Temporal dynamics of Levy flights of photons in a hot vapor

Abstract

Multiple scattering of light by resonant vapor is characterized by Levy-type superdiffusion with a step size distribution $P(x) \propto 1/x^{1+α}$, with $0 < α < 2$. The Levy parameter $α$ was measured from $P(x)$, steady fluorescence, frequency-dependent fluorescence and time-resolved transmission, all of them in the forward direction. Here we report first measurements of this quantity from timeresolved backward fluorescence, i.e., photons that are backward diffused from light pulses exciting a hot rubidium vapor. We show experimentally that $α$ can be extracted from this diffuse reflection, and the results are consistent with time-resolved transmission (i.e., photons that are forward diffused) and steady frequency-dependent forward fluorescence. Theoretical simulations are consistent with these results. We also show that, although we measure $α = 1$ for both transmission and reflection, the backward photons have a non-negligible amount of single scattering events even for high density, contrary to the forward photons where multiple scattering dominates.

Figures (7)

• Figure 1: (a) Scheme of the experimental setup. The laser diode (LD) is stabilized by a saturated-absorption spectroscopy (SA). The laser goes to a Rb cell in an oven. The photodetectors PD1 and PD2 measures, respectively, the coherent transmission and the diffuse transmission. (b) and (c) An AOM produces pulses. Its first-order beam (not shown) drives the vapor in order to measure the temporal diffuse transmission (b) or the diffuse reflection (c).
• Figure 2: (a) Diffuse transmission $T_\mathrm{diff}(\Delta)$ as a function of the laser detuning for three different temperatures: $30^\circ \text{C}$ (dark blue), $70^\circ \text{C}$ (red) and $110^\circ \text{C}$ (black). The top grey curve is the Rb saturated absorption (S.A.). (b) Measured diffuse transmission $T_\mathrm{diff}(0)$ as a function of sample density $n$ (black circles). The red dashed line is a fit of the experimental data with Eq. \ref{['Tdiff_vs_n']}.
• Figure 3: (a) Normalized temporal diffuse transmission $T_\mathrm{diff}(t)$ as a function of the normalized time $t/\tau_0$ for three different temperatures: $30^\circ \text{C}$ (red), $70^\circ \text{C}$ (blue) and $80^\circ \text{C}$ (gray). The dashed black lines are the respective theoretical fitting curves in the interval $I(t)/I_0\in[0.3, 0.8]$. (b) Decay times $\tau/\tau_0$ as a function of the density $n$ from $T_\mathrm{diff}(t)$ shown in panel (a). The different colors separate low and high densities. The dashed lines are the respective theoretical adjusts using Eq. \ref{['tau_fit']}.
• Figure 4: (a) Normalized temporal diffuse reflection $R_\mathrm{diff}(t)$ as a function of the normalized time $t/\tau_0$ for three different temperatures: $20^\circ \text{C}$ (blue; $n=4.6\times 10^{15}$ atoms/m$^3$), $80^\circ \text{C}$ (gray; $n=3.7\times 10^{17}$ atoms/m$^3$) and $125^\circ \text{C}$ (red; $n=9.7 \times 10^{18}$ atoms/m$^3$). The dashed black lines are the respective theoretical fitting curves in the interval $R_\mathrm{diff}(t)/R_0\in[0.3, 0.8]$. (b) Decay times $\tau/\tau_0$ as a function of the density $n$ from $R_\mathrm{diff}(t)$ shown in panel (a). The different colors separate low and high densities. The dashed lines are the respective theoretical adjusts using a power law function.
• Figure 5: (a) Steady diffuse transmission (blue circles) and reflection (black asterisks) from simulations as a function of the vapor density. The vertical axis is normalized by the total amount of input photons, which is $2,000$. (b) Experimental diffuse reflection in arbitrary units in the steady state as a function of density.