New limits on spin-dependent Lorentz- and

CPT-violating interactions

Michael Romalis

Princeton University

Experimentalist’s Motivation Is the space truly isotropic?

Remove magnetic field, other known spin interactionsRemove the Earth

E

Spin Up Spin Down

Is there still an “Up” and a “Down” ?

First experimentally addressed by Hughes, Drever (1960)

V.W. Hughes et al, PRL 4, 342 (1960)R. W. P. Drever, Phil. Mag 5, 409 (1960); 6, 683(1961)

Is the space really isotropic? –ask astrophysicists

Cosmic Microwave Background Radiation Map

The universe appears warmer on one side!

v = 369 km/sec ~ 10 c

Well, we are actually moving relative to CMB rest frame

Space and time vector components mix by Lorentz transformation A test of spatial isotropy becomes a true test of Lorentz invariance

(i.e. equivalence of space and time)

A theoretical framework for 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

L = – (m + a + b5) +i2 ( + c + d5)

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

Fermions:Alan Kostelecky

Although see arXiv:1103.0168v1

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

Amelino-Cameli

n - preferred direction, ~ 1/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

Effective Lagrangian:

Summary of SERF Atomic Magnetometer

Alkali metal vapor in a glass cell

MagnetizationMagnetization

Magnetic Field

Linearly Polarized Probe light

Circularly Polarized Pumping light

Polarization angle rotation

By x

z

y

Cell contents[K] ~ 1014 cm-3

He buffer gas, N2 quenching

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)

Magnetic field self-compensation

Magnetic field sensitivity

Sensitivity of ~1 fT/Hz1/2 for both electron and nuclear interactionsFrequency uncertainty of 20 pHz/month1/2 for 3He

20 nHz/month1/2 for electrons Reverse co-magnetometer orientation every 20 sec to operate in the region of best sensitivity

Best operating region

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

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

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)

Improvement in spin anisotropy limits

Recent compilation of CPT limits

V.A. Kostelecky and N. Russell

arXiv:0801.0287v3

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 quite excluded

Natural size for CPT violation ?

Need 10GeV for 1/Mpl

2 effects

10 GeV

CPT-even Lorentz violation

Maximum attainable particle velocity

Implications for ultra-high energy cosmic rays, Cherenkov radiation, etc Best limit c00 ~ 10-23 from Auger ultra-high energy cosmic rays

Many laboratory limits (optical cavities, cold atoms, etc)

Motivation for 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!

Search for CPT-even Lorentz violation with nuclear spin

Need nuclei with orbital angular momentum and total spin >1/2 Quadrupole energy shift proportional to the kinetic energy of the

valence nucleon

Previosly 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

First results with Ne-Rb-K co-magnetometer Replace 3He with 21Ne

A factor of 10 smaller gyromagnetic ratio of 21Ne makes the co-magnetometer have 10 times better energy resolution for anomalous interactions

Use hybrid optical pumping KRb21Ne Allows control of optical density for pump beam, operation with 1015/cm3 Rb density,

lower 21Ne pressure.

Eventually expect a factor of 100 gain in sensitivity Differences in physics:

Larger electron spin magnetization (higher density and larger 0)

Faster electric quadrupole spin relaxation of 21Ne Quadrupole energy shifts due to coherent wall interactions

Sensitivity already better than K-3HeFast damping of transients

21Ne Semi-sidereal Fits Data not perfect, but already an order of magnitude more sensitive

than previous experiments

N-S

E-W

A< 1 fT

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!

Classic axion-mediated forces

Monopole-Monopole:

Monopole-Dipole:

Dipole-Dipole:

221

~4

fr

eggV

mrss

mm

3222

21

~1

)ˆˆ(8 f

err

mrS

M

ggV mrps

md

4322132

2

2121

211

~1

)ˆˆ(33

)ˆˆ)(ˆˆ(16 f

err

mSS

rr

m

r

mrSrS

MM

ggV mrpp

dd

J. E. Moody and F. Wilczek, Phys. Rev. D 30, 130 (1984)

Uncertainty (1) = 18 pHz or 4.3·1035 GeV 3He energy after 1 month (smallest energy shift ever measured)

2= 0.87aTaTbb ne 56.005.0

K-3He co-magnetometer

Sensitivity: 0.7 fT/Hz1/2

Search for nuclear spin-dependent forces

Spin Source: 1022 3He spins at 20 atm.

Spin direction reversed every 3 sec with Adiabatic Fast Passage

New limits on neutron spin-dependent forces

Constraints on pseudo-scalar coupling:

Anomalous spin forces between neutrons are:< 210 of their magnetic interactions< 210 of their gravitational interactions

Present workLimit from gravitational experiments for Yukawa coupling only (Adelberger et al)

)()()(2 5 xxx

m

gLDer

)()()( 5 xxxigLYuk

Limit on proton nuclear-spin dependent forces (Ramsey)

First constraints of sub-gravitational strength!

Recent limit from Walsworth et alPRL 101, 261801 (2008)

G. Vasilakis, J. M. Brown, T. W. Kornack, MVR, Phys. Rev. Lett. 103, 261801 (2009)

Conclusions Set new limit on Lorentz and CPT violation for neutrons at

3×10-33 GeV, improved by a factor of 30

Highest energy resolution among Lorentz-violating experiments

Search for anomalous spin-dependent forces between neutrons with energy resolution of 4×10-35 GeV, first constrain on spin forces of sub-gravitational strength

Search for CPT-even Lorentz violation with 21Ne is underway, limits maximum achievable velocity for neutrons (cn-c)~10-28

Can achieve frequency resolution as low as 20 pHz, path to sub-pHz sensitivity, search for 1/MPl

2 effects