Cooperative Emission of a Coherent Superflash of Light

We investigate the transient coherent transmission of light through an optically thick cold strontium gas. We observe a coherent superflash just after an abrupt probe extinction, with peak intensity more than three times the incident one. We show that this coherent superflash is a direct signature of the cooperative forward emission of the atoms. By engineering fast transient phenomena on the incident field, we give a clear and simple picture of the physical mechanisms at play.

Figure 1

(a) A schematic representation of the electric fields in the complex plane. (b) Transmission $I_t/I_0$ in the stationary regime as a function of the probe detuning $\delta /\mathrm{\Gamma }$. The blue dots are the experimental data and the black solid line is the theoretical prediction. (c) Temporal evolution of the normalized transmitted intensity for $\delta =-11.2\mathrm{\Gamma }$. The red curve shows the normalized incident intensity, the black curve the experimental signal, the blue line the level of $I_t/I_0$ and the green open circle the value of $I_s/I_0$. The inset is a zoom around $t=0$ of the coherent superflash, with the black curve showing the theoretical prediction assuming instantaneous switch off of the probe. (d) $I_s/I_0$ in the stationary regime as a function of the probe detuning. The black solid line is the theoretical prediction and the green dots are the experimental data. The vertical dashed lines at $|\delta |=11.7\mathrm{\Gamma }$ in (b) and (d) show the expected positions of the maximum values of the forward scattered intensity. In the experiment, $T=3.3(2)\mathit{\mu }\mathrm{K}$ and $b_0=19(3)$, the other parameters being given in the text.

Figure 2

Prediction for the $I_s/I_0$ ratio vs parameters $b_0$ (optical thickness at resonance) and detuning $|\delta |/\mathrm{\Gamma }$ for $T=3.3(2)\mathit{\mu }\mathrm{K}$. The black dashed line indicates the optical thickness of our experiment. The white solid line represents the linear dependence on $b_0$ of the detuning at which maximum value of $I_s/I_0$ is attained.

Figure 3

Reconstruction of $E_s$ in the complex plane. The false color scale gives the probe detuning. The white region corresponds to the superflash regime, the light gray area shows the region with the normal coherent flash, and the dark gray area gives the region forbidden by energy conservation. The dots and stars are the experimental values (see text for more details). The transparent ellipses around several experimental data depict the error estimates. The solid and dashed curves are theoretical predictions, respectively, at $b_0=19$ and $b_0=3$ for a temperature $T=3.3\mathit{\mu }\mathrm{K}$.

Figure 4

Temporal evolution (blue curves) with an abrupt change of phase of $-0.4\pi$ at $t=0$ for a probe detuning of (a) $\delta =-19.3\mathrm{\Gamma }$ and (b) $\delta =+20.7\mathrm{\Gamma }$. The insets show a schematic representation of the electric fields in the complex plane at the time pointed by the arrows.