Speckle-intensity correlations of photons scattered by cold atoms

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.

Figure 1

Amplitudes for light scattering from mode $a=({\mathbf{k}}_a,{\mathbf{\epsilon }}_a)$ to $b=({\mathbf{k}}_b,{\mathbf{\epsilon }}_b)$ in a first pulse and from $a^{\prime }$ to $b^{\prime }$ in a second pulse, across a dilute cloud of immobile point scatterers. (a) Possible paths $I,J,K,L$, drawn with four representative scatterers each. (b) Pairing $I=J$ and $J=K$, yielding the product ${\overline{T}}_{ab}{\overline{T}}_{a^{\prime }{b}^{\prime }}$ of average intensities. (c) Pairing $I=L$ and $J=K$, describing intensity correlations $\overline{\delta T_{ab}\delta T_{a^{\prime }{b}^{\prime }}}$.

Figure 2

Decorrelation rate, Eq. (52), as a function of ground-state angular momentum $J_{\text{g}}$ (in units of $\hslash$) for the three possible dipole transition types $|J_{\text{e}}-J_{\text{g}}|\le 1$. The hatched area indicates the region ${\gamma }_0^{\left(c\right)}<0$ forbidden by the Rayleigh bound. Except for the nondegenerate case $J_{\text{g}}=0$ of isotropic dipoles, where the rate vanishes and the Rayleigh law applies, the decorrelation rate is always larger than unity, signaling a rapid loss of correlations.