Number-State Reconstruction with a Single Single-Photon Avalanche Detector

TL;DR

This paper introduces a cost-effective, single-detector method for reconstructing photon number states using maximum-likelihood techniques, enabling accurate measurement of photon numbers up to 10 with a single SPAD.

Contribution

The authors develop a novel methodology for photon number-state reconstruction using only one SPAD, simplifying and reducing the cost of quantum light measurement setups.

Findings

Accurate reconstruction of photon numbers up to approximately 10 photons.

Effective for high photon rates exceeding 40 million counts per second.

Consistent measurement of $g^{(2)}(0)$ for anti-bunched light.

Abstract

Single-photon avalanche detectors (SPADs) are crucial sensors of light for many fields and applications. However, they are not able to resolve photon number, so typically more complex and more expensive experimental setups or devices must be used to measure the number of photons in a pulse. Here, we present a methodology for performing photon number-state reconstruction with only one SPAD. The methodology, which is cost-effective and easy to implement, uses maximum-likelihood techniques with a detector model whose parameters are measurable. We achieve excellent agreement between known input pulses and their reconstructions for coherent states with up to $\approx$ 10 photons and peak input photon rates up to several Mcounts/s. When detector imperfections are small, we maintain good agreement for coherent pulses with peak input photon rates of over 40 Mcounts/s, greater than one photon per detector dead time. For anti-bunched light, the reconstructed and independently measured pulse-averaged values of $g^{(2)}(0)$ are also consistent with one another. Our algorithm is applicable to light pulses whose pulse width and correlation time scales are both at least a few detector dead times. These results, achieved with single commercially available SPADs, provide an inexpensive number-state reconstruction method and expand the capabilities of single-photon detectors.