Cooperative Emission of a Pulse Train in an Optically Thick Scattering Medium

An optically thick cold atomic cloud emits a coherent flash of light in the forward direction when the phase of an incident probe field is abruptly changed. Because of cooperativity, the duration of this phenomena can be much shorter than the excited lifetime of a single atom. Repeating periodically the abrupt phase jump, we generate a train of pulses with short repetition time, high intensity contrast, and high efficiency. In this regime, the emission is fully governed by cooperativity even if the cloud is dilute.

Figure 1

(a) Experimental setup: a laser beam is sent through an acousto-optic modulator (AOM), which may be used to switch on and off the incident beam, followed by an electro-optic modulator (EOM), which abruptly changes the phase of the incident probe field, $E_0$. (b) A pulse train generated at a repetition time of $T_R=0.12{\mathrm{\Gamma }}^{-1}$ by a periodic abrupt phase change of $\pi$. Here, the probe laser is at resonance. (c) Electric fields just before and just after an abrupt phase jump of $\pi$ are represented schematically in the complex plane. Before the phase jump, the forward scattered field $E_s$ destructively interferes with $E_0$. After the phase jump, they constructively interfere. The transmitted field is denoted by $E_t$.

Figure 2

Initial decay time of the coherent flash versus the probe detuning at $k\overline{v}/\mathrm{\Gamma }=3.4$. The zero temperature resonant optical thickness is $b_0(0)=120$. The blue open circles and plain curve are, respectively, the experimental data points and the theoretical curve for an abrupt switch off of the probe. The two horizontal black dashed lines give the theoretical predictions at resonance and at large detuning. The red squares and dashed curve are the experimental data points and theoretical prediction for an abrupt phase jump of $\pi$. The blue dotted line and the red dash-dotted line are numerical predictions taking into account the finite response time of the experimental scheme (see text for more details).

Figure 3

Figures of merit of the generated pulse train (a) at resonance and (b) at $|\delta |=11.3\mathrm{\Gamma }$. The red solid and blue dashed curves are the theoretical predictions for the intensity contrast $I_c/I_0$ and transfer efficiency $⟨I_t⟩/I_0$, respectively. The red dots and blue open circles are the corresponding experimentally measured values.