Phase Coherence of Elongated Bose-Einstein Condensates

1
The QEDVacuum Magnetic Birefringence
(BMV)Experiment
Laboratoire National Champs Magnétiques Intenses,
Toulouse, France M. Fouché, Agathe Cadène,
Paul Berceau, Rémy Battesti, Carlo Rizzo
2
Magnetic Birefringence
Epar
Eperp
Linear polarization
Linear polarization
Elliptic polarization
Induced magnetic birefringence Dn ( n// n-
) a 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

• 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
laser l1064 nm
M1
B
M2
P
LB
Iext
A
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
R. Battesti et al., EPJD 46, 323 (2008)
7
Pulsed transverse magnetic field

• Time evolution

• Longitudinal profile

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

• Ellipticity

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

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Interferometers in the world

Lc 3 km 6.4 m 4 km 2.27 m
t 159 ms 442 ms 970 ms 1.08 ms
F 50 70 000 230 450 000
Dn 1 kHz 360 Hz 164 Hz 147 Hz
a
p c t
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

13
Data acquisition
14
Data analysis

• Both signals It and Iext are used

Cavity static ellipticity 10-6
polarizers extinction 4.10-7
Ellipticity to be measured, proportional to B²(t)
for
15
Data analysis
for
with g sign of G
takes into account the first order low pass
filtering of the cavity cutoff frequency
nc1/4pt 75 Hz
P. Berceau et al., Appl. Phys. B 100, 803 (2010)
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Results in N2

• Magnetic birefringence of nitrogen vs pressure

P. Berceau et al., Phys. Rev. A 85, 013837 (2012)
Group
PVLAS
QA
BMV
17
Results in vacuum
Pulses realized in same experimental conditions,
(rad)
at 3s confidence level Systematic effects
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Systematic effects
kCM (2.1 ? 0.1) 10-19 T-2 at 3s confidence level

• Possible Cotton-Mouton effects
• Residual gaz
• Plt10-7 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

? Ggt0, B parallel to Ox
? Ggt0, B antiparallel to Ox
4 new data series YGB
? Glt0, B antiparallel to Ox
? Glt0, 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., arXiv1302.5389 (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, 032006 (2008) PVLAS,
2012 G. Zavattini et al., Int. J. of Mod. Phys.
A 27, 1260017 (2012)
A. Cadène et al., arXiv1302.5389 (2013)
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Conclusion

• Status

• 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 gt 300 T2m

• Improvement of the ellipticity sensitivity
  (Decrease of G2 and s2 (10-8))