Intensity Correlations and Mesoscopic Fluctuations of Diffusing Photons in Cold Atoms

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.

Figure 1

Photons in each pair of pulses are scattered by atoms at identical positions ${\mathbf{r}}_i$ but with distinct and uncorrelated quantum numbers ($m_i$, $m_f$) and ($m_i^{\prime }$, $m_f^{\prime }$). After a time $T\gg \tau$, a new measurement is performed after the atoms moved to new positions ${\mathbf{r}}_i^{\prime }$.

Figure 2

Angular correlation function $C_{ab{a}^{\prime }{b}^{\prime }}$ plotted as a function of $q=k_0\Delta {\widehat{\mathbf{s}}}_a$ for an atomic transition between nondegenerate ($j_g=0$, $j_e=1$, dashed line) and degenerate energy levels ($j_g=1$, $j_e=2$, solid line). The nondegenerate case describes the classical Rayleigh scattering of a polarized wave. These curves correspond to $L=7l$. The inset gives the dependence of intensity fluctuations $C_{abab}$ upon the width $L$ (the dashed line is the Rayleigh law).