[Paper Review] How well can superconducting nanowire single-photon detectors resolve photon number?

Timon Schapeler, Niklas Lamberty+6 more|arXiv (Cornell University)|Oct 19, 2023

Quantum Information and Cryptography25 references4 citations

TL;DR

This paper demonstrates that superconducting nanowire single-photon detectors (SNSPDs) can resolve photon numbers up to five using principal component analysis (PCA) of electrical output signals. The study identifies the rising edge and amplitude as the most informative signal features, and confirms that a time tagger measuring relative edge times achieves near-optimal photon-number resolution with sub-2 ps timing resolution, enabling multiphoton detection without detector multiplexing.

ABSTRACT

The data set consists of 1.1 million electrical output signals (traces) from a superconducting nanowire single-photon detector (SNSPD) from Single Quantum. These traces were recorded with an oscilloscope (21 GHz bandwidth, 128GSa/s) for varying incident mean photon numbers between 0.5 and 5 in steps of 0.5 photons per pulse (generated with a laser, i.e., coherent states). More information can be found in the accompanying publication.

Motivation & Objective

• To determine which features of SNSPD electrical output signals carry the most photon-number information.
• To evaluate the photon-number-resolving capability of a commercially available SNSPD without multiplexing architectures.
• To compare PCA-based analysis with a practical time tagger method for real-time photon-number discrimination.
• To quantify the confidence of photon-number readout using a statistical measure derived from Gaussian-fitted histograms.
• To establish that temporal measurements of rising and falling edges can substitute for amplitude measurements in photon-number resolution.

Proposed method

• Principal component analysis (PCA) is applied to full electrical output traces from an SNSPD to identify the dominant signal features most correlated with photon number.
• The analysis focuses on the rising edge and amplitude of the detector pulse as primary sources of photon-number information.
• A time tagger is used to record relative time differences between a trigger signal and the rising/falling edges of the SNSPD output, forming a two-dimensional histogram for classification.
• The confidence measure $ C_n = \int_{-\infty}^{\infty} \frac{p(w|n)^2 p(n)}{p(w)} dw $ is computed to quantify the probability of correct photon-number identification.
• Histograms of projected weights from PCA and time tagger data are fitted with Gaussian functions to model the distribution of responses per photon number.
• The performance of PCA and time tagger methods is compared using the confidence measure, with emphasis on timing resolution and overlap of photon-number distributions.

Experimental results

Research questions

• RQ1 Which features of the SNSPD electrical output signal carry the most information about incident photon number?
• RQ2 Can PCA of full detector traces identify optimal signal components for photon-number resolution?
• RQ3 How does the performance of a time tagger measuring edge times compare to amplitude-based or PCA-based methods in resolving photon numbers?
• RQ4 To what extent can a single SNSPD achieve unambiguous discrimination between one- and two-photon events using temporal signal features?
• RQ5 What is the maximum photon number that can be resolved with high confidence using a time tagger, and how does system jitter affect this?

Key findings

• The rising edge and amplitude of the SNSPD electrical signal contain the highest correlation with photon number, making them the most informative features for resolution.
• Unambiguous discrimination between one- and two-photon events is achieved using the PCA-based method.
• Partial photon-number resolution up to five photons is demonstrated using the PCA approach.
• The time tagger method achieves slightly higher confidence in photon-number identification than PCA, due to its sub-1.9 ps timing resolution compared to the oscilloscope’s ~8 ps resolution.
• The time tagger method effectively substitutes for amplitude measurement, enabling high-resolution photon counting with a single SNSPD.
• System jitter limits the resolution of the time tagger method, particularly for higher photon numbers, suggesting that reducing jitter would further improve performance.