Subradiance and superradiance-to-subradiance transition in dilute atomic clouds

We experimentally study subradiance in a dilute cloud of ultracold rubidium (Rb) atoms where $n \lambda_a^3 \approx 10^{-2}$ ($n$: atomic density, $\lambda_a$ excitation wavelength) and the on-resonance optical depth of the cloud is of order unity. We show that in the strong excitation regime, the subradiant time-scales depend on the excitation fraction of the cloud; i.e., to the intensity of the excitation pulse. In this regime, the decay dynamics are highly complicated and there is not a single decay time-constant. Instead, the decay time constant varies during the dynamics. Specifically, we were able to observe signatures of superradiant-to-subradiant transition; i. e., initially the decay rate is faster than independent decay (superradiant emission), while at later times it transitions to slower (subradiant emission). We also discuss a theoretical model whose numerical results are in good agreement with the experiments.