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Fundamental Symmetry Tests
with Atoms
Michael Romalis
Princeton University
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1. Atomic Parity Violation
2. Limits on CP violation from Electric Dipole Moments
3. Tests of CPT and Lorentz symmetries
Atomic parity violation
Parity transformation:
ri  ri
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!
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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%
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Relation to Standard Model Parameters
Exchange of virtual Z0 boson: HW 

HWe  [  N  Z (1  4 sin 2 W )]
Weak charge Qw


GF
e   5e C1u u  u  C1d d  d  ...
2
GF
 5  (r)
8
Nuclear (neutron) distribution
EPV  kPV QW
Best Atomic Calculation in Cs: 0.27% error - Derevianko (Reno, 2009)
Phys. Rev. Lett. 102, 181601 (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, 071601 (2009)
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Impact on Electroweak Physics
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T and CP violation by a permanent EDM
 Time Reversal:
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t–t
I  –I
dd
I
d  –d  0
d =dI
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d  0  violation of time reversal symmetry
 Vector:
 CPT theorem also implies violation of CP symmetry
EDM  T violation  CP violation
• Relativistic form of interaction:
L = d  E = – i d   5F 
2
Requires a complex phase
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EDM Searches
Nuclear
High Energy
Theory
Nuclear
Atomic
Neutron
n
Experiments
Molecular
Atomic
Diamagnetic
Atoms
Hg, Xe, Rn
Paramagnetic
Atoms
Tl,Cs, Fr
Molecules
PbO, YbF, TlF
Atomic
Theory
Atomic
Theory
Atomic
Theory
Nuclear
Theory
QCD
QCD
Quark
EDM
Quark
Chromo-EDM
Electron
EDM
Fundamental Theory  Supersymmetry, Strings
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 CPviolating phases that generally produce large EDMs.

Raw energy sensitivity:
d ~
em
, 10 – 27 e cm 
2

=100 TeV

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
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Experimental Detection of an EDM
• Measure spin-precession frequencies
B
E
d
w1
w1 =
B

2  B+ 2dE
h
E
H = –   B – d E

d
w1
 
w2 = 2 B 2dE
h
w1 – w2 = 4dE
h
• Statistical Sensitivity:
Single atom with coherence time t:
dw = t1
h
N uncorrelated atoms measured for time T >> t: d d =
1
2E 2tTN
Search for EDM of the neutron
 Historically, nEDM
experiments eliminated
many proposals for CP
violation
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ILL neutron EDM Experiment
n, 199Hg
40 mHz
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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
V
Rotating field
causes
frequency
shift
E and B0 into page
dBz/dz
dn = 0.61.5(stat)0.8(syst) 10-26 ecm
|dn| < 3.0  10-26 ecm (90% CL)
Factor of 2 improvement
dBz/dz
C.A. Baker et al
Phys. Rev. Lett. 97, 131801 (2006)
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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
1
m
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Electron EDM
 Electron has a finite charge, cannot be at rest in an electric field
 For purely electrostatic interactions
F = eE = 0
E = 0 — Schiff shielding, 1963
 Can be circumvented by magnetic interactions, extended nucleus
F = eE+B = 0, E  0
 Enhanced in heavy atoms:
3
2
d a  d e Z
 Strong spin-orbit magnetic interaction
 Large Nuclear Coulomb field
 Relativistic electrons near the nucleus
Thallium: d Tl = – (585 ± 50) d e
Sandars, 1965
Cs: 114,
Fr: 1150
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Berkeley Tl EDM Experiment
Tl (~700 C)
Tl detectors
Mixing chamber
Beam stop
Light pipe
photodiodes
Na (~350 C)
378 nm laser beams
70 Hz
Analyzer
Na detectors
590 nm laser beams
RF 2
Collimating slits
E-field
(120 kV/cm)
1m
Atomic beams
B
Collimating slits
RF 1
590 nm laser beams
• 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.)
Na detectors
State Selector
Tl detectors
378 nm laser beams
Beam stop
Tl (~700 C)
Mixing
chamber
Na (~350 C)
B. Regan, E. Commins, C. Schmidt,
D. DeMille, Phys. Rev. Lett. 88,
071805 (2002)
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)
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199Hg
EDM Experiment
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: 300 sec
Electrical Resistance: 21016 W
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Recent improvements in 199Hg Experiment
 Use four 199Hg cells instead of two to
reduce magnetic field noise and have
better systematic checks
inner
cells
w1
w2
w3
E
E
outer
cells
w4
 Magnetic Gradient Noise Cancellation
S = w2  w3  1/3 w1  w4
 Leakage Current Diagnostic
L = w2  w3  w1  w4
 Larger signal due to cell improvements
 Frequency uncertainty 0.1 nHz
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New
199Hg
EDM Result
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 About 1 year of data
 Changed all components of the system:
 d(199Hg) = (0.49±1.29stat±0.76syst)×10−29 e cm
W. C. Griffith, M. D.
199
−29
|d( Hg)| < 3.1×10 e cm (95% C.L.) Swallows, T. H. Loftus,
M. V. Romalis, B. R.
Factor of 7 improvement
Heckel, E. N. Fortson
Phys. Rev. Lett. 102,
101601 (2009)
Continued work on
199Hg
 Still a factor of 10-20 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
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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
 2
 x 2 x  5 r 2
3


S
dx

x


5
3


x
ch 

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E
Recent work by Haxton, Flambaum on form of Schiff moment operator
Schiff moment induces parity mixing of atomic states, giving an
atomic EDM:
da = RA S
RA - from atomic wavefunction calculations, uncertainty 50%
B. P. Das et al,
V. Dzuba et al.
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Interpretation of nuclear EDMs
 The Schiff moment is induced by CP nucleon-nucleon
interaction:

 Due to coherent interactions between the valence nucleon and
the core
S  RN gNN
 Large uncertainties due to collective effects
gNN
n
p
Engel, Flambaum
 CP-odd pion exchange dominated by chromo-EDMs of
quarks
g
 Factor of 2 uncertainty in overall coefficient due to approximate
cancellation
q
(1)
gNN
~ ~
 RQCD ( du  dd )
 Other effects: nucleon EDMs, electron EDM, CPviolating nuclear-electron exchange
q
Pospelov et al.
Sen’kov
Oshima
Flambaum
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Jon Engel calculations for 199Hg(2010)
isovector
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Octupole Enhancement
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  1| 1|/2
|+
DE
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  |  |/2
P, T
  |  |/2
  1| 1|/2

|
  V PT  
Slab ~ e Z A2/3 2 32/DE
Sintr ~ eZA23
DE
~
 3 A1 / 3
DE
2 , 3 ~0.1
Haxton & Henley; Auerbach, Flambaum & Spevak; Hayes, Friar &
Engel; Dobaczewski & Engel
223Rn
t1/2
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Deth (keV)
DEexp (keV)
105 S (efm3)
1028 dA (e cm)
23.2 m
7/2
37
-1000
2000
223Ra
11.4 d
3/2
170
50.2
400
2700
225Ra
14.9 d
1/2
47
55.2
300
2100
223Fr
22 m
3/2
75
160.5
500
2800
225Ac
10.0 d
3/2
49
40.1
900
229Pa
1.5 d
5/2
5
0.22
12000
199Hg
129Xe
1/2
1/2
-1.4
-5.6
1.75
0.8
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Oven:
225Ra
EDM measurement with
225Ra
Transverse
cooling
Zeeman
Slower
Statistical uncertainty:
Magneto-optical
trap
100
days
10 days
100 kV/cm
100
10 s
1064
10%
-26 e cm Phase II
dd = 3 x 10-28
• 225Ra / 199Hg enhance factor ~ 1,000
• dd(199Hg) = 1.5 x 10-29 e cm
EDM
measurement
Optical
dipole trap
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Limits on EDMs of fundamental particles
EDM: e d – d < 610 – 27 e cm
d
u
• Neutron EDM:
e(d d +0.5d u)+1.3d d –0.32d u <310 –26 e cm
• Electron EDM: d e < 3 10 – 26 m e e cm
d~m
md
•
199Hg Atom
New 199Hg
Limit
CMSSM
m1/2 = 250 GeV
m0 = 75 GeV
tan = 10
New limits
on ,A
K.A. Olive, M. Pospelov, A. Ritz, and Y. Santoso, PRD 72, 075001 (2005)
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More recent EDM Analysis
 Electron, neutron and
Hg limits provide
complimentary
constraints for some, but
not all, possible CPviolating phases
Y. Li, S. Profumo, and M.
Ramsey-Musolf,
JHEP08(2010)062
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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
In each case symmetry violations were found before corresponding
particles could be produced directly
 CPT symmetry is a unique signature of physics beyond quantum
field theory.
 Provides one of few possible ways to access Quantum Gravity
effects experimentally.
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A theoretical framework for CPT and Lorentz violation
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 Introduce an effective field theory with explicit Lorentz violation
Fermions:

 
–




=
(m
+
a
+
b
) +


5
L
i 

  



+ d 5 )
2 (  + c
a,b - CPT-odd
c,d - CPT-even
Alan Kostelecky
 a,b,c,d 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,
231602 (2002)
Although see arXiv:1103.0168
 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
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Phenomenology of Lorentz/CPT violation
 Modified dispersion relations: E2 = m2 + p2 + h p3 Jacobson
Amelino-Cameli

2
Dimention-5 operator: L   5k (n  ) 
Myers, Pospelov, Sudarsky
n - preferred direction, k ~ h/Mpl
Applied to fermions: H = h m2/MPl S·n
 Non-commutativity of space-time: [x,x] = 
L  (F)(F F)
Spin coupling
to preferred
direction
Witten, Schwartz
 - a tensor field in space, []  1/E2
 Interaction inside nucleus: NN  eijkjkSi
Pospelov,Carroll
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Spin Lorentz violation
 Spin coupling:
L = – b  5  = – 2b ·S c.f.
CPT-violating
interaction
Experimental Signatures
L  e    A  
ge
B S
2m
Magnetic moment
interaction
b is a (four-)vector
field permeating all
space
 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
h1= 21 B + 21 (b·nS)
h2= 22 B + 22 (b·nS)
1 2 2  1 2 

   (b  n S )
1 2 h  1 2 
nS – direction of spin sensitivity in the lab
b
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K-3He Co-magnetometer
1. Optically pump potassium atoms at high density
(1013-1014/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
8
B K = 3 k 0 M He
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 spinexchange 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!
J. C. Allred, R. N. Lyman, T. W. Kornack, and
MVR, PRL 89, 130801 (2002)
I. K. Kominis, T. W. Kornack, J. C. Allred and
MVR, Nature 422, 596 (2003)
T.W. Kornack and MVR, PRL 89, 253002
(2002)
T. W. Kornack, R. K. Ghosh and MVR, PRL
95, 230801 (2005)
Magnetic field self-compensation
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Co-magnetometer Setup
 Simple pump-probe arrangement
 Measure Faraday rotation of fardetuned probe beam
 Sensitive to spin coupling
orthogonal to pump and probe
 Details:
 Ferrite inner-most shield
 3 layers of -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
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Rotating
K-3He
 Rotate – stop – measure – rotate
 Fast transient response crucial
 Record signal as a function of
magnetometer orientation
W
b eff 

Have we found Lorentz violation?
Pz eW y  1 1 
  
S
R e n 
co-magnetometer
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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
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Long-term operation of the experiment
 N-S signal riding on top of Earth
rotation signal,
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20 days of non-stop running with
minimal intervention
 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
bX    YEW ; bX    XNS / sin 
S EW   XEW cos(2t   )  YEW sin(2t   )  C EW
bY   XEW ; bY    YNS / sin 
S NS   XNS cos(2t   )  YNS sin(2t   )  C NS
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Final results

Anamolous magnetic field constrained:
xHexe = 0.001 fT ± 0.019 fTstat ± 0.010 fTsys
yHeye = 0.032 fT ± 0.019 fTstat ± 0.010 fTsys
J. M. Brown, S. J. Smullin,
T. W. Kornack, and M. V. R.,
Phys. Rev. Lett. 105, 151604
(2010)

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 0.002 fT by torsion
pendulum experiments (B.R. Heckel et al, PRD 78, 092006 (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, 105021 (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
Previous limit
|bnxy| = (6.4 ± 5.4) 1032 GeV
D. Bear et al, PRL 85, 5038 (2000)
199
Improvement in spin anisotropy limits
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Recent compilation of Lorentz-violation limits
1033 GeV
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Many new limits
in last 10 years
Natural size for CPT
violation ?
m2
b ~h
M pl
m - fermion
mass or SUSY
breaking scale
Existing limits:
h ~ 109  1012
1/Mpl effects are
already quite excluded
V.A. Kostelecky
and N. Russell
arXiv:0801.0287
v4
Fine-tuning ?
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.L    5h (n  )2  ) are CPTviolating, 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 ~10-31-10-33,
still not significantly constrained, could be the lowest order at
which Lorentz violation appears
Pospelov, Mattingly
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CPT-even Lorentz violation
L = –  (m + a   + b  5  ) +

i 


 + d 5  )  
2 (  + c
 Maximum attainable particle velocity
vMAX  c(1  c00 c0 j vˆj  c jk vˆj vˆk
a,b - CPT-odd
c,d - CPT-even
Coleman and Glashow
Jacobson
)
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
Something special needs to happen when particle
momentum reaches Plank scale!
Astrophysical Limits on Lorentz Violation
Synchrotron radiation in the
Crab Nebula:
ce < 6 ×1020
Brett Altschul
Spectrum of Ultra-high energy
cosmic rays at Auger:
c-cp < 6 ×1023
Scully and Stecker
Spin limits can do better….!
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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:
EQ ~ (c11  c22  2c33 ) p x2  p y2  2 p z2
I,L
px2  py2  2 pz2  0
pn
 Previously has been searched for in two experiments using 201Hg and 21Ne with
sensitivity of about 0.5 Hz
 Bounds on neutron cn<1027 – already most stringent bound on c coefficient!
Suppressed by vEarth
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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 comagnetometer
 Overall, the experimental procedure is identical except the signal can
be at either 1st or 2nd harmonic of Earth rotation rate
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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
Tensor frequency
shift resolution
~ 4 nHz
E-W
Earth rotation signal
is ~10 times larger in
magnetic field units
N-S
Causes extra drift of
N-S signal due to
changes in sensitivity
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Results of Tensor Lorentz-Violation Search
× 10-29
2w
1w
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
 Constrain 4 out of 5 spatial tensor components of
c at 1029 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
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Recent compilation of Lorentz limits
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1033 GeV
Natural size for CPT-even
Lorentz violation ?
1029
GeV
m2
c ~h
M pl2
m - SUSY
breaking scale?
h 1 allowed for m =1 TeV
V.A. Kostelecky
and N. Russell
arXiv:0801.0287
v4
Need to get to
c ~ 10-3110-32
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!
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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.
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