Probing the indistinguishability of single photons generated by Rydberg atomic ensembles

We investigate the indistinguishability of single photons retrieved from collective Rydberg excitations in cold atomic ensembles. The Rydberg spin waves are created either by off-resonant two-photon excitation to the Rydberg state or by Rydberg electromagnetically induced transparency. To assess the indistinguishability of the generated single photons, we perform Hong-Ou-Mandel experiments between the single photons and weak coherent states of light. We analyze the indistinguishability as a function of the detection window, and we infer a high value of indistinguishability going from $89\%$ for the full waveform to $98\%$ for small detection windows, for the case of photons generated by off-resonant excitation. In the same way, we also investigate the indistinguishability of single photons generated by Rydberg EIT, showing values lower than those corresponding to single photons generated by off-resonant excitation. These results are relevant for the use of Rydberg atoms as quantum network nodes.

Figure 1

(a) Schematic representation of the experimental setup. An input probe pulse (in red) is sent to the experiment with a spatial distribution given by the probe beam (shadowed red). The control beam (in blue) is counterpropagated with the probe, and both are focused in the center of the atomic cloud by two aspheric lenses. (b) The emitted single photon (SP) interferes with a WCS pulse in a HOM experiment, consisting of a fiber-based beamsplitter and two single-photon detectors SPD1 and SPD2. (c) Level scheme and transitions used in the experiment, where ${\delta }_p$ and ${\delta }_c$ are the detuning of the probe and control beams with regard to the intermediate level. ${\mathrm{\Omega }}_p$: probe Rabi frequency, ${\mathrm{\Omega }}_c$: control Rabi frequency, DM: dichroic mirror.

Figure 2

Representation of the probe and control optical pulses used for the photon generation under (a) OR and (b) EIT conditions, normalized to their maximum value. SP shows the retrieved photon temporal distribution counts with respect to the input probe.

Figure 3

Normalized coincidences between two different experimental trials, as a function of the number of trials between them, for (a) the OR excitation case and (b) the EIT case. (c) Variation of $g_{\mathrm{\Delta }t}^{\left(2\right)}$ as a function of the probability of generating a single photon on the output $P_{\mathrm{SP}}$, for the OR case. Error bars correspond to one standard error. The behaviour with $P_{\mathrm{SP}}$ in the EIT case is shown in Fig. 8.

Figure 4

Hong-Ou-Mandel measurements with photons generated with the OR scheme. (a) Temporal distribution of counts for the indistinguishable (top panel) and distinguishable (bottom panel) case. For the indistinguishable case, the single-photon (SP) and WCS pulse overlap in time, while for the distinguishable case, a delay between them is introduced. Two detection windows are selected with duration $\mathrm{\Delta }t=500$ ns (blue shaded region) and $\mathrm{\Delta }t=100$ ns (orange shaded region). (b) Visibility obtained by varying the mean number of photons in the WCS, for both observation windows. The shaded areas correspond to the error bars of $\eta$.

Figure 5

Hong-Ou-Mandel measurements with photons generated with the EIT scheme. (a) Temporal distribution of counts for the indistinguishable (top panel) and distinguishable (bottom panel) case. (b) Visibility obtained by varying the mean number of photons in the WCS, for a time observation window of $\mathrm{\Delta }t=600$ ns (blue points) and $\mathrm{\Delta }t=100$ ns (red points). The shaded areas correspond to the error bars of $\eta$.

Figure 6

Variation of the indistinguishability factor $\eta$ between the WCS and SP (top panel), variation of the generation probability $P_{\mathrm{SP}}$ of a single photon (second panel), and variation of the $g_{\mathrm{\Delta }t}^{\left(2\right)}$ (bottom panel) as a function of the detection window $\mathrm{\Delta }t$, for OR excitation and EIT conditions.

Figure 7

Top: time-resolved coincidences for (a) OR excitation and (b) EIT excitation, for a bin size of 20 ns, covering the whole extension of the pulse. Bottom: corresponding visibilities. For those measurements $|\overline{\alpha }{|}^2/2p_1\approx 0.5$ and the measured $g_{\mathrm{\Delta }t}^{\left(2\right)}$ are $0.27\pm 0.01$ for OR and 0.17 $\pm 0.01$ for EIT.

Figure 8

Results of the HOM measurement under EIT conditions as a function of the mean number of input photons. Top pannel: Variation of the indistinguishability factor $\eta$ between the WCS and the emitted photon. For that measurement, there was a frequency shift of 320 kHz between the WCS and the single photon. Middle pannel: Variation of the generation probability of a single photon $P_{\mathrm{SP}}$. Bottom panel: Variation of the second-order autocorrelation function $g_{\mathrm{\Delta }t}^{\left(2\right)}$. Note that the error bars on the $x$-axis are mainly due to the error in detection efficiency, given by the systematic error of the power meter.