Direct single-shot observation of millimeter wave superradiance in Rydberg-Rydberg transitions

We have directly detected millimeter wave (mm-wave) free space superradiant emission from Rydberg states ($n \sim 30$) of barium atoms in a single shot. We trigger the cooperative effects with a weak initial pulse and detect with single-shot sensitivity and 20 ps time resolution, which allows measurement and shot-by-shot analysis of the distribution of decay rates, time delays, and time-dependent frequency shifts. Cooperative line shifts and decay rates are observed that exceed values that would correspond to the Doppler width of 250 kHz by a factor of 20 and the spontaneous emission rate of 50 Hz by a factor of $10^5$. The initial superradiant output pulse is followed by evolution of the radiation-coupled many-body system toward complex long-lasting emission modes. A comparison to a mean-field theory is presented which reproduces the quantitative time-domain results, but fails to account for either the frequency-domain observations or the long-lived features.