Abstract
Parametric singlephoton sources are well suited for largescale quantum networks due to their potential for photonic integration. Active multiplexing of photons can overcome the intrinsically probabilistic nature of these sources, resulting in neardeterministic operation. However, previous implementations using spatial and temporal multiplexing scale unfavorably due to rapidly increasing switching losses. Here, we break this limitation via frequency multiplexing in which switching losses remain fixed irrespective of the number of multiplexed modes. We use lownoise optical frequency conversion for efficient frequency switching and demonstrate multiplexing of three modes. We achieve a generation rate of 4.6 × 10^{4} photons per second with an ultralow g^{(2)}(0) = 0.07 indicating high singlephoton purity. Our scalable, allfiber multiplexing system has a total loss of just 1.3 dB, such that the 4.8 dB multiplexing enhancement markedly overcomes switching loss. Our approach offers a promising path to creating a deterministic photon source on an integrated chipbased platform.
Introduction
Deterministic and high quality singlephoton sources are essential to photonic quantum technologies including communications and information processing. An ideal singlephoton source should emit indistinguishable photons in welldefined spatiotemporal and spectral modes with high probability and negligible multiphoton noise. Efforts to build such sources have focused primarily on the following two approaches: sources that rely on nonlinear processes such as spontaneous parametric down conversion (SPDC) or fourwave mixing, and single emitters such as quantum dots, color centers, and cavitycoupled atoms and ions^{1}. With recent engineering efforts for improved fabrication and control of individual emitters, quantum dots with high brightness and photon purity have been demonstrated^{2,3,4}.
Parametric sources have specific advantages such as spectral tunability and can be easily adapted to a wide variety of experimental conditions. They have thus been used for pioneering quantum information experiments including quantum teleportation, loopholefree Bell tests, and boson sampling^{5,6,7,8,9}. These sources operate at room temperature and provide highly indistinguishable photons with flexible control over the spectral and temporal properties of the photons^{10,11,12,13}. Such sources have proved to be highly versatile, producing photons spanning the visible to the infrared, with bandwidths ranging from a few hundred kHz to a few THz^{14,15,16}. Moreover, parametric sources can be fully integrated onto monolithic CMOScompatible platforms to generate narrow band entangled photons with high brightness^{17,18,19}. However, these sources are fundamentally limited by multiphoton generation, resulting in probabilistic operation with a maximum heralding efficiency of 25% from a single source.
Active feedforward switching of photons from multiple identical sources is a promising technique that can overcome the probabilistic operation of a single source^{20,21,22,23,24}. By operating individual sources in a regime with low pair production probability, such schemes allow for increasing the singlephoton probability without additional multiphoton generation. A key requirement for efficient multiplexing is a lowloss N × 1 switching network that accommodates a sufficiently large number of modes N to achieve deterministic operation. Deterministic operation can be achieved with as few as N = 17 multiplexed modes with a lossless switching network and photonnumber resolving (PNR) detectors^{25}. Recently, there have been a number of promising demonstrations of multiplexed sources using the spatial and temporal degrees of freedom of a photon^{26,27,28,29,30,31,32}. However, for both spatial and temporal multiplexing, switching losses increase with the number of modes N, which deteriorates enhancement achieved from multiplexing beyond a few modes. Deterministic operation is therefore challenging to achieve without the use of bulky freespace setups^{31}.
Here, we propose and demonstrate an alternative scheme using frequency multiplexing where losses do not scale with the number of modes. Frequency multiplexing allows for multiple switching operations in a single spatial mode, thus effectively implementing an N × 1 switch in a monolithic optical structure such as a single mode fiber or waveguide. Therefore, distinct from other schemes, switching losses remain fixed irrespective of the number of multiplexed modes N. We perform active “frequency switching” using tunable quantum frequency translation via Bragg scattering fourwave mixing (BSFWM)^{33,34,35,36}, which we realize with close to unity efficiency and ultralow noise^{37,38}. We present a proofofprinciple demonstration of frequency multiplexing using three frequency modes in an entirely fiberbased setup that leverages on lowloss offtheshelf dense wavelength division multiplexing (DWDM) components. With this lowloss and lownoise setup we achieve generation rates of 46 kHz multiplexed photons with coincidencestoaccidentals ratio exceeding 100 and g^{(2)}(0) of 0.07. In addition, we show that BSFWM is efficiently tunable over a large bandwidth of more than 1 THz and therefore our system can be scaled to include a large number of frequency modes, which is critical for deterministic photon generation using multiplexing.
Results
Principle and theory
Figure 1 illustrates our frequency multiplexing scheme. A single source that generates broadband frequency correlated photon pairs is used to create narrowband frequency channels {ω_{0}, ω_{1}...}. One photon from the pair (heralding photon, not shown) is used to herald the presence of the signal photon. Due to energy conservation, the two photons are correlated in frequency, with the heralding photon providing information about the frequency of the signal photon. This heralding information is used to translate the frequency of the signal photon to the target frequency channel ω_{t} using tunable frequency conversion. We thus effectively implement an active frequency switch to route photons from multiple frequency bins to a single output frequency channel. In order to be viable as an N × 1 switch for large N, the tunable frequency conversion must be efficient over a sufficiently large bandwidth. For this purpose, we use BSFWM, a thirdorder nonlinear parametric process involving coherent interaction between two quantum fields at different frequencies mediated by two strong classical pumps^{35}. Contrary to frequency conversion based on parametric amplification, BSFWM is theoretically noiseless and preserves all quantum properties of the translated photons. BSFWM allows for independent control of the input and target frequencies by selectively activating auxiliary pumps in the interaction (Fig. 1b). Since phase matching can be achieved by symmetric placement of the classical pumps and quantum fields about the zerodispersion wavelength of the nonlinear medium, the same setup can be reconfigured to target different frequency shifts by tuning the pump wavelength (Supplementary Note 1). For efficient conversion, it is critical that the bandwidth of individual channels be less than the acceptance bandwidth Δν_{BS} of the BSFWM process for two fixed pumps. This alloptical frequency switch can support ultrafast operation, with the repetition rate limited only to the inverse bandwidth 1/Δν_{BS}. Finally, we note that all frequency switching takes place in a single spatial mode (nonlinear fiber/waveguide), as shown in Fig. 1c. As additional channels only require additional BSFWM pumps, no scaling losses are introduced in the path of the single photons.
To understand clearly the characteristics of our frequency multiplexing scheme, we analyze how the performance scales with increasing N. Several architectures have been explored for active N × 1 switching of photons in spatial and temporal multiplexing schemes. Typically, these architectures use 2 × 2 switches as building blocks for a general N × 1 switch. We compare the performance of the fixedloss scheme with the logtree network which is generally used for spatial multiplexing and multipass binary switches (or storage cavities) generally used in temporal multiplexing^{30,31}. An N × 1 logtree network has a depth \(\lceil\log_{2} N \rceil\). Assuming a switching efficiency of η_{s} per switch, the losses scale as \(\eta_{s}^{\lceil \log_{2}N \rceil}\)^{39}. The losses from multipass binary switching scale exponentially as \(\eta _{\rm{s}}^N\) in the worst case, but we consider an optimized implementation as in ref. ^{31}. For our fixedloss scheme, the switching losses are η_{s} irrespective of N.
Figure 2a shows the scaling performance of various schemes. We assume a switching efficiency η_{s} = 0.85 (0.7 dB loss) per switch and all other components, including detectors, are assumed to be ideal. We optimize the emission probability per source p_{single}(n = 1) for each N (Supplementary Note 2). The maximum heralding probability for a single source (N = 1) is 0.25. For both logtree and multipass schemes, the single photon probability reaches a maximum of 0.41 and 0.50, respectively, and saturates due to switching losses for less than N = 10 multiplexed sources. In contrast, for the fixedloss scheme, additional multiplexed sources always result in an improvement in the singlephoton heralding probability, with a heralding probability of 0.60 for N = 10 sources. For N = 40 sources, the fixedloss scheme achieves p_{mux}(n = 1) = 0.75, compared with a maximum of 0.89 with a noloss ideal switching network. Our scheme therefore has an advantage in the intermediate regime of 10 to 20 multiplexed modes as well as asymptotically for large N. In order to quantify the effects of practical variability in switching efficiency in implementations of multiplexed sources, we analyze the sensitivity of different schemes to switching losses in Fig. 2b. For a moderate increase in losses to 1.2 dB per switch and 30 multiplexed modes (η_{s} = 0.75, N = 30), the singlephoton probability drops significantly from 0.86 (η_{s} = 1) to 0.21, 0.29 for the logtree and multipass schemes, but is reduced only moderately to 0.65 for the fixedloss scheme. Thus, the frequency multiplexing scheme is significantly more robust to switching losses as compared to competing switching architectures in other multiplexed sources.
Experimental setup
We experimentally demonstrate multiplexing of three frequency modes. Figure 3 shows our experimental setup. Our multiplexed source is based on broadband SPDC in a periodically poled lithiumniobate crystal (PPLN) pumped with a 543nm CWlaser, generating photon pairs at 940 nm (heralding photons) and 1280 nm (heralded signal photons). The heralding photons are sent to a filtering setup consisting of reflecting Bragg gratings (RBG), creating three channels CH0, CH1, CH2 with heralding photons at ω_{h,0}, ω_{h,1}, ω_{h,2}, respectively, with 100GHz bandwidth (Supplementary Note 3). Each channel is collected into a singlemode fiber and sent to a silicon avalanche singlephoton detector (APD), which provides heralding information to the logic circuit. The source crystal temperature is tuned to maximize photon pair production at ω_{1} = 1280.65 nm and ω_{2} = 1280.1 nm, and the pair production at ω_{0} = 1284.45 nm is lower by a factor of 0.65. The heralded signal photons {ω_{0} = 1284.45 nm, ω_{1} = 1280.65 nm, ω_{2} = 1280.1 nm} are injected into the multiplexing setup, comprised of a 100m nonlinear fiber, wavelengthdivisionmultiplexing couplers and a pump filter. A single channel centered at ω_{t} = 1284.45 nm and 100 GHz wide, is selected with a tunable grating and then sent to a superconducting nanowire singlephoton detector (SNSPD) with a quantum efficiency of 53%.
The nonlinear process of BSFWM is driven by two pump waves generated by distributed feedback lasers diodes, which determine the frequency shift and hence the input and output frequency channels. The diodes are driven with a 5nslong pulsed current source, and the optical pulses (for convenience aligned to the Cband ITU grid) are amplified to a peak level of 10 W via cascaded erbiumdoped fiber amplifiers (EDFA). The pump pulses are combined together, temporally synchronized and aligned in polarization. In order to achieve fast switching operations, we utilize lasers at predetermined wavelengths that are selectively turned on and off via a fast logic circuit controlled by a field programmable gate array (FPGA) (see inset in Fig. 3). We measure the conversion efficiency for both process ω_{1} → ω_{t} and ω_{2} → ω_{t} to be 93% (Supplementary Note 1).
Singlephoton rate
We first characterize the singlephoton rates as functions of SPDC pump power for each individual channel and for the multiplexed source, as shown in Fig. 4a. The multiplexed (MUX) source has an enhanced coincidence rate by 4.8 dB as compared to the mean photon rate of the individual channels. This enhancement significantly overcomes the losses of the setup (1.3 dB), resulting in a net enhancement of 3.5 dB (220%) in the singlephoton rate. At maximum SPDC pump power (25 mW), we measure a heralding rate of 1 MHz with a brightness of 23 kHz detected coincidences per second. We estimate a singlephoton generation rate of 46 kHz after correcting for detector efficiency (3 dB). Supplementary Note 4 provides detailed characterization of the system efficiency and losses. We note that although simply increasing the pump power of the SPDC source can increase the singlephoton generation rate of a single source, this would lead to increased multiphoton generation.
Coincidencestoaccidentals ratio
We measure the coincidencestoaccidentals ratio (CAR), a standard figure of merit to characterize the multiphoton generation of parametric sources. Figure 4b compares the CAR for the multiplexed source and each individual channel. For fair comparison we also measure the coincidence rate and CAR at ω_{t}, directly from the SPDC source, without the multiplexing setup in place (referred to as the NoMUX source). We operate in a regime in which the singlephoton count rate is much higher than the darkcount rate of the detectors, and therefore the accidental counts are dominated by multiphoton generation, which is inversely proportional to the SPDC pump power. The multiplexed source has a CAR that is a factor of 2 higher throughout as compared to the NoMUX source. For low count rates, the multiplexed source has a CAR exceeding 1000 and remains high at 100 at the maximum count rate. These measurements confirm that the strong classical pumps used in BSFWM do not introduce significant spurious noise photons even at a high pump trigger rate of 1 MHz.
Singlephoton purity
Finally, we measure the purity of the photons from the multiplexed source by the secondorder correlation function \(g^{(2)} = \left\langle {\hat N_{\mathrm{a}}\hat N_{\mathrm{b}}} \right\rangle /\left\langle {\hat N_{\mathrm{a}}} \right\rangle \left\langle {\hat N_{\mathrm{b}}} \right\rangle\) where \(\hat N_{\mathrm{a}}\) and \(\hat N_{\mathrm{b}}\) are photon number operators corresponding to the two arms of a HanburyBrown–Twiss setup^{40}. Figure 4c shows the measured g^{(2)}(0) for the multiplexed source and the NoMUX source, for various singlephoton rates. At the maximum count rate, the multiplexed source has a low g^{(2)}(0) of 0.07 ± 0.005. For the same low singlephoton rate of 5.6 kHz, the multiplexed source and the NoMUX source have g^{(2)}(0) of 0.015 ± 0.002 and 0.056 ± 0.005 respectively. The average SPDC pump power required to achieve the same photon rate is a factor of 3 lower for the multiplexed source as compared to the NoMUX source, and therefore has significantly reduced multiphoton generation. The improved single photon purity of the multiplexed source is therefore a strong indicator of successful multiplexing.
The performance of our frequency multiplexed source is comparable with the best multiplexed source demonstrated todate which implements temporal multiplexing on a freespace optics platform^{31}. A complete comparison with other relevant works has been included in Supplementary Note 5. We achieve a singlephoton generation rate of 46 kHz with an ultralow g^{(2)}(0) of 0.07, compared with previously demonstrated 19.3 kHz with a high g^{(2)}(0) of 0.48^{31}. Due to the low loss of our frequency switch (1.3 dB), we achieve a multiplexing enhancement factor of 2.2 with just three frequency modes. We measure a raw heralding efficiency of 2.3% and detectorcorrected efficiency of 4.6%. This efficiency is mainly limited by the fibercollection and spectral filtering loss at the SPDC source and is independent of our “frequency switching” setup. Collection efficiencies as high as 90% can be achieved by minimizing all transmission and filtering losses, and careful modematching, which would correspond to an order of magnitude improvement in the singlephoton generation rates^{9,41}. Another important figure of merit for comparing the different multiplexing implementations is the maximum possible switching speed. In principle, our alloptical frequency switch allows for efficient conversion with repetition rates as high as the inverse of the BSFWM acceptance bandwidth (100 GHz in this system). Our current implementation can support a repetition rate of 5 MHz and is only limited by the amplification required for the BSFWM pumps. This amplification requirement can be reduced by increasing the BSFWM interaction length or using highly nonlinear fibers as the interaction medium, enabling significantly higher repetition rates.
Pulsed operation and scaling
In order to approach deterministic photon generation, pulsed operation together with a large number of multiplexed modes is necessary. Our system supports pulsed operation at high repetition rates. The efficiency of our “frequency switch” is partially limited to 93% due to the fluctuations in BSFWM pump power induced by the randomized trigger arising from CW operation of the singlephoton source. We measure efficiencies as high as 95% using the same setup with periodic pump triggering. In Fig. 5 we show that BSFWM remains efficient over ten frequency modes by tuning the frequency shift Δω between the input and target frequency from 700 GHz (CH1) to 1700 GHz (CH11). This is achieved by shifting one pump by over 1 THz in steps of 200 GHz and tuning the other pump by a small amount (<10 GHz) such that phase matching remains optimal at the target frequency ω_{t} (1284.45 nm). The frequency conversion efficiency is maintained at 95% while the acceptance bandwidth reduces by a factor of 2 due to effects of higher order dispersion (Supplementary Note 6). We summarize the predicted scaling performance of our system in Table 1. With just ten multiplexed modes, we expect that our system can achieve a singlephoton heralding probability exceeding 50% (per input pump pulse) with a singlephoton generation rate of 2.5 MHz (Supplementary Note 6).
Generation of indistinguishable photons
In addition to high brightness and purity, the generation of highly indistinguishable photons is critical to many quantum protocols. Due to CW operation and the highly nondegenerate nature of our downconversion source, a demonstration of indistinguishability through quantum interference of consecutive photons is beyond our current experimental setup. However, we have previously demonstrated HongOuMandel interference between photons of different frequencies using BSFWM as a frequency beamsplitter, indicating that the two photons are rendered indistinguishable after interaction^{42}. Since our scheme uses narrow filtering, we can generate indistinguishable photons using a pulsed pump with the downconversion phasematching bandwidth matched to the filtering bandwidth. For example, using a short 1 mm PPLN crystal with 100 GHz channel filtering results in an expected indistinguishability of 89% (Supplementary Note 7). However, using a shorter crystal will inevitably reduce the brightness of the photon source. This tradeoff can be overcome using microresonatorbased photon sources based on cavityenhanced spontaneous fourwave mixing. By matching the spectral linewidth of the pump pulse to the resonator linewidth, it is possible to generate discrete uncorrelated joint spectral amplitudes with an expected indistinguishability of 92%^{43}. Moreover, using advanced interferometric coupling, the effective pump resonance linewidth can be broadened to generate fully unentangled photon pairs with an expected indistinguishability of more than 99%^{44,45}. Therefore, using microresonator based sources together with frequency multiplexing, it is possible to generate indistinguishable photons in pure spectral and temporal modes.
Discussion
We have demonstrated a frequency multiplexed source with three modes, using highly efficient lownoise quantum frequency translation. We emphasize that adding additional channels adds complexity only to the BSFWM pump configuration, and no new components need to be added in the path of the single photons. This ensures that losses remain independent of the number of multiplexed modes. The single spatial mode operation of frequency switching maintains relative polarization stability of photons from different channels from generation to detection, ensuring that the photons are rendered indistinguishable after frequency translation. We note that recently, multiple research groups have proposed the use of frequency multiplexing as a resource for both continuous variable^{46,47} and circuitbased singlephoton QIP applications^{48,49}. These proposals emphasize the strong potential of frequency multiplexing for addressing the scaling losses and resource overheads in quantum systems. However, most proposals rely on electrooptic modulators (EOMs) to frequency translate single photons. Recent work^{50} discusses a spectrally multiplexed singlephoton source using EOMs, but no enhancement in the singlephoton rate is demonstrated due to high system losses. In addition, EOMs typically have a limited timebandwidth product close to unity, limiting the maximum frequency shift and the bandwidth of the target pulses. This significantly limits practical implementations to a few frequency modes while exacerbating photon loss due to narrow filtering. Alternatively, our implementation of BSFWM allows for tunable conversion over 1 THz with an acceptance bandwidth of 100 GHz with few nanosecond pump pulses, which addresses these issues. BSFWM is fully compatible with the existing optical telecommunication architecture that harnesses DWDM. The applications of such lowloss high repetition rate frequency multiplexing go beyond singlephoton sources and can prove to be highly advantageous for allphotonic quantum repeaters that rely on active feedforward heralding signals^{51}. Our scheme is also entirely adaptable to monolithic CMOScompatible integrated platforms. In particular, integrated comb sources where photons are already confined in welldefined frequency bins can eliminate the need for filtering^{17,18,19} while generating spectrally pure photons^{43}. Thermal tuning using integrated heaters can be used to precisely control and stabilize the microring resonance. Moreover, implementations of BSFWM in nanophotonic waveguides can significantly reduce pump power and amplification requirements^{52} while dispersion engineering can provide flexible phasematching conditions. The higher loss tolerance of frequency multiplexing makes it an ideal choice for integrated multiplexed sources as compared to other schemes which require free space optics to maintain low loss. The precision, flexibility and repeatability offered by integration will be critical for future quantum networks which will require thousands of identical photon sources operating simultaneously. Frequency multiplexing can thus uniquely harness both fiber and integrated technologies optimized for classical applications to address challenges of scalability in quantum technologies.
Data availability
All data generated and/or analyzed during this study are available from the corresponding author on reasonable request.
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Acknowledgements
This work was funded by the National Science Foundation under Grants PHY1404300 and EFMA1641094. S.C. acknowledges the F.R.S.FNRS for financial support. S.R. acknowledges funding by the DFG (Emmy Noether Program). We thank Aseema Mohanty for useful comments on the manuscript.
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Affiliations
Department of Applied Physics and Applied Math, Columbia University, New York, NY, 10027, USA
 Chaitali Joshi
 , Alessandro Farsi
 & Alexander L. Gaeta
Applied and Engineering Physics, Cornell University, Ithaca, NY, 14850, USA
 Chaitali Joshi
Laboratoire d’ Information Quantique, Université Libre de Bruxelles, Bruxelles, 1050, Belgium
 Stéphane Clemmen
Institut für Physik, HumboldtUniversität zu Berlin, Berlin, 12489, Germany
 Sven Ramelow
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Contributions
S.C. conceived the idea and performed initial theoretical and experimental groundwork. C.J., A.F. and S.R. implemented the experiment. C.J. and A.F. performed the experiment, collected, and analyzed the data. All authors contributed to interpreting the data. C.J. and A.F. prepared the manuscript in consultation with all authors. A.L.G. supervised the project.
Competing interests
The authors declare no competing financial interests.
Corresponding author
Correspondence to Alexander L. Gaeta.
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1.
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