Fig. 1. (Color online) The photon-number resolving detection setup. (a) SG: signal generator; VOA: variable optical attenuator; APD: single-photon avalanche diodes based on InGaAs/InP; UNIC: ultra-narrowband interference circuits; BSF: band stop filter with a cut-off frequency of 2.5 GHz; APM: amplifier; OSC: oscilloscope; TDC: time-digital-converter. (b) Ultranarrow interference circuit (UNIC) consists of two couplers (CPL) with a power splitting ratio of 9 : 1, a π-resistance attenuator (ATT) and a surface acoustic wave band pass filter (SAW). (c) Transmission spectrum of raw out and BSF out.

Fig. 2. (Color online) InGaAs/InP APD has intrinsic photon number resolution. (a) Temporal evolution of the avalanche peak voltage distribution for a detected flux of three photons/pulse. (b) The temporal voltage distribution at different time delays of 0.11 ns (black), 0.22 ns (green), and 0.4 ns (red), respectively.

Fig. 3. (Color online) The evolution of peak output signal distribution measured for different voltage applied and incident photon fluxes on the APD. The bias voltages (detection efficiencies) of the three columns are 69.5 V (34%), 70.5 V (45%), and 71.0 V (49%), respectively. The incident photon fluxes in the three rows are 0.45, 3.55, and 7.08, respectively.

Fig. 4. (Color online) The bias voltage (black, left axis) and detection efficiency (red, right axis) vs. the mean voltage of one-photon peak voltage at a fixed photon flux μ = 2.98 photons/pulse.

Fig. 5. (Color online) Quantitative analysis of photon number resolution for a detected flux μ = 7.08 photons/pulse. (a) Probability density distributions of avalanche peak voltages. The red solid line is a fit to the experiment data (symbols), indicating the sum of individual Gaussians (blue dashed line) of different photon numbers. (b) The mean voltage of peak output signal is proportional to the number of photons induced avalanches. (c) Comparison of the theoretical Poisson distribution (red) and the distribution of each photon number state of the APD (blue).