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Journal of Modern Optics

Multiple scattering of photons by a cold atomic gas

Éric Akkermans, Ohad Assaf

Published Nov 10, 2007• 0 citations
Publisher

Abstract

We show that photons propagating in a mesoscopic gas of atoms acquire a correlation stronger than the value predicted by Rayleigh law. This enhanced correlation results from cross-terms based on the effects of spatial disorder and atomic quantum internal degrees of freedom. The great sensitivity of these cross-terms upon dephasing, such as a Zeeman splitting induced by a magnetic field, opens the possibility of a new kind of high precision spectroscopy.

DOI
10.1080/09500340701576296

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Comment on “Intensity Correlations and Mesoscopic Fluctuations of Diffusing Photons in Cold Atoms”

Benoît Grémaud, Dominique Delande, Cord Axel Müller +1 more

In a recent Letter (Phys. Rev. Lett. \textbf{98}, 083601 (2007), arXiv:cond-mat/0610804), O. Assaf and E. Akkermans claim that the angular correlations of the light intensity scattered by a cloud of cold atoms with internal degeneracy (Zeeman sublevels) of the ground state overcome the usual Rayleigh law. More precisely, they found that they become exponentially large with the size of the sample. In what follows, we will explain why their results are wrong and, in contrary, why the internal degeneracy leads to lower intensity correlations.

arXiv:0705.0366•Physical Review Letters•May 14, 2008•3 citations
We show that photons propagating in a mesoscopic gas of atoms acquire a correlation stronger than the value predicted by Rayleigh law. This enhanced correlation results from cross-terms based on the effects of spatial disorder and atomic quantum internal degrees of freedom. The great sensitivity of these cross-terms upon dephasing, such as a Zeeman splitting induced by a magnetic field, opens the possibility of a new kind of high precision spectroscopy.
We show that an enhanced intensity correlation shows up in the diffusion of photons multiply scattered by an atomic gas of large optical depth b . This enhancement occurs only for scattering atoms that are Zeeman degenerate and it leads to a deviation from the Rayleigh law. The fluctuations measured by their variance, display a resonance peak as a function of an applied magnetic field. The resonance width is proportional to the small factor 1/ b . We derive closed analytic expressions for all these physical quantities which are directly accessible experimentally.
We study the angular correlation function of speckle patterns that result from multiple scattering of photons by cold atomic clouds. We show that this correlation function becomes larger than the value given by Rayleigh law for classical scatterers. These large intensity fluctuations constitute a new mesoscopic effect specific to atom-photon interactions, that could not be observed in other systems such as weakly disordered metals. We provide a complete description of this behavior and expressions that allow for a quantitative comparison with experiments.
We present an analysis of the dephasing present in the multiple scattering of photons by atoms with a quantum internal structure. The corresponding phase coherence times τϕτ_ϕτϕ​ are obtained as a function of the Zeeman degeneracy of the atomic dipole transition and the polarization state of the photons. These results allow for an explanation of the recent experiments on coherent backscattering of photons from a gas of cold rubidium atoms where the height of the backscattering cone depends on the atomic internal degrees of freedom coupled to the polarization of the photons. Some consequences of these results are presented, and analogies with the case of electronic systems are highlighted.
We show that a new interference effect appears in the intensity fluctuations of photons multiply scattered by an atomic gas of large optical depth b. This interference occurs only for scattering atoms that are Zeeman degenerate and it leads to a deviation from the Rayleigh law. The fluctuations measured by their variance, display a resonance peak as a function of an applied magnetic field. The resonance width is proportional to the small factor 1/b. We derive closed analytic expressions for all these physical quantities which are directly accessible experimentally.
The irradiation of a dilute cloud of cold atoms with a coherent light field produces a random intensity distribution known as laser speckle. Its statistical fluctuations contain information about the mesoscopic scattering processes at work inside the disordered medium. Following up on earlier work by Assaf and Akkermans [Phys. Rev. Lett. 98, 083601 (2007)], we analyze how static speckle-intensity correlations are affected by an internal Zeeman degeneracy of the scattering atoms. It is proven on general grounds that the speckle correlations cannot exceed the standard Rayleigh law. On the contrary, because which-path information is stored in the internal atomic states, the intensity correlations suffer from strong decoherence and become exponentially small in the diffusive regime applicable to an optically thick cloud.
In a recent Letter (Phys. Rev. Lett. \textbf{98}, 083601 (2007), arXiv:cond-mat/0610804), O. Assaf and E. Akkermans claim that the angular correlations of the light intensity scattered by a cloud of cold atoms with internal degeneracy (Zeeman sublevels) of the ground state overcome the usual Rayleigh law. More precisely, they found that they become exponentially large with the size of the sample. In what follows, we will explain why their results are wrong and, in contrary, why the internal degeneracy leads to lower intensity correlations.