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Fundamental Symmetry Tests

with Atoms

Michael RomalisPrinceton 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

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Atomic parity violationAtomic parity violation

Parity transformation:

i i r r

Electromagnetic forces in an atom conserve parity

[Hatomic, P]=0

Atomic stationary states are eigenstates of Parity

But weak interactions maximally violate Parity!

Tiny virtual contribution of Z-boson exchange can be measured!

Electromagnetic Weak

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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

Experimentalaccuracy on

PV amplitude EPV:

0.35%

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Relation to Standard Model ParametersRelation to Standard Model Parameters

Exchange of virtual Z0 boson: 5 1 1 ...2F

W u d

GH e e C u u C d d

Weak charge Qw Nuclear (neutron) distribution

)(8

)]sin41([ 52 r

GZNH F

WeW

WPVPV QkE

Best Atomic Calculation in Cs: 0.27% error - Derevianko (Reno, 2009)

Phys. Rev. Lett. 102, 181601 (2009)

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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

d = d II

t – t

I –I

d d

Time Reversal:

d –d 0

EDM T violation CP violation CPT theorem also implies violation of CP symmetry

Vector:

d 0 violation of time reversal symmetry

• Relativistic form of interaction:

Requires a complex phase

L = dE = – i2

d5F

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EDM Searches

QuarkEDM

ElectronEDM

QCD

NuclearTheory

AtomicTheory

Neutronn

DiamagneticAtoms

Hg, Xe, Rn

ParamagneticAtoms

Tl,Cs, Fr

QuarkChromo-EDM

MoleculesPbO, YbF, TlF

AtomicTheory

AtomicTheory

QCD

Fundamental Theory Supersymmetry, Strings

Nuclear Atomic Molecular

Hig

h E

nerg

yN

ucle

ar

The

ory

Experiments A

tom

ic

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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 em2 , 10 – 27 e cm =100 TeV

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Experimental Detection of an EDM

H = – B – dE

1 =2+ 2dE

h2 =

2 B 2dEh

1– 2 = 4dEh

Single atom with coherence time

N uncorrelated atoms measured for time T >> :

• Statistical Sensitivity:

B E

d 1

B E

d 1

• Measure spin-precession frequencies

= 1

d = h2E

1

2TN

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Search for EDM of the neutron

Historically, nEDM experiments eliminated many proposals for CP violation

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ILL neutron EDM Experiment

40 mHz

n, 199Hg

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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

Recent nEDM result

dBz/dz

dBz/dz

dn = 0.61.5(stat)0.8(syst) 10-26

ecm |dn| < 3.0 10-26 ecm (90% CL)

Factor of 2 improvementC.A. Baker et al

Phys. Rev. Lett. 97, 131801 (2006)

Rotating field causes

frequency shift

E and B0 into page

VV

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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

1m

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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

— Schiff shielding,

1963

Can be circumvented by magnetic interactions, extended nucleus

F = eE+B = 0, E 0 Enhanced in heavy atoms:

Strong spin-orbit magnetic interaction Large Nuclear Coulomb field Relativistic electrons near the nucleusdTl = – (585 ± 50) de

da de2Z 3

Cs: 114, Fr: 1150

E = 0

Sandars, 1965

Thallium:

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Berkeley Tl EDM ExperimentMixing chamber

Na detectors

Na detectors

590 nm laser beams

590 nm laser beams

RF 1

RF 2

Tl detectors

Light pipeTl detectors

photodiodes

Beam stop

Beam stop

Collimating slits

Collimating slits

E-field (120 kV/cm)

State Selector

Analyzer

378 nm laser beams

378 nm laser beams

B

Atomic beams

Na (~350 C)Tl (~700 C) Mixing chamber

Na (~350 C)Tl (~700 C)

1 m•Na atoms used as a co-magnetometer

70 Hz

de = (6.9 7.4)10-28 ecm

|de| < 1.610-27 ecm (90% C.L.)

B. Regan, E. Commins, C. Schmidt, D. DeMille, Phys. Rev. Lett. 88, 071805 (2002)

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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 cmOnly 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)

I199Hg EDM Experiment

Solid-state Quadrupled UV laser

High purity non-magnetic vessel Hg Vapor cells

100,000 hours of operation

Spin coherence time: 300 secElectrical Resistance: 21016

All materials tested with SQUID

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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

Larger signal due to cell improvements

Frequency uncertainty 0.1 nHz

1

2

3

4

inner cells

outercells

Magnetic Gradient Noise Cancellation

Leakage Current Diagnostic

S =

E

E

L =

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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

|d(199Hg)| < 3.1×10−29 e cm (95% C.L.)Factor of 7 improvement

New 199Hg EDM Result

W. C. Griffith, M. D. Swallows, T. H. Loftus,

M. V. Romalis, B. R. Heckel, E. N. Fortson

Phys. Rev. Lett. 102, 101601 (2009)

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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 TheoremElectrons 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%da = RA S

xrxxxdxS

ch

223

35

52

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Recent work by Haxton, Flambaum on form of Schiff moment operator

B. P. Das et al,V. Dzuba et al.

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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

Interpretation of nuclear EDMs

gNN

np

Engel, FlambaumNNN gRS

)~~

()1(duQCDNN ddRg

Pospelov et al.

g

q q

Sen’kovOshima

Flambaum

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Jon Engel calculations for 199Hg(2010)isovector

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Octupole EnhancementI

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|+

|

E

P, T

EA

E

V PT

3/13~

Sintr ~ eZA23 Slab ~ e Z A2/3 2 E

223Rn 223Ra 225Ra 223Fr 225Ac 229Pa 199Hg 129Xe

t1/2 23.2 m 11.4 d 14.9 d 22 m 10.0 d 1.5 d

I 7/2 3/2 1/2 3/2 3/2 5/2 1/2 1/2

eth (keV) 37 170 47 75 49 5

Eexp (keV) -- 50.2 55.2 160.5 40.1 0.22

105 S (efm3) 1000 400 300 500 900 12000 -1.4 1.75

1028 dA (e cm) 2000 2700 2100 2800 -5.6 0.8

2 , Haxton & Henley; Auerbach, Flambaum & Spevak; Hayes, Friar &

Engel; Dobaczewski & Engel

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EDM measurement with EDM measurement with 225225RaRaTransverse

cooling

Oven:225Ra

Zeeman Slower Magneto-optical

trap

Opticaldipole trap

EDMmeasurement

Statistical uncertainty:

100 kV/cm10 s 104

10%

10 days

d = 3 x 10-26 e cm

100 s 106

100 days

d = 3 x 10-28 e cm Phase II

• 225Ra / 199Hg enhance factor ~ 1,000

• d(199Hg) = 1.5 x 10-29 e cm

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• 199Hg Atom EDM:

• Neutron EDM:

• Electron EDM:

Limits on EDMs of fundamental particles

d e < 3 – 26 m em d

e cm

e(d d+0.5d u)+1.3d d –0.32d u <3 –26 e cm

e dd

– du

< 6 –27

e cm

d ~ m

New 199HgLimit

CMSSMm1/2 = 250 GeVm0 = 75 GeV

tan= 10

K.A. Olive, M. Pospelov, A. Ritz, and Y. Santoso, PRD 72, 075001 (2005)

New limits on ,A

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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

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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

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

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A theoretical framework for CPT and Lorentz violation

Introduce an effective field theory with explicit Lorentz violation

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)

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 = – (m + a + b5) +i2 ( + c + d5)

a,b - CPT-oddc,d - CPT-even

Fermions:Alan Kostelecky

Although see arXiv:1103.0168

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Modified dispersion relations: E2 = m2 + p2 + p3 Jacobson

Amelino-Cameli

n - preferred direction, ~ /Mpl

Applied to fermions: H = m2/MPl S·n

Non-commutativity of space-time: [x,x] = Witten, Schwartz

- a tensor field in space, [

Interaction inside nucleus: NNijkjkSi Pospelov,Carroll

Phenomenology of Lorentz/CPT violation

25 )(nL

))(( FFFL

Myers, Pospelov, Sudarsky

Spin coupling to preferred direction

Dimention-5 operator:

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Experimental Signatures

Spin coupling:

L = – b5 = – 2b ·S c.f.

Spin Lorentz violation

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

h1= 21 B + 21 (b·nS)

h2= 22 B + 22 (b·nS))(

2

2

2

1

1

2

2

1

1S

hnb

nS – direction of spin sensitivity in the lab

b is a (four-)vector field permeating all

space

CPT-violating interaction

Magnetic moment interaction

b

SBm

geAe

2

L

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K-3He Co-magnetometer1. 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

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!

BK = 83 0MHe

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)

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Magnetic field self-compensation

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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 -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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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

ne

yez

eff

R

PS

b

11

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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

NSNSY

NSX

NS

EWEWY

EWX

EW

CttS

CttS

)2sin()2cos(

)2sin()2cos(

20 days of non-stop running with minimal intervention

sin/;

sin/;NS

YYEWXY

NSXX

EWYX

bb

bb

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

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Final results Anamolous magnetic field constrained:

xHex

e = 0.001 fT ± 0.019 fTstat ± 0.010 fTsys

yHey

e = 0.032 fT ± 0.019 fTstat ± 0.010 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 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)10GeV

byn = (2.5 ± 1.6)10GeV

|bnxy| < 3.7 10GeV at 68% CL

Previous limit |bn

xy| = (6.4 ± 5.4) 1032 GeVD. Bear et al, PRL 85, 5038 (2000)

J. M. Brown, S. J. Smullin, T. W. Kornack, and M. V. R., Phys. Rev. Lett. 105, 151604 (2010)

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Improvement in spin anisotropy limits

199

IRecent compilation of Lorentz-violation limits

V.A. Kostelecky and N. Russell

arXiv:0801.0287v4

Many new limits in last 10 years

plM

mb

2~

m - fermion mass or SUSY breaking scale

Existing limits: ~ 10 10

1/Mpl effects are already quite excluded

Natural size for CPT violation ?

Fine-tuning ?

10 GeV

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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 ~10-31-10-33,

still not significantly constrained, could be the lowest order at which Lorentz violation appears

25 )(nL

Pospelov, Mattingly

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CPT-even Lorentz violation

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

L = – (m + a + b5) +i2 ( + c + d5)

a,b - CPT-oddc,d - CPT-even

)ˆˆˆ1( 000 kjjkjjMAX vvcvcccv Coleman and Glashow

Jacobson

Something special needs to happen when particle momentum reaches Plank scale!

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Astrophysical Limits on Lorentz Violation

Synchrotron radiation in the Crab Nebula:

ce < 6 ×10

Brett Altschul

Spectrum of Ultra-high energy cosmic rays at Auger:

c-cp < 6 ×10

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:

Previously has been searched for in two experiments using 201Hg and 21Ne with sensitivity of about 0.5 Hz

Bounds on neutron cn<10 – already most stringent bound on c coefficient!

222332211 2)2(~ zyxQ pppcccE

Suppressed by vEarth

I,L

pn02 222 zyx ppp

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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 KRb21Ne

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

ISearch 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

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Results of Tensor Lorentz-Violation Search

× 10-29 East-West North-South Comb.

cxxcyy

cxx+cyy

cyz+czy

cxz+czx

Constrain 4 out of 5 spatial tensor components of c at 10 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

V.A. Kostelecky and N. Russell

arXiv:0801.0287v4

10 GeV

plMm

c2

~m - SUSY breaking scale?

allowedfor m =1 TeV

Natural size for CPT-even Lorentz violation ?

2

Need to get to c ~ 10-3110-32

10 GeV

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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.