1. The QED Vacuum Magnetic Birefringence (BMV) Experiment
Laboratoire National Champs Magnétiques Intenses, Toulouse, France
M. Fouché, Agathe Cadène, Paul Berceau, Rémy Battesti, Carlo Rizzo

2. Magnetic Birefringencex y E
Epar B E
Eperp
Linear polarization
Linear polarization
Elliptic polarization
Induced magnetic birefringence :
Dn = ( n// – n┴ ) α B2
This effect exists in any medium

3. Vacuum Magnetic Birefringence
QED theory predicts that this effect also exists in vacuum
Due to the creation of virtual positron-electron pairs
 nonlinear interaction between electromagnetic fields
Calculated in the 70s :
At the lower orders in a
Fondamental constants : Codata 2010
O(a3)
Dn measurement to a few ppm 
Pure QED test
O(a4) ?
O(a5) ?
Z. Bialynicka-Birula and I. Bialynicki-Birula, Phys. Rev. D 2, 2.34 (1970)
V. I. Ritus, Sov.Phys. JETP 42, 774 (1975)

4. Experimental challenge
with
Extremely small
Not yet experimentally observed 
BMV project
Development of a very sensitive ellipsometer in order to be able to observe this fundamental prediction for the first time

5. The ellipsometer P A laser M1 l=1064 nm B M2 LB Iext It
P and A : polarisers crossed at maximum extinction
Ellipticity :
Key elements :
 Magnetic field : special magnets developed at LNCMI to have a B2LB as high as possible
 Fabry-Perot cavity : to increase the optical path in B
R. Battesti et al., EPJD 46, 323 (2008)

6. Pulsed transverse magnetic field
X coil geometry  high transverse magnetic field
Unconventional magnets developed at LNCMI
L = 25 cm
laser beam I B1 B2 B
laser
R. Battesti et al., EPJD 46, 323 (2008)

7. Pulsed transverse magnetic field
Time evolution:
Longitudinal profile:
B (T)
time (ms)
I = 8300 A
U = 4000 V
tpulse = 4 ms
B = 14.3 T
B²Lmag = 28 T²m
E = 100 kJ
= m
Pulses in vacuum:

8. Coil in its cryostat
External reinforcement to contain the magnetic pressure
Hole to let the laser in
12mm
Immersion in liquid nitrogen to avoid consequences of heating

9. The Fabry-Perot cavity
Lc= 2.27 m
Ellipticity :
1’’

10. The Fabry-Perot cavity
Finesse :
photon lifetime in the cavity (Lc = 2.27 m long) :
t = 1.08 ms
flight distance in the cavity = 325 km

11. Interferometers in the worldLc
3 km
6.4 m
4 km
2.27 m t
159 ms
442 ms
970 ms
1.08 ms
F = 50
70 000
230
Dn =
1 kHz
360 Hz
164 Hz
147 Hz a
p c τ Lc c
2LcF
One of the sharpest cavities of the world

12. BMV experimental setup
Pulsed transverse magnetic field B as high as possible
Increase of the path of light in the medium : Fabry-Perot cavity
high reflectivity mirrors
work in a clean room

13. Data acquisition Laser locked on the cavity TEM00 mode
Alignment of the cavity mirrors
TEM00 mode
Laser locked on the cavity
Data analysis
Shot

14. Data analysis Both signals It and Iext are used: for M1 B M2 P Iext A
Lmag B M2 M1
Both signals It and Iext are used:
Cavity static ellipticity
≈ 10-6
polarizers extinction ≈
Ellipticity to be measured, proportional to B²(t)
for

15. Data analysis Y(t) fitted by for with g = sign of G in T-2
takes into account the first order low pass filtering of the cavity
cutoff frequency: nc=1/4pt = 75 Hz
P. Berceau et al., Appl. Phys. B 100, 803 (2010)

16. Relative uncertainties
Results in N2
Magnetic birefringence of nitrogen vs pressure
3.1×10-2
2.2×10-2
9×10-4
< 5×10-4
4×10-2
2×10-2
3.5×10-2
3×10-4
type A
type B
Relative uncertainties
measurements
linear fit
1s confidence level
P. Berceau et al., Phys. Rev. A 85, (2012)
Group
PVLAS
Q&A
BMV

17. Results in vacuum at 3s confidence level Systematic effects
Pulses realized in same experimental conditions,
(rad)
at 3s confidence level
Systematic effects

18. Systematic effects Possible Cotton-Mouton effects:
kCM = (2.1  0.1) T-2 at 3s confidence level
Possible Cotton-Mouton effects:
Residual gaz :
P<10-7 mbar
Gaz analyser: most important contributions come from N2 and O2 
CM effect of cavity mirrors
Bmirror = 150 mT
No Cotton-Mouton systematic effect

19. New data acquisition procedure
Using symmetry properties of
 G>0, B parallel to Ox
 G>0, B antiparallel to Ox
4 new data series YGB
 G<0, B antiparallel to Ox
 G<0, B parallel to Ox
We then derive a more general expression for Y(t)
= function with a given symmetry
+ even parity
- odd parity
Cotton-mouton effect  S-+

20. New data acquisition procedure
Symmetry functions can be measured with a linear combination of functions Y
Allow to measure and to overcome systematic effects that might mimic the CM effect
A. Cadène et al., arXiv: (2013)
at 3s confidence level

21. Comparison
BFRT Collaboration: R. Cameron et al., Phys. Rev. D 47, 3707 (1993)
PVLAS, 2008: E. Zavattini et al., Phys. Rev. D 77, (2008)
PVLAS, 2012: G. Zavattini et al., Int. J. of Mod. Phys. A 27, (2012)
A. Cadène et al., arXiv: (2013)

22. Conclusion Status Future
Coupled high magnetic field and one the best Fabry-Perot cavities
Measurements performed on gases and in vacuum
Needed sensitivity improvement: almost 4 orders of magnitude
Future
Increase the transverse magnetic field : new XXL-coil
B2Lmag > 300 T2m
Improvement of the ellipticity sensitivity (Decrease of G2 and s2 (10-8))