Developing a photon-number-resolving detection chain for quantum communication protocols involving mesoscopic states of light

Abstract: We present the characterization of a photon-number-resolving detection chain based on Silicon photomultipliers (SiPM) coupled to a 14 bit, 1 Gs\s digital acquisition system embedding an FPGA-based signal processing pipeline that performs real-time baseline subtraction, digital deconvolution, and charge integration. Three SiPM models manufactured by Hamamatsu are tested and compared in the mesoscopic intensity regime using both classical coherent states and quantum twin-beam states, enabling a systematic investigation of the effects of pixel pitch, pile-up, and photon detection efficiency on the detector performance.

• The paper presents a SiPM-based digital detection chain that achieves high-fidelity photon-number resolution for mesoscopic quantum communication.
• It integrates FPGA digital processing, including baseline subtraction, deconvolution, and charge integration, to accurately benchmark both coherent and twin-beam states.
• Measurements reveal resolution of over 40 photons with detailed FoM analysis underscoring optimal pixel pitch and quantum efficiency for enhanced performance.

Photon-Number-Resolving Detection Chain for Mesoscopic Quantum Communication

Introduction

The development of quantum communication protocols leveraging mesoscopic states of light necessitates detection systems with high photon-number resolution, high dynamic range, and compatibility with fast and flexible digital signal processing. Silicon photomultipliers (SiPMs), with their intrinsic photon-number-resolving (PNR) capabilities, are attractive for such applications due to their room-temperature operation, compactness, and cost-effectiveness. However, SiPMs suffer from several limitations—particularly dark count rate, optical cross-talk, and pile-up effects—which must be addressed to ensure precise photon-number statistics reconstruction in realistic quantum communication settings.

This work presents a comprehensive characterization of a digital detection chain for PNR applications, integrating three Hamamatsu SiPM models with a 14-bit, 1 GS/s FPGA-based digital acquisition system. The chain supports advanced signal processing: real-time baseline subtraction, digital deconvolution, and programmable charge integration. The system is benchmarked with both classical coherent states and quantum twin-beam (TWB) entangled states in the mesoscopic photon regime, with a systematic evaluation of pile-up, pixel-pitch, and quantum efficiency influences on the overall performance.

System Architecture and Signal Processing

The detection chain comprises three SiPM models (MPPC-S13360-1325CS, -1350CS, and S15639-1325PS) interfaced via a custom amplification and differential transmission stage to a DAQ141 digitizer. The FPGA implements an elaborate pipeline: baseline restorer, pole-zero compensation filter for ballistic deficit correction, synchronous integration with digital gate control, and real-time event-by-event data handling.

The digital domain pipeline confers reproducibility, parameter tunability, and real-time monitoring, with direct implications for parameter scanning and stability. The design is particularly suited for high-rate quantum optics experiments, eliminating analog baseline drift and allowing full software-defined operation.

Experimental Methods

Classical and quantum light states serve as test signals: phase-stabilized coherent pulses and multimode TWB entangled states generated via spontaneous parametric down-conversion pumped by a sub-ps Yb:KGW laser system. Carefully controlled delivery via multi-mode fibers ensures mode-matching to SiPM sensor dimensions and minimizes pile-up probability.

Critical metrics for validation include:

• Peak visibility and figure of merit (FoM) for PNR discrimination,
• Reconstruction and statistical fidelity of photon-number distributions,
• Noise reduction factor and correlation coefficients for entanglement quantification.

Dynamic Range and PNR Discrimination

The PNR capability extends to over 40 resolved photons under optimal conditions. Pulse-height spectra reveal that visibility ($v > 0.9$) is maintained up to approximately 15 photons, with resolvable peaks ($v > 0.1$) up to 80 (Figure 1). The FoM analysis substantiates these findings; the 25PS model, in particular, achieves FoM $\geq 1$ up to $\sim$35 peaks due to its higher gain and quantum efficiency.

(Figure 1)

Figure 1: Pulse-height spectra for coherent states at increasing mean photon numbers (top to bottom), with visibility of individual photon-number peaks demonstrating the chain's discrimination range.

The non-uniform peak separation at higher photon number indices—attributable to intrinsic SiPM nonlinearity and pile-up—does not inhibit practical photon-number resolution, provided quantitative discrimination metrics are met. The system's real-time adaptability enables compensation strategies, including linearization and post-processing corrections.

Statistical Characterization with Classical and Quantum States

Statistical accuracy is corroborated via Fano factor, correlation coefficient ($\Gamma$), and noise reduction factor ($R$) reconstructions across both classical and quantum regimes. Notably, measurements with the 50CS at higher photon numbers reveal the onset of pile-up, with the Fano factor dropping below unity—directly contravening quantum statistical predictions for TWB states—while 25CS and 25PS maintain $F \geq 1$ consistent with theory.

(Figure 2)

Figure 2: Correlation coefficient ($\Gamma$) and noise reduction factor ($R$) versus mean detected photon number, benchmarking different SiPM models in mesoscopic TWB state reconstruction.

The results emphasize that optimal SiPM selection for mesoscopic detection should prioritize minimal pixel pitch to suppress pile-up, while maximizing quantum efficiency ensures faithful entanglement signature recovery. The acquisition system demonstrates low-noise operation, enabling quantifiable photon-number statistics at mean detected photon numbers as low as 0.07, a crucial asset for high-loss quantum channels.

High-Rate PNR Operation and Fidelity

Synchronous detection at rates up to 1 MHz preserves PNR fidelity and statistical accuracy, as evidenced by FoM and infidelity analyses for coherent states. However, at 10–20 MHz, performance degrades due to amplifier limitations, manifesting as increased infidelity ($>10^{-4}$ for mean $v > 0.1$0) and super-Poissonian variance, indicative of excess noise and response cross-talk (Figure 3). No significant dark count or cross-talk-induced broadening arises at low photon counts, confirming negligible baseline noise.

(Figure 3)

Figure 3: Infidelity ($v > 0.1$1) between measured and theoretical Poissonian photon number distributions as a function of mean detected photon number at various system repetition rates.

Synchronization of the detection gate to the optical source is shown to be essential: deterministic, clock-domain-coherent operation dramatically enhances discrimination and stability.

Implications and Future Directions

This analysis verifies that SiPM-based digital PNR chains can reliably resolve mesoscopic photon statistics for quantum communications, provided pixel geometry and quantum efficiency are optimized, and that the system operates within the amplifier's dynamic range. The digital pipeline's flexibility and real-time feedback capabilities are instrumental for protocol deployment, especially in scenarios demanding rapid adaptation and monitoring (e.g., QKD channel state estimation, conditional state preparation, or quantum receiver calibration).

Limitations arising at high repetition rates are currently imposed by the amplifier's bandwidth and not the SiPM or digitizer. The authors identify replacement with a purpose-built front-end as a decisive step toward MHz–tens of MHz photon-number-resolved quantum communication, further extending practical applicability.

Conclusion

The research demonstrates that a digitally instrumented SiPM-based detection chain is capable of high-fidelity PNR detection of both classical and nonclassical mesoscopic light states suitable for advanced quantum communication protocols. The system, validated across multiple SiPM architectures, offers a robust, real-time, and scalable solution, with current limits dictated only by the analog front-end. Anticipated progress through faster amplifiers and advanced synchronization schemes should enable the integration of such chains into next-generation quantum networks, facilitating applications ranging from high-rate QKD to quantum-enhanced sensing with mesoscopic photon statistics.