Absolute calibration of single-photon and multiplexed photon-number-resolving detectors

Single-photon detectors are widely used in modern quantum optics experiments and applications. Like all detectors, it is important for these devices to be accurately calibrated. A single-photon detector is calibrated by determining its detection efficiency; the common method to measure this quantity requires comparison to another detector. Here, we suggest a method to measure the detection efficiency of a single-photon detector without requiring an external reference detector. Our method is valid for individual single-photon detectors as well as multiplexed detectors, which are known to be photon number resolving. The method exploits the even-number photon-statistics of a nonlinear source, as well as the nonlinear loss of a single-photon detector that occurs when multiple photons are incident simultaneously. We have analytically modeled multiplexed detectors and used the results to experimentally demonstrate the calibration of a single-photon detector without the need for an external reference detector.

Figure 1

The experimental setup for (a) SMSV state and (b) TMSV state. DM - dichroic mirror, PBS - polarizing beam splitter, BS - beam splitter, HWP - half wave-plate, BPF - bandpass filter, NDF - adjustable neutral density filter, DUT - detector under test. Note that the detector denoted as “ref” is only for comparison to the coincidence calibration procedure. See Fig. 4 and text for more details.

Figure 2

The odds of a detection event as a function of the NDF transmission for two separate detectors. Solid and empty symbols denote data from using TMSV and SMSV, respectively. Solid and dashed lines are fits to Eqs. (7) and (8), respectively. SPD #1 is represented in blue circles and SPD #2 is represented in pink boxes. Error bars are assumed to be due to Poissonian noise and intensity fluctuations (see Fig. 6). The maximal error bar is $2.1\times {10}^{-5}$ and is smaller than the symbol size; $3.3\times {10}^{-5}$, and thus not displayed.

Figure 3

The odds of a detection event as a function of the NDF transmission for SPD #1 when the pump power is varied. Green diamonds are for pump power of 250 mW, pink downward triangles for 240 mW, blue triangles for 215 mW, red circles for 180 mW, and black boxes for 145 mW. Error bars are assumed to be due to Poissonian noise and intensity fluctuations (see Fig. 6). The maximal error bar is $2.1\times {10}^{-5}$ and is smaller than the symbol size; $3.3\times {10}^{-5}$, and thus not displayed.

Figure 4

Detailed experimental setup. DM: dichroic mirror, PBS: polarizing beam splitter, BS: beam splitter, HWP: half wave-plate, BPF: bandpass filter, NDF: adjustable neutral density filter, DUT: detector under test, SMF: single-mode fiber, MMF: multimode fiber, BD: beam dump.

Figure 5

The average number of incident photons as a function of the pump power.

Figure 6

Residuals and error calculation for TMSV SPD #1 (see Fig 2).