Slow Diffusion of Light in a Cold Atomic Cloud

We study the diffusive propagation of multiply scattered light in an optically thick cloud of cold rubidium atoms illuminated by a quasiresonant laser beam. In the vicinity of a sharp atomic resonance, the energy transport velocity of the scattered light is almost 5 orders of magnitude smaller than the vacuum speed of light, reducing strongly the diffusion constant. We verify the theoretical prediction of a frequency-independent transport time around the resonance. We also observe the effect of the residual velocity of the atoms at long times.

Figure 1

Radiation trapping (RT) experimental scheme. A pulsed probe beam is sent through the center of a laser-cooled atomic cloud. The transmitted diffuse light is collected as a function of time in a solid angle close to the forward direction.

Figure 2

Decay of resonant light trapped in the atomic cloud. We record the decay as we vary the number of atoms in the cloud. (a) shows the data for three optical thicknesses (solid lines): $b=34$ (1), 19 (2), and 2.4 (3), and the Monte Carlo results (dashed lines). The measured decay constant ${\tau }_{\mathrm{0}}$ is plotted in (b) as a function of the optical thickness $b$ (circles). It is compared to the prediction of Eq. (2) for a sample with Gaussian density (solid line), and to the MC calculation (dashed line).

Figure 3

Variation of transport time with frequency. We measure the “early” time ($2<t/{\tau }_{\mathrm{n}\mathrm{a}\mathrm{t}}<10$) decay constant ${\tau }_{\mathrm{i}}$ (in all these experiments, after an initial transient over $\approx 2{\tau }_{\mathrm{n}\mathrm{a}\mathrm{t}}$ due to the higher Holstein modes, an exponential decay is observed for at least $10{\tau }_{\mathrm{n}\mathrm{a}\mathrm{t}}$, as in Fig. 2) as a function of the detuning ${\delta }_{\mathrm{L}}$ from resonance, in two separate experiments. (a) The number $N_{\mathrm{a}\mathrm{t}}$ of atoms in the cloud is fixed, with an optical thickness at ${\delta }_{\mathrm{L}}=0$ of 22.4. The circles correspond to the experimental data and the solid line to the MC simulation. (b) For each value of ${\delta }_{\mathrm{L}}$, we adjust $N_{\mathrm{a}\mathrm{t}}$ to maintain a fixed optical thickness $b\approx 10.7\pm 1.0$. ${\tau }_{\mathrm{i}}$ is then nearly constant.

Figure 4

Role of the temperature of the atomic sample. We measure RT as a function of the residual velocity $v_{\mathrm{r}\mathrm{m}\mathrm{s}}$ of the atoms in the cloud, for detuned laser light ${\delta }_{\mathrm{L}}=+1.5\Gamma$. The optical thickness is fixed, $b=2.2$. (a) shows three experimental decay curves, clearly nonexponential because of the occurrence of some frequency redistribution, for $v_{\mathrm{r}\mathrm{m}\mathrm{s}}=0.15$ (1), 0.42 (2), and 1.72 (3) m$/$s. We plot in (b) the amplitude of the decay signal after a time $t=8{\tau }_{\mathrm{n}\mathrm{a}\mathrm{t}}$, as a function of $v_{\mathrm{r}\mathrm{m}\mathrm{s}}$. Dashed lines are the MC results without adjustable parameters.