The coherent backscattering spectrum of two atoms

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

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

Coherent Backscattering (CBS) of light • Enhancement factor • (measure of phase coherence)

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

Dephasing mechanisms • Residual thermal motion • Raman scattering • This talk: • nonlinear inelastic scattering v k ΔωD=(k’-k)·v is kept << k’

Single-atom resonance fluorescence Powerful laser field: W=-dge·E/ =(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)

Saturation and interference - saturation parameter Saturation regime: s>>1 • Interference with reference • laser  0 • Young’s double-slit experiment • from 2 independent atoms: • interference  0

Saturation effect in CBS 88Sr experiment (Nice):  shrinks vs. s T. Chanelière et al. PRE 70, 036602 (2004) Optical thickness b=3.5 (double scattering) Jg=0Je=1 transition CBS enh. factor  m=0 m=+1 m=-1 m=0 Saturation parameter s h II h channel

Toy model of CBS • Hamiltonian 2 { H=HA+HF+HAF+HAL 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

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)

The coherent backscattering spectrum    • Seven CBS resonances • Constructive or destructive interference !

Dressed state analysis LLL pump probe

Re-scattering of the low-frequency sideband Laser-driven transition CBS transition L+ L- LL, L L

Re-scattering of the Mollow triplet Laser-driven transition CBS transition L L, L, L, L, L, L  L L, L- L L+

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+

The complete picture CBS transition Laser-driven transition L L, L, L, L, L, L  L L, L L L- L L+

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

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

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

The coherent backscattering spectrum of two atoms