Photon-Number-Resolving Detector Based on a Cascade of Waveguide-Coupled Quantum Emitters

TL;DR

This paper proposes a photon-number-resolving detector using a cascade of waveguide-coupled quantum emitters, deriving its theoretical performance and demonstrating potential advantages over conventional detectors.

Contribution

It introduces a novel cascade-based PNR detector design, providing analytical expressions for its precision and analyzing its performance in both linear and nonlinear regimes.

Findings

The proposed detector can outperform conventional schemes under realistic conditions.

Analytical formulas for detector precision in the linear regime are derived.

Performance depends on system parameters like emitter number and coupling strength.

Abstract

We investigate the operation of a photon-number-resolving (PNR) detector consisting of a cascade of waveguide-coupled lambda-type emitters, where each waveguide-coupled emitter extracts a single photon from the input light and sends it to a single-photon detector. Using Green's function and input-output formalisms, we derive the scattering matrices and photon-photon correlators for individual scatterers. By cascading these results, we obtain a closed-form expression for the detector's precision in the linear regime and predict how correlations generated by nonlinear photon-photon interactions influence this precision. To evaluate the performance of this PNR detector in the nonlinear regime, we apply the quantum trajectory method to the cascaded setup, calculating the achievable precision and analyzing its dependence on key system parameters, such as the number of emitters and their coupling strength to the waveguide. We compare the performance of the proposed PNR detector with that of a conventional PNR scheme based on spatial demultiplexing via beamsplitters. Our results indicate that the proposed scheme can outperform conventional detectors under realistic conditions, making it a promising candidate for next-generation PNR detection.