Observation of Suppression of Light Scattering Induced by Dipole-Dipole Interactions in a Cold-Atom Ensemble

We study the emergence of collective scattering in the presence of dipole-dipole interactions when we illuminate a cold cloud of rubidium atoms with a near-resonant and weak intensity laser. The size of the atomic sample is comparable to the wavelength of light. When we gradually increase the number of atoms from 1 to $\sim 450$, we observe a broadening of the line, a small redshift and, consistently with these, a strong suppression of the scattered light with respect to the noninteracting atom case. We compare our data to numerical simulations of the optical response, which include the internal level structure of the atoms.

Figure 1

(a) Experimental setup. The atoms are initially confined in a microscopic single-beam dipole trap (not shown) (wavelength 957 nm, depth 1 mK, and a waist $1.6\mu \mathrm{m}$, oscillation frequencies ${\omega }_x={\omega }_y=2\pi \times 62\mathrm{kHz}$ and ${\omega }_z=2\pi \times 8\mathrm{kHz}$). The excitation laser propagates along the quantization axis $x$, set by a $B\sim 1\mathrm{G}$ magnetic field. We collect the scattered light along $z$, after a polarizer $P$ oriented at an angle of 55° with respect to $x$, using a lens $L$ with a large numerical aperture ($\mathrm{NA}=0.5$) and an image intensifier followed by a CCD camera (I-CCD). (b) Simulation of the distribution of nearest neighbors for a single stochastic realization of a cloud of $N=450$ atoms. (c) Structure of ${}^{87}\mathrm{Rb}$ atoms relevant to this work. The excitation light at frequency $\omega$ is near resonant with the transition at $\lambda =2\pi c/{\omega }_0=780\mathrm{nm}$.

Figure 2

Amount of scattered light detected $n_z(N,\mathrm{\Delta })$, versus the detuning $\mathrm{\Delta }$ of the excitation light for numbers of atoms $N=1$, 5, 20, 50, 200, 325, 450 (from bottom to top). The amplitudes of the curves are normalized to the amount of light detected at resonance for a single atom, $n_z(N=1,\mathrm{\Delta }=0)$. Solid lines: Lorentzian fits to the data. Typical uncertainties: 10% (vertically) and 20% (horizontally).

Figure 3

(a) FWHM and (b) line shift $\delta \omega$ with respect to the atomic frequency for $N=1$ atom, in units of $\mathrm{\Gamma }$. Filled symbols: data extracted from the Lorentzian fits shown in Fig. 2, versus the number of atoms. Dashed lines: phenomenological fits of the FWHM and shift by, respectively, ${\mathrm{\Gamma }}_{\mathrm{c}}/\mathrm{\Gamma }=1.49(6)\times N^{0.08(1)}$, and $\delta {\omega }_{\mathrm{c}}/\mathrm{\Gamma }=47(9)\times 10^{-5}N$. The error bars are from the fits of Fig. 2. Green solid line: results of the simulation (see text).

Figure 4

(a) Scattered light detected in the $z$ direction, versus the number of atoms, for different detunings of the laser: $\mathrm{\Delta }=0$ (red circles), $\pm \mathrm{\Gamma }$ (up or down open triangles), and $\mathrm{\Delta }=\pm 2.5\mathrm{\Gamma }$ (up or down filled triangles). The intensity for each atom number is normalized to the single atom case at the same detuning. Red line: result of the simulation (see text) with widths of the cloud ${\sigma }_{\rho }$ and ${\sigma }_z$. Black diamond: model with widths $2{\sigma }_{\rho }$ and $2{\sigma }_z$. (b) Ratio $R(N,\mathrm{\Delta })/R(N=1,\mathrm{\Delta })$ versus the number of atoms (see text). Dashed line in (a) and (b): case of noninteracting atoms.

Figure 5

Comparison between experiment and theory for the number of detected photons $n_z(N,\mathrm{\Delta })$ (normalized to the single atom case at resonance) for $N=450$. The red, blue, and green lines correspond to samples with widths ${\sigma }_{\rho }$ and ${\sigma }_z$, multiplied by a factor 1, 1.44, and 2, respectively.