Coherent Scattering of Near-Resonant Light by a Dense Microscopic Cold Atomic Cloud

We measure the coherent scattering of light by a cloud of laser-cooled atoms with a size comparable to the wavelength of light. By interfering a laser beam tuned near an atomic resonance with the field scattered by the atoms, we observe a resonance with a redshift, a broadening, and a saturation of the extinction for increasing atom numbers. We attribute these features to enhanced light-induced dipole-dipole interactions in a cold, dense atomic ensemble that result in a failure of standard predictions such as the “cooperative Lamb shift”. The description of the atomic cloud by a mean-field model based on the Lorentz-Lorenz formula that ignores scattering events where light is scattered recurrently by the same atom and by a microscopic discrete dipole model that incorporates these effects lead to progressively closer agreement with the observations, despite remaining differences.

Figure 1

(a) Experimental setup. A microscopic cloud of ${}^{87}\mathrm{Rb}$ atoms is illuminated by a linearly polarized probe laser focused down to a waist $w=1.2\mu \mathrm{m}$. $P$: polarizer. $L$: Lens allowing the mode matching between the laser probe beam and the single-mode fiber ($F$) in the absence of atoms. APD: avalanche photodiode. Inset: cloud rms widths (left) and intensity radiation pattern (right), calculated using a microscopic approach (see text). The coherent part, $|{\mathcal{E}}_{\text{coh}}(\omega ){|}^2$, dominates the incoherent part, which is more isotropic and is orders of magnitude smaller. (b) Example of temporal signals recorded on the APD with $N=180$ atoms (green line) and without atoms (blue line). The laser is nearly resonant with the atoms, with a frequency detuning $\mathrm{\Delta }=0.3\mathrm{\Gamma }$. Each run consists of 1000 illuminations with a duration of 300 ns each. Temporal bins: 6 ns. Gray area: time interval used for the steady-state analysis.

Figure 2

(a) Measured transfer function of the cloud in steady state versus probe detuning $\mathrm{\Delta }$ for $N=(10,83,180)$ atoms (top to bottom); error bars: statistical (one standard deviation), shot noise limited. Solid lines: Lorentzian fit by $|\mathcal{S}(\omega ){|}^2$. Dotted lines: results of the coupled dipole equations including the 12 levels of the $F_{\mathrm{g}}=2-F_{\mathrm{e}}=3$ transition (see text). (b) Comparison between the predictions of the Lorentz model (solid line) and the microscopic, 12-level atom model (dotted line) for $N=(1,10,83,180)$ (top to bottom).

Figure 3

Fit results of the data of Fig. 2 with the function $|\mathcal{S}(\omega ){|}^2$. Error bars are from the fit. (a) Amplitude $A$. Solid green line: phenomenological fit to guide the eye, yielding a saturation (dotted line) at 0.7. (b) Shift of the center frequency ${\mathrm{\Delta }}_c={\omega }_c-{\omega }_0$. Solid line: linear fit. (c) Full width at half maximum ${\mathrm{\Gamma }}_c$. Solid line: linear fit. Dashed lines in (b) and (c): predictions by Friedberg, Hartmann, and Manassah detailed in the text. The prediction for the width has been offset to match the data for $N=0$.