The coherent backscattering spectrum

1
The coherent backscattering spectrum of two atoms
Vyacheslav Shatokhin (Stepanov Institute of
Physics, Minsk, Belarus) Thomas Wellens
(University of Erlangen-Nürnberg,
Germany) Benoît Grémaud (LKB, Paris,
France) Andreas Buchleitner (MPI-PKS, Dresden,
Germany)
CEWQO 2007, Palermo
2
Outline

• Coherent backscattering (CBS) of light
• CBS from cold atoms
• Single-atom resonance fluorescence
• Toy model of CBS
• CBS enhancement factor
• The CBS spectrum
• Outlook
• Conclusion

3
Coherent Backscattering (CBS) of light

• Enhancement factor
• (measure of phase coherence)

4
CBS of light from cold atoms
Experiments since 1999 Institut Non Linéaire
(Nice, France) Old Dominion University
(Norfolk, USA)
Why cold atoms? (large cross-sections, negligible
inhomogeneous broadening (due to motion),
atom-photon interactions are very well
understood)
Motivation observation of strong localization
random lasers
Problem dephasing mechanisms spoil interference
5
Dephasing mechanisms

• Residual thermal motion
• Raman scattering
• This talk
• nonlinear inelastic scattering

v
k
??D(k-k)v is kept ltlt??
k
6
Single-atom resonance fluorescence
Powerful laser field W-dgeE/
? (?L -?ge) ?? ?ge
P.A. Apanasevich, Opt. Spektr. (1964) B.R.
Mollow, PR 188, 1969 (1969)
C. Cohen-Tannoudji and S. Reynaud, J. Phys. B 10,
345 (1977)
Incoherent (inelastic)
d(w-wL) coherent (elastic)
7
Saturation and interference
- saturation parameter
Saturation regime sgtgt1

• Interference with reference
• laser ? 0
• Youngs double-slit experiment
• from 2 independent atoms
• interference ? 0

8
Saturation effect in CBS
88Sr experiment (Nice) ? shrinks vs. s T.
Chanelière et al. PRE 70, 036602 (2004)
Optical thickness b3.5 (double
scattering) Jg0?Je1 transition
CBS enh. factor ?
m0
m1
m-1
m0
Saturation parameter s
h II h channel
9
Toy model of CBS

• Hamiltonian

2 ?
HHAHFHAFHAL
Laser

• Two atoms (random r1 and r2)

CBS
2 ?
photonic bath

• one exchanged photon due to far
• field dipole-dipole interaction

• Hamiltonian ? master equation

(Lehmberg,1970)

• Configuration averaging

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Coherent inelastic backscattering
Moderate s linear decrease of ? in qualitative
agreement with the Sr experiment Physical
reason partial distinguishability of the
interfering amplitudes T.Wellens et al. PRA 70,
023817 (2004)
2-s/4
Large s

• due to the residual
  self-interference of inelastically scattered
  photons!
• V.S. , C.A. Müller, A. Buchleitner, PRL 94,
  043603 (2005)

11
The coherent backscattering spectrum
??????
?????
???

• Seven CBS resonances
• Constructive or destructive interference !

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Dressed state analysis
?L? ?L??? ?L??
pump
probe
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Re-scattering of the low-frequency sideband
Laser-driven transition
CBS transition
?L?
?L??? ?L ???, ?L
?L-?
?L
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Re-scattering of the Mollow triplet
Laser-driven transition
CBS transition
?L??? ?L ???, ?L,
?L, ?L??, ?L??,
?L ??? ?L? ?L???,
?L-?
?L
?L?
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The Autler-Townes doublet
Laser-driven transition
CBS transition
?L????? ?L????
S.H. Autler and C.H. Townes, Phys. Rev. 100, 703
(1955)
?L-?
?L
?L?
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The complete picture
CBS transition
Laser-driven transition
?L??? ?L ???, ?L,
?L, ?L??, ?L??,
?L ??? ?L? ?L???,
?L????? ?L?????
?L-?
?L
?L?
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Interference character
?L?
?L
?L
?L
?L?
?L?
?L?
?L?/2
?L-?
?L-?
?L
?L-?
?L
?L
?L
?L
?L
?L
?L
?L-2?
?L
?L-2?
?L?/2
?L?/2
18
Outlook quantum optical theory of multiple
scattering

• The Pi follow from single-atom pump-probe
  master equation!

• Generalization to large number of atoms using
  techniques known
• from multiple scattering theory

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Conclusion

• Impact of inelastic processes on coherent
  backscattering
• master equation approach for two-atom model
• Inelastic scattering does contribute to CBS
  interference
• Interference character is defined by the
  relative phase shifts
• between the frequency-dependent interfering
  amplitudes
• Outlook quantum optical theory of multiple
  scattering