Photon statistics of light fields based on single-photon-counting modules

Single-photon-counting modules (SPCM’s), with their high quantum efficiency, have been widely used to investigate effectively the photon statistics of various light sources, such as the single-photon state and emission light from controlled molecules, atoms, and quantum dots. However, such SPCM’s cannot distinguish the arrivals of one photon and two (or more than two) photons at a moment, which makes measurement correction in real experiments. We analyze the effect of SPCM’s on photon statistics based on the Hanbury-Brown-Twiss configuration when the total efficiency and background are considered, and it shows that the measured second-order degree of coherence and Mandel $Q$ factor for different quantum states, including single-photon states and squeezed vacuum states, are corrected in different forms. A way of determining the squeezing of a squeezed vacuum state based on single-photon detection is presented.

Figure 1

HBT configuration with the detection efficiency $\eta$ and coherent background $\mid \beta ⟩$.

Figure 2

The measured second-order degree of coherence $g^{\left(2\right)}$ (a) and Mandel $Q$ factor (b) of the single-photon state as a function of overall efficiency $\eta$ under different backgrounds: $\gamma =0$, 0.0022, 0.01, and 0.1. The star represents the experimental data in Ref. 9.

Figure 3

The second-order degree of coherence $g^{\left(2\right)}$ via the measured mean photon number $\alpha$ (a) and detection efficiency $\eta$ (b) for the thermal state.

Figure 4

Mandel parameter $Q$ as a function of the measured mean photon number $\alpha$ (a) and the overall efficiency $\eta$ (b) for the thermal field. In (b) the mean photon number $\alpha =1$.

Figure 5

The measured second-order degree of coherence $g^{\left(2\right)}$ of the squeezed vacuum state as a function of squeezing parameter $r$ (a) and detection efficiency $\eta$ (b) under different backgrounds and overall efficiencies. The squeezing parameter $r=1$ in (b).

Figure 6

Mandel $Q$ factor of squeezed vacuum state as a function of squeezing parameter $r$ (a) and overall efficiency $\eta$ (b). The squeezing parameter $r=1$ in (b).