Light Transport in Cold Atoms and Thermal Decoherence

We use the coherent backscattering interference effect to investigate experimentally and theoretically how coherent transport of light inside a cold atomic vapor is affected by the residual motion of atomic scatterers. As the temperature of the atomic cloud increases, the interference contrast decreases dramatically. This emphasizes the role of motion-induced decoherence for resonant scatterers even in the sub-Doppler regime of temperature. We derive analytical expressions for the corresponding coherence time.

Figure 1

CBS enhancement factor (●) as a function of the 1D typical atomic velocity $v$ and its comparison to a Monte-Carlo calculation assuming either a Gaussian (dashed line) or a Lorentzian (solid line) atomic velocity distribution. The CBS peak is recorded in the helicity nonpreserving channel, with resonant laser light ($\delta =0$). The optical thickness of the cloud is set constant at $b\simeq 13$. For rubidium, the velocity scale $\Gamma /k$ is $4.6\mathrm{m}/\mathrm{s}$.

Figure 2

CBS dephasing induced by the atomic motion, in the simplest case of two atoms moving with different velocities ${\mathbf{v}}_1$ and ${\mathbf{v}}_2$. The CBS effect builds on the two-wave interference between amplitudes associated to reversed multiple scattering paths (arrows). The Doppler effect induces frequency redistribution of the scattered light. Although the outgoing frequencies are identical, the intermediate frequencies differ, yielding a phase-coherence loss and thus a reduction of the CBS contrast.

Figure 3

Numerical calculation of the CBS interference decay for multiple scattering order $N=2$ (□) and $N=40$ (○). The upper velocity range refers to curves $\mathbf{a}$ and $\mathbf{b}$, while the lower one refers to curves $\mathbf{1}$ and $\mathbf{2}$. Note the very different velocity ranges. We compare two situations: resonant excitation $\delta =0$ ($\mathbf{1}$ and $\mathbf{a}$) and detuned excitation $\delta \gg kv$ ($\delta =50\Gamma$ for $\mathbf{2}$ and $\delta =5\Gamma$ for $\mathbf{b}$). Although the CBS contrast is improved, a detuned excitation is not sufficient to circumvent the motion-induced decoherence.