Transcript Power Point presentation

Instability of optical
speckle patterns in
cold atomic gases ?
S.E. Skipetrov
CNRS/Grenoble
http://lpm2c.grenoble.cnrs.fr/People/Skipetrov/
(Part of this work was done in collaboration with Roger Maynard)
Multiple scattering
Incident wave
Detector
Random medium
Multiple scattering
Incident wave
Detector
Random medium
Multiple scattering
Incident wave
Detector
l
l
Random medium
L
Multiple scattering in nonlinear media
Disorder
Nonlinear part of the dielectric constant
Main message of this talk:
This intensity is NOT the average intensity !
This is speckle !
Instability of speckle pattern :
Intuitive arguments
Weak nonlinearity: Self-phase modulation
… in a homogeneous medium
L
Laser beam
Intensity
Nonlinear medium
Deterministic nonlinear phase shift:
Weak nonlinearity: Self-phase modulation
… in a disordered medium
L
Laser beam
l
Intensity
Nonlinear medium
Path length
Random nonlinear phase shift :
Fluctuations of nonlinear phase shift
Average nonlinear phase shift :
Fluctuation of the nonlinear phase shift :
Fluctuations of nonlinear phase shift
Instability of speckle pattern
where
We define a bifurcation parameter
For
the multiple scattering speckle pattern should
become extremely sensitive to any perturbations and finally
UNSTABLE
Instability of speckle pattern :
Diagrammatic calculation
Scattered field
One has to sum contributions of all wave paths :
Scattered intensity
One has to sum contributions of all pairs of wave paths :
Short-range correlation
of intensity fluctuations
Long-range correlation
of intensity fluctuations
Langevin equation :
Random Langevin currents :
Correlation of Langevin currents :
If disorder is modified …
If
is modified by
,
will be modified by
Dynamic equation for
Random response function with correlation given by
Instability of speckle pattern :
Linear stability analysis
Linear stability analysis
Linear stability analysis
Bifurcation
parameter
Instability region
Time correlation of scattered field
Expected manifestation of instability
in experiment
Dashed lines:
Linear medium
Solid lines:
Nonlinear medium
Instability of speckle pattern :
Cloud of two-level atoms
Two-level atom
b
Life time of the upper level :
Transition linewidth :
a
Detuning factor :
Saturation intensity :
Saturation parameter :
“Cloud” of two-level atoms
Number of atoms per wavelength3 :
Mean free path at resonance
Value of
for
and for
and
:
:
Scattering and nonlinearity
in a cloud of atoms
Bifurcation parameter
Instability
threshold
Realistic parameters [Labeyrie et al. PRA 67, 033814 (2003)], Rb85 :
and
Bifurcation parameter
Instability
threshold
density  2
Realistic parameters [Labeyrie et al. PRA 67, 033814 (2003)], Rb85 :
Bifurcation parameter maximized over D
Instability
threshold
density  2
saturation parameter
Realistic parameters [Labeyrie et al. PRA 67, 033814 (2003)], Rb85 :
Bifurcation diagram
Instability region
saturation parameter
Realistic parameters [Labeyrie et al. PRA 67, 033814 (2003)], Rb85 :
Obvious experimental difficulties
• Instability can be masked by thermal motion of atoms
► Temperature of the atomic cloud should be lowered
• Speckle dynamics beyond the threshold is not known
with certainty
► One should ensure the absence of other possible
sources of decorrelation
• At too large intensities atoms will be accelerated by the
incident beam
► Instability threshold should be reached by increasing
the size L of the atomic cloud and not only the laser
intensity
Conclusions
• Nonlinear response of a disordered medium can render
the multiple-scattering speckle pattern unstable at
arbitrarily low laser intensities, provided the sample size
is large enough
• Cold atomic gases are possible candidates for observation of the instability phenomenon
• Full description of interaction of (powerful) laser light with
atomic gases requires self-consistent treatment accounting
for “scattering” of atoms on light potential
FIN