Fig. 4: Distribution of detected photon number and lifetime.

The detected photon number distribution, relative to the mean background photon number, in reflection within a region of interest, by preparing the ancilla in either the \(\left\vert {g}^{{\prime} }\right\rangle\) (blue) or the \(\left\vert P\right\rangle\) (orange) state. For the former, we obtain a Poissonian distribution (N = 1000 repetitions) corresponding to the photon counts in the EIT configuration (solid blue line). Preparing the ancilla in \(\left\vert P\right\rangle\), the histogram acquires a tail towards high reflected photon numbers (N = 1300 repetitions). This histogram is a combination of counts due to Rydberg-induced reflection (dashed orange line), and counts at low photon numbers due to imperfect Rydberg preparation and Rydberg decay. A Monte Carlo simulation including our experimental uncertainties reproduces the essential features of the observed histogram (solid orange line and shaded region; see Supplementary Information). The inset displays the transmission signal (T) for variable delay time δt between Rydberg excitation and probe pulse (70 repetitions). We extract the Rydberg lifetime of τ = 27(5) μs from an exponential fit (solid line). The dashed green line is the expected transmission signal for an ancilla Rydberg fraction of \({P}_{\left\vert P\right\rangle }=0.96\). Error bars denote the s.e.m.