Coherent and incoherent multiple scattering

We compare two different models of transport of light in a disordered system with a spherical Gaussian distribution of scatterers. A coupled dipole model, taking into account all interference effects, is compared to an incoherent model, using a random walk of particles. Besides the well-known coherent backscattering effect and a well pronounced forward lobe, the incoherent model reproduces extremely well all scattering features. In an experiment with cold atoms, we use the momentum recoil imparted on the center of mass of the sample as a partial probe of the light-scattering properties. We find that the force acting on the center of mass of the atoms is not well suited to exhibit the coherence effects in light propagation under multiple-scattering conditions.

Figure 1

Emission diagram (log scale) normalized to the independent N atom case, for the RW approach (black points) and the CD model (blue line) with $b=8$.

Figure 2

Normalized radiation pressure force acting on the center of mass of the atomic cloud as a function of the laser detuning $\delta$ (in unit of $\Gamma$), at constant saturation parameter $s\left(\delta \right)$. The experimental result for $b_0=2.19$ (red circles) are compared to the coherent CD model ($b_0=2.19$, blue line) and incoherent RW model (black squares) with corresponding optical thickness $b\left(\delta \right)$.

Figure 3

Normalized radiation pressure force as a function of the optical thickness. The experimental data for $b_0=0.96$ (green triangles) and $b_0=2.9$ (red diamonds) are compared to the results of the CD simulations, obtained for $b_0=0.96$ (green dash-dotted line), $b_0=2.9$ (red dotted line), and $b_0=10$ (blue plain line), and of the RW model (gray squares). For the experimental data and the CD model, $b\left(\delta \right)$ is varied at fixed $b_0$ by changing the detuning. The CD data are superimposed as $b\left(\delta \right)$ appears as a universal parameter, and fluctuations are very small.

Figure 4

(a) Local optical thickness $b_0$ seen by the laser field propagating along the direction ${\widehat{e}}_z$. The white line represents the multiple-scattering limit $b_0=1$. (b) Excitation amplitude of the atomic dipole compared to the single atom limit $|{\beta }_j{|}^2/{\left|{\beta }_1\right|}^2$. (c) Phase of the atomic dipole ${\varphi }_j$. $\varphi =0$ corresponds to the laser field phase corrected from its propagation along ${\widehat{e}}_z$. (d) Local force compared to the single atom case $F_z/F_1$. All data are computed for a Gaussian sphere with $b_0=8$.