Experimental generation of single photons via active multiplexing

An on-demand single-photon source is a fundamental building block in quantum science and technology. We experimentally demonstrate the proof of concept for a scheme to generate on-demand single photons via actively multiplexing several heralded photons probabilistically produced from pulsed spontaneous parametric down-conversions (SPDCs). By utilizing a four-photon-pair source, an active feed-forward technique, and an ultrafast single-photon router, we show a fourfold enhancement of the output photon rate. Simultaneously, we maintain the quality of the output single-photon states, confirmed by correlation measurements. We also experimentally verify, via Hong-Ou-Mandel interference, that the router does not affect the indistinguishability of the single photons. Furthermore, we give numerical simulations, which indicate that photons based on multiplexing of four SPDC sources can outperform the heralding based on highly advanced photon-number-resolving detectors. Our results show a route for on-demand single-photon generation and the practical realization of scalable linear optical quantum-information processing.

Figure 1

Scheme and calculations of generating on-demand single photons via multiplexing with active feed-forward from spontaneous parametric down-conversion (SPDC). (a) A 2-SPDC module consists of two 1-SPDC sources coupled with a photon router. Each 1-SPDC source produces a pair of photons probabilistically from a nonlinear crystal (NLC) pumped by laser pulses whose power is split by a beam splitter (BS). The signal of each avalanche photodiode (APD) detector, indicated by the black arrows, is feed-forwarded and controls the photon router to direct one of the successfully created photons to a single output. This output single photon along with the output feed-forward signal can then be used in the next level. Suitable individual optical delays (not shown) are incorporated in order to erase the output photons’ temporal distinguishability from different sources. (b) Similarly, a 4-SPDC multiplexing system can be realized by coupling two 2-SPDC modules with another photon router. An $m$-SPDC multiplexing system requires $m$ SPDC sources and $(m-1)$ routers. (c) The calculated gain, $G$, of using a multiplexed system is plotted as a function of the number of SPDC sources, $m$, where only integer values of $m$ is relevant (blue solid line). The trivial gain of using a 1-SPDC source is shown for comparison (red solid line). The mean photon pair number per SPDC source is $\mathrm{N̄}=0.1$, indicated with the vertical dashed line in (d), and the horizontal black dashed line represents the saturation limit ${\text{lim}}_{m\to \infty }G=\frac{1}{1-e^{-\mathrm{N̄}}}\approx 10.5$. In addition, we show the gain when using multiplexing with a 0.95 transmission per path router and 0.97 of the polarization router (blue dashed line) in order to illustrate loss effects. For details, see the main text and Appendix . (d) Calculation result of the gain $G$ as a function of both the numbers of SPDC sources $m$ and the mean photon pair number per SPDC source $\mathrm{N̄}$.

Figure 2

Experimental setup. (a) Two pairs of the polarization entangled photons (1 and 2, 3 and 4) were generated from two $\beta$-barium-borate crystals (BBO1 and BBO2) via SPDC, where half-wave plates ($\lambda$/2) and compensating BBO crystals were used to counter walkoff effects in the down-conversion crystal, and single-mode fibers and interference filters (IFs) were used to clean their spatial and spectral modes, respectively. Photons 1 and 4 entered into spatial modes a and d respectively. Photons 2 and 3 entered into spatial modes b and c and were delayed in single-mode fibers ($\approx$97 m) with respect to photons 1 and 4. This allowed the logic and electronics to have enough time to control the EOMs in the router. Due to the sequential configuration of the sources (see Appendix ), appropriate individual fiber delays are implemented to eliminate the output photons’ temporal distinguishability from different sources. The layout of the ultrafast photon router is shown in (b). See text and Appendix for details and notations. (c) The experimental scheme of a 4-SPDC multiplexed system with active feed-forward. Sources I and II (III and IV) generated photon pairs from BBO 1 (BBO 2). Sources I and II (III and IV) were inherently overlapped via the noncollinear phase matching, as explained in the text. The polarization states of photons 1 and 4 were measured with PBSs and single-photon counting modules (SPCMs). The detection signals of photons 1 and 4 were fed into the logic and then used to control the ultrafast photon router. Depending on whether photon 1 or photon 4 was detected, the ultrafast photon router would be switched on or off. Thus, all the photons exited from mode ${\mathrm{b}}^{\prime }$ and no photons exited from ${\mathrm{c}}^{\prime }$. The quality of the output single photons was quantified via measurements of the correlation function, $g^2(0)$.

Figure 3

Experimental HOM two-photon interference performed with the photon router. The twofold coincidences are measured between two detectors placed directly behind two outputs of the photon router [b${}^{\prime }$ and ${\mathrm{c}}^{\prime }$ in Fig. 2b] and are plotted over the relative delay of the interfering photons [realized by changing the length of path c in Fig. 2b]. By adjusting the voltage applied on the EOMs, we set the phase of the MZI and hence varied the reflectivity (and transmittivity) of the router. When the phase of the MZI is $\pi /2$, HOM two-photon interference shows up (red circles). This is because the distinguishability of the two input photons’ spatial modes has been erased by the router. Consequently, the minimum coincidence counts occur for the temporal overlap of the two photons, i.e., zero time delay. The red solid line is a Gaussian fit to the data with a visibility of $88.7\%\pm 3.8\%$. When the phase is 0, path-length-difference insensitive coincidence counts are obtained (black squares) and no HOM two-photon interference shows up, because the two photons remain distinguishable in their spatial modes. The black solid line is the average of the coincidence counts for 0 phase setting. Background has not been subtracted. Error bars indicate $\pm 1$ standard deviation.

Figure 4

Experimental results. The correlation function at zero delay $g^2(0)$ is plotted vs the counts in 350 s for 1-SPDC (black circles), 2-SPDC (red triangles), and 4-SPDC (blue squares) multiplexed systems, where all of them contain the router circuitry. The $g^2(0)$ function saturates at the value 1 for large count rates, i.e., for large pump powers. The $g^2(0)$ data shown are in linear regime of low count rates and hence fitted with lines through the origin. Using multiplexed systems, one can increase the count rate while keeping constant the signal-to-noise ratio and hence the $g^2(0)$ function. In other words, increasing the number of SPDC sources enables one to increase the count rate with the same signal-to-noise ratio or (if one turns down the pump power) improves the quality of the single-photon output while maintaining the count rate of the output. Error bars indicate $\pm 1$ standard deviation.

Figure 5

Dependence of the photon correlation $g^{(2)}(0)$ vs the heralding output probability ${\text{P}}_{\mathrm{output}}$, determined in a numerical simulation of SPDC-based HSPSs with different types of detectors (see Appendix and Ref. [41]). The heralding output probability ${\text{P}}_{\mathrm{output}}$ is defined as the ratio of the twofold coincidence counts (between trigger and output) and the laser repetition rate. The blue curve is for a 1-SPDC source with a standard bucket photon detector (D) with 60% detection efficiency for the trigger photon. The red curve is assuming a photon-number-resolving detector (PNRD) with 95% efficiency. Remarkably, as shown by the green curve, a 4-SPDC multiplexed system with standard detectors is able to outperform a 1-SPDC heralding source realized with a highly advanced PNRD.