Optimization of periodic single-photon sources based on combined multiplexing

We consider periodic single-photon sources with combined multiplexing in which the outputs of several time-multiplexed sources are spatially multiplexed. We give a full statistical description of such systems in order to optimize them with respect to maximal single-photon probability. We carry out the optimization for a particular scenario which can be realized in bulk optics and its expected performance is extremely good at the present state of the art. We find that combined multiplexing outperforms purely spatially or time-multiplexed sources for certain parameters only, and we characterize these cases. Combined multiplexing can have the advantages of possibly using less nonlinear sources, achieving higher repetition rates, and the potential applicability for continuous pumping. We estimate an achievable single-photon probability between 85% and 89%.

Figure 1

Scheme of the combined multiplexer. ${\mathrm{TM}}_k$ is the $k\mathrm{th}$ time multiplexer, ${\mathrm{D}}_k$'s are detectors, ${\mathrm{PR}}_k$'s are photon routers. ${\mathrm{i}}_k$ and ${\mathrm{s}}_k$ denote the idler and signal arm of the $k\mathrm{th}$ nonlinear photon pair source. Dashed lines represent electronic control lines.

Figure 2

Scheme of the bulk optical photon router. PCs denote Pockels cells and PBS is a polarizing beam splitter. $V_r$ denotes the reflection efficiency and $V_t$ the transmission efficiency of the PBS.

Figure 3

The achievable maximal single-photon probability $P^{\left(1\right)}$ at the optimal choice of the input mean photon number ${\lambda }_{\text{opt}}$ as a function of the number of multiplexed time windows $N$ on semilogarithmic scale for various numbers of spatially multiplexed time multiplexers $M$. Loss parameters are the following: $V_r=0.996,V_t=0.97,V_p=0.95,V_{p0,S}=0.996,V_D=0.9,V_b=1$. Points connected with continuous lines correspond to single-photon probabilities of combined multiplexers operating with the priority logic choosing the photon in the arm of the spatial multiplexer with the lowest loss and points with dotted lines to the one which simply routes the first arriving photon to the output.

Figure 4

The achievable maximal single-photon probability $P^{\left(1\right)}$ at the optimal choice of the input mean photon number ${\lambda }_{\text{opt}}$ as a function of the number of multiplexed time windows $N$ on semilogarithmic scale for various numbers of spatially multiplexed time multiplexers $M$. Loss parameters are the following: $V_r=0.996,V_t=0.97,V_p=0.95,V_{p0,S}=0.985,V_D=0.9,V_b=1$.

Figure 5

The achievable maximal single-photon probability $P^{\left(1\right)}$ at the optimal choice of the input mean photon number ${\lambda }_{\text{opt}}$ as a function of the number of multiplexed time windows $N$ on semilogarithmic scale for various numbers of spatially multiplexed time multiplexers $M$. Loss parameters are the following: $V_r=V_{r,S}=0.996,V_t=V_{t,S}=0.97,V_p=0.95,V_{p0,S}=0.9922,V_D=0.9,V_b=1$.

Figure 6

The achievable maximal single-photon probability $P^{\left(1\right)}$ at the optimal choice of the input mean photon number ${\lambda }_{\text{opt}}$ as a function of the number of multiplexed time windows $N$ on semilogarithmic scale for various numbers of spatially multiplexed time multiplexers $M$. Loss parameters are the following: $V_r=0.993,V_{r,S}=0.996,V_t=0.99,V_{t,S}=0.98,V_p=0.95,V_{p0,S}=0.995,V_D=0.9,V_b=1$.