Hanle Effect in Coherent Backscattering

We study the shape of the coherent-backscattering (CBS) cone obtained when resonant light illuminates a thick cloud of laser-cooled rubidium atoms in the presence of a homogenous magnetic field. We observe new magnetic field-dependent anisotropies in the CBS signal. We show that the observed behavior is due to the modification of the atomic-radiation pattern by the magnetic field (Hanle effect in the excited state).

Figure 1

Experimental CBS cones. The far-field backscattered intensity is plotted as a function of the two azimuthal scattering angles (maximum intensity at center; we use a logarithmic scale for the isolines for a better visualization of the wings where the anisotropy is more pronounced; the lowest isoline corresponds to roughly 10% of the peak value). The total angular range is 2 mrad. $\mathbf{P}$ denotes the incident polarization. (a) $B=0$, top: $\mathrm{l}\mathrm{i}\mathrm{n}\parallel \mathrm{l}\mathrm{i}\mathrm{n}$, bottom: $\mathrm{l}\mathrm{i}\mathrm{n}\perp \mathrm{l}\mathrm{i}\mathrm{n}$; (b) both cones in $\mathrm{l}\mathrm{i}\mathrm{n}\perp \mathrm{l}\mathrm{i}\mathrm{n}$, top: $B=-8\mathrm{G}$, bottom: $B=+8\mathrm{G}$; note the $90°$ flip when $B$ changes sign. (c) $B=+10\mathrm{G}$ and ${\delta }_{\mathrm{L}}=-2.6\Gamma$, top: $\mathrm{l}\mathrm{i}\mathrm{n}\parallel \mathrm{l}\mathrm{i}\mathrm{n}$, bottom: $\mathrm{l}\mathrm{i}\mathrm{n}\perp \mathrm{l}\mathrm{i}\mathrm{n}$.

Figure 2

Theoretical CBS cones (double scattering). (a) and (b) use the $J=0\to J^{\prime }=1$ transverse plane model described in text (same parameters as in Fig. 1). (c): cones in $\mathrm{l}\mathrm{i}\mathrm{n}\parallel \mathrm{l}\mathrm{i}\mathrm{n}$ (top) and $\mathrm{l}\mathrm{i}\mathrm{n}\perp \mathrm{l}\mathrm{i}\mathrm{n}$ (bottom) for a $F=3\to F^{\prime }=4$ transition and $B=0$ (semi-infinite medium); the cones shapes are rounded off compared to (a), but the symmetry properties are identical.

Figure 3

Magneto-optical rotations. (a): measured dipole rotation $\varphi$ ($\square$) and Faraday rotation per mean-free path ${\theta }_F$ ($\blacksquare$). The curves correspond to the theory for a $F=3\to F^{\prime }=4$ transition (see text for sign conventions). Note that the two rotations have opposite signs. (b): measured CBS flip angle ${\alpha }_f$ ($▴$) compared to the $F=3\to F^{\prime }=4$ model neglecting all propagation effects (solid line).