Transcript transparencies - Rencontres de Moriond

New limits on spin-dependent Lorentz- and
CPT-violating interactions
Michael Romalis
Princeton University
Experimentalist’s Motivation
 Is the space truly isotropic?
DE
Spin Up
Spin Down
Remove magnetic field, other known spin interactions
Remove the Earth
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!
 Well, we are actually moving relative to CMB rest frame
v = 369 km/sec ~ 10-3 c
 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
Fermions:
m
m y
–
y
g
g
g
=
(m
+
a
+
b
) +
m
m
5
L
iy g
m
m  ny
g
g
g
+ dmn 5 )
2 ( n + cmn
a,b - CPT-odd
c,d - CPT-even
Alan Kostelecky
 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,
231602 (2002)
Although see arXiv:1103.0168v1
 CPT-violating interactions break Lorentz symmetry, give anisotropy signals
 Can search for CPT violation without the use of anti-particles
Phenomenology of Lorentz/CPT violation
 Modified dispersion relations: E2 = m2 + p2 + h p3 Jacobson
Amelino-Cameli
m
Effective Lagrangian: L = yg h (nm  )2 y
5
Myers, Pospelov, Sudarsky
nm - preferred direction, h ~ 1/Mpl
Applied to fermions: H = h m2/MPl S·n
 Non-commutativity of space-time: [xm,xn] = qmn
L = (qmnFmn)(F abFab)
Spin coupling
to preferred
direction
Witten, Schwartz
qmn - a tensor field in space, [q] = 1/E2
 Interaction inside nucleus: NqmnsmnN  eijkqjkSi
Pospelov,Carroll
Summary of SERF Atomic Magnetometer
Alkali metal vapor in a glass cell
Magnetic Field
Linearly Polarized
Probe light
z
y
Cell contents
[K] ~ 1014 cm-3
He buffer gas, N2 quenching
x
Magnetization
Circularly Polarized
Pumping light
Polarization angle rotation
 By
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
8p
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
Magnetic field sensitivity
Best operating region
 Sensitivity of ~1 fT/Hz1/2 for both electron and nuclear interactions
Frequency 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
Rotating K-3He co-magnetometer
 Rotate – stop – measure – rotate
 Fast transient response crucial
 Record signal as a function of
magnetometer orientation

b eff =
g
Have we found Lorentz violation?
Pzg e y  1 1 
 - 
S=
R ge gn 
Long-term operation of the experiment
 N-S signal riding on top of Earth
rotation signal,
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 = - b YEW ; bX = - b XNS / sin 
S EW = b XEW cos(2pt -  )  bYEW sin(2pt -  )  C EW
bY = b XEW ; bY = - b YNS / sin 
S NS = b XNS cos(2pt -  )  bYNS sin(2pt -  )  C NS
Final results

Anamolous magnetic field constrained:
bxHe-bxe = 0.001 fT ± 0.019 fTstat ± 0.010 fTsys
byHe-bye = 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)
Improvement in spin anisotropy limits
Recent compilation of CPT limits
10-33 GeV
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 quite
excluded
V.A. Kostelecky
and N. Russell
arXiv:0801.0287
v3
Need 10-37GeV
for 1/Mpl2 effects
CPT-even Lorentz violation
L = – y (m + a mg m + bm g 5 g m)y +
n
iy g
m
m
g + dmn g5 g )  y
2 ( n + cmn
 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
 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
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
EQ ~ (c11  c22 - 2c33 ) p x2  p y2 - 2 p z2
 Previosly 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!
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 KRb21Ne
 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 k0)
 Faster electric quadrupole spin relaxation of 21Ne
 Quadrupole energy shifts due to coherent wall interactions
Fast damping of transients
Sensitivity already better than K-3He
21Ne
Semi-sidereal Fits
 Data not perfect, but already an order of magnitude more sensitive
than previous experiments
N-S
A< 1 fT
E-W
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:
Vmm
q 
g 1s g s2 e - mr
=~  
4p r
f
2
 Monopole-Dipole:
Vmd =
q
m 1 
(Sˆ2  rˆ)  2 e-mr ~ 3
8p M 2
f
r r 
g1s g 2p
 Dipole-Dipole:
2
 ˆ

m
3m 3  ˆ ˆ  m 1   - mr
1
ˆ
ˆ
ˆ
Vdd =
(
S

r
)(
S

r
)


(
S

S
)

e
~
 1
2
1
2  2

2
3
3 
16pM 1M 2 
r
r
r
r
r
f4




g 1p g 2p
J. E. Moody and F. Wilczek, Phys. Rev. D 30, 130 (1984)
Search for nuclear spin-dependent forces
Spin Source:
1022 3He spins at 20 atm.
Spin direction reversed
every 3 sec with
Adiabatic Fast Passage
be - bn = 0.05aT  0.56aT
2= 0.87
K-3He comagnetometer
Sensitivity:
0.7 fT/Hz1/2
Uncertainty (1) = 18 pHz or 4.3·10-35 GeV 3He energy after 1 month
(smallest energy shift ever measured)
New limits on neutron spin-dependent forces
 Constraints on pseudo-scalar coupling:
LDer =
g
 ( x )g mg 5 ( x ) m ( x )
2m
LYuk = -ig( x)g 5( x)( x)
Limit on proton nuclear-spin
dependent forces (Ramsey)
Recent limit from
Walsworth et al
PRL 101, 261801 (2008)
Present work
Limit from gravitational
experiments for Yukawa
coupling only (Adelberger et al)
G. Vasilakis, J. M. Brown, T. W.
Kornack, MVR, Phys. Rev.
Anomalous spin forces between neutrons are:
< 210-8 of their magnetic interactions
< 210-3 of their gravitational interactions
Lett. 103, 261801 (2009)
First constraints of subgravitational strength!
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/MPl2 effects