Michael Romalis
Princeton University


Is the space truly isotropic?
D
E
Spin Up Spin Down

Remove magnetic field, other known spin interactions

Remove the Earth
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)


Introduce an effective field theory with explicit Lorentz violation
Fermions:
L = – i
2 y y
(
( m + a m g n + c mn g m g m
+ b m g
+ d mn
5 g g m
5
) y g m
)
+
 n y a , b CPT-odd c , d CPT-even
Alan Kostelecky
 a m
, b m
, c mn
, d mn 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: E 2 = m 2 + p 2 + h p 3
Effective Lagrangian:
L = y g
5 h
( n m
 m
)
2 y
Jacobson
Amelino-Cameli
Myers, Pospelov, Sudarsky
 n m
- preferred direction, h
~ 1/M pl

Applied to fermions: H = h m 2 / M
Pl
S
· n
Spin coupling to preferred direction

Non-commutativity of space-time: [x m
,x n
] = q mn
L =
( q mn
F mn )( F ab
F ab )
 q mn
- a tensor field in space, [ q] = 1/E 2

Interaction inside nucleus : N q mn s mn
N
 e ijk q jk
S i
Witten, Schwartz
Pospelov,Carroll

Alkali metal vapor in a glass cell
Magnetic Field y z
Linearly Polarized
Probe light
Cell contents
[K] ~ 10 14 cm -3
He buffer gas, N
2 quenching
Circularly Polarized
Pumping light x
Polarization angle rotation
 B y

3
1.
Optically pump potassium atoms at high density
(10 13 -10 14 /cm 3 )
2.
3 He nuclear spins are polarized by spin-exchange collisions with K vapor
3.
Polarized 3 He creates a magnetic field felt by K atoms 8 p
B
K
=
3 k
0
M
He
4.
Apply external magnetic field B z to cancel field B
K

K magnetometer operates near zero magnetic field
5.
At zero field and high alkali density K-K spin-
6.
exchange relaxation is suppressed
Obtain high sensitivity of K to magnetic fields in spin-exchange relaxation free (SERF) regime
Turn most-sensitive atomic magnetometer into a
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) co-magnetometer!

Best operating region

Sensitivity of ~1 fT/Hz 1/2 for both electron and nuclear interactions

Frequency uncertainty of 20 pHz/month 1/2 for 3 He
20 nHz/month 1/2 for electrons

Reverse co-magnetometer orientation every 20 sec to operate in the region of best sensitivity

3

Rotate – stop – measure – rotate

Fast transient response crucial

Record signal as a function of magnetometer orientation b eff =
 g
Have we found Lorentz violation?
S
=
P z g e
R
 y

 g
1 e
g
1 n




N-S signal riding on top of Earth rotation signal,

Sensitive to calibration
20 days of non-stop running with minimal intervention

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 b
X b
Y
= b
Y
EW
;
= b
X
EW
; b
Y b
X
= b
X
NS
= b
Y
NS
/ sin
/ sin


S
EW
S
NS =
= b
X
EW b
NS
X cos( 2 p t cos( 2 p t
-

)


)
 b
Y
EW b
Y
NS sin( 2 p t sin( 2 p t

)

C
EW

)

C
NS


Anamolous magnetic field constrained: b x
He
b x e = 0.001 fT ± 0.019 fT stat
± 0.010 fT sys b y
He
b y e = 0.032 fT ± 0.019 fT stat
± 0.010 fT sys
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 b e are constrained at the level of 0.002 fT by torsion pendulum experiments (B.R. Heckel et al , PRD 78 , 092006 (2008).)

3 He 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).
b x n = (0.1 ± 1.6)

10
-33
GeV b y n = (2.5 ± 1.6)

10
-33
GeV
| b n xy
| < 3.7

10
-33
GeV at 68% CL
|b n xy
Previous limit
| = (6 .
4 ± 5 .
4)

10
-
32 GeV
D. Bear et al , PRL 85 , 5038 (2000)

V.A. Kostelecky and N. Russell arXiv:0801.0287
v3
10
-33
GeV
Many new limits in last 10 years
Natural size for CPT violation ?
b ~ h m
2
M pl m - fermion mass or SUSY breaking scale
Existing limits: h
~ 10
-9 -
10
-12
1 /M pl effects are quite excluded
Need 10
-37
GeV for 1/M pl
2 effects

L = – i y y
(
( m + a m g n + c mn g m g m
+ b m g
+ d mn
5 g g
5 m
) y g m
)
2

Maximum attainable particle velocity
+
 n y v
MAX
= c
c
00
c
0 j v
j a , b CPT-odd c , d CPT-even
c jk v
j v
k
Coleman and Glashow
Jacobson

Implications for ultra-high energy cosmic rays, Cherenkov radiation, etc

Best limit c
00
~ 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
E
Q
~ ( c
11
 c
22
-
2 c
33
) p x
2  p
2 y
-
2 p z
2

Previosly has been searched for in two experiments using 201 Hg and 21 Ne with sensitivity of about 0.5 m
Hz

Bounds on neutron c n
~10
-27 coefficient!
– already most stringent bound on c
Suppressed by v
Earth


Replace 3 He with 21 Ne

A factor of 10 smaller gyromagnetic ratio of 21 Ne makes the co-magnetometer have 10 times better energy resolution for anomalous interactions

Use hybrid optical pumping K

Rb

21 Ne

Allows control of optical density for pump beam, operation with 10 15 /cm 3 Rb density, lower 21 Ne pressure.

Eventually expect a factor of 100 gain in sensitivity

Differences in physics:

Larger electron spin magnetization (higher density and larger k
0
)

Faster electric quadrupole spin relaxation of 21 Ne

Quadrupole energy shifts due to coherent wall interactions
Fast damping of transients Sensitivity already better than K3 He

21

Data not perfect, but already an order of magnitude more sensitive than previous experiments
N-S
E-W
A< 1 fT


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!


Monopole-Monopole:
V mm
= -
1 g g s
4 p s
2 e
mr r

Monopole-Dipole:
~


 q f 

 2
V md
= g s
1 g
2 p
8 p
M
2
( S
ˆ
2
 r
ˆ
)  m r
1 r
2

 e
mr

Dipole-Dipole:
~ q f
3
V dd
= g
1 p g
2 p
16 p
M
1
M
2



( S
ˆ
1
 r
ˆ
)( S
ˆ
2
 r
ˆ
)

 m
2 r

3 m
 r
2
3 r
3


-
( S
ˆ
1

S
ˆ
2
)

 r m
2

1 r
3




 e
mr
~
1 f
4
J. E. Moody and F. Wilczek, Phys. Rev. D 30 , 130 (1984)

Spin Source:
10 22 3 He spins at 20 atm.
Spin direction reversed every 3 sec with
Adiabatic Fast Passage b e b n =
0 .
05 aT

0 .
56 aT 
2 = 0.87
K3 He comagnetometer
Sensitivity:
0.7 fT/Hz 1/2
Uncertainty (1

) = 18 pHz or 4.3·10 -
35 GeV 3 He energy after 1 month
(smallest energy shift ever measured)


Constraints on pseudo-scalar coupling:
L
Der = g
2 m

( x ) g m g
5

( x )
 m 
( x ) L
Yuk = 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
Anomalous spin forces between neutrons are:
< 2

10
-8 of their magnetic interactions
< 2

10
-3 of their gravitational interactions
Limit from gravitational experiments for Yukawa coupling only (Adelberger et al )
G. Vasilakis, J. M. Brown, T. W.
Kornack, MVR, Phys. Rev.
Lett. 103 , 261801 (2009)
First constraints of subgravitational strength!


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 21 Ne is underway, limits maximum achievable velocity for neutrons (c n
-c)~10 -28

Can achieve frequency resolution as low as 20 pHz, path to sub-pHz sensitivity, search for 1/M
Pl
2 effects