sensitivity over K-3He co-magnetometer
Overall, the experimental procedure is identical except the signal can be at either 1st or 2nd harmonic of Earth rotation rate

49. Search for CPT-even Lorentz violation with 21Ne-Rb-K co-magnetometer
About 2 month of data collection
Just completed preliminary analysis
Sensitivity is about a factor of 100 higher than previous experiments
Limited by systematic effects due to Earth rotation
N-S
E-W
Tensor frequency shift resolution
~ 4 nHz
Earth rotation signal is ~10 times larger in magnetic field units
Causes extra drift of N-S signal due to changes in sensitivity

50. Results of Tensor Lorentz-Violation Search
× 10-29
East-West
North-South
Comb.
cxx-cyy
0.86 ±1.1 ±0.56
3.6 ±2.8 ±1.6
1.2 ±1.1
cxx+cyy
0.14 ±1.1 ±0.56
0.57 ±2.8 ±1.6
0.19 ±1.1
cyz+czy
5.2 ±3.9 ±2.1
-4.2 ±15 ±18
4.8 ±4.3
cxz+czx
-4.1 ±2.2 ±2.4
17 ±14 ±13
-3.5 ±3.2
2 w
1 w
Constrain 4 out of 5 spatial tensor components of cmn at level
Improve previous limits by 2 to 3 orders of magnitude
Most stringent constrains on CPT-even Lorentz violation!
Assume Schmidt nucleon wavefunction – not a good approximation for 21Ne – need a better wavefunction
Assume kinetic energy of valence nucleon ~ 5 MeV

51. Recent compilation of Lorentz limits
10-33 GeV pl M m c 2 ~ h
m - SUSY breaking scale?
h >1 allowed for m =1 TeV
Natural size for CPT-even Lorentz violation ?
Need to get to
c ~
10-29 GeV
V.A. Kostelecky and N. Russell
arXiv: v4

52. Systematic errors
Most systematic errors are due to two preferred directions in the lab: gravity vector and Earth rotation vector
If the two vectors are aligned, rotation about that axis will eliminate most systematic errors
Amundsen-Scott South Pole Station
Within 100 meters of geographic South Pole
No need for sidereal fitting, direct measurement of Lorentz violation on 20 second time scale!

53. Conclusions
Precision atomic physics experiments have been playing an important role in searches for New Physics
Currently severely constrain CP violation beyond the Standard Model
Place stringent constraints on CPT and Lorentz violation at the Planck scale
Important constraints on spin-dependent forces, variation of fundamental constants, other ideas.