# Quantum Networks for Single Photon Detection

## TL;DR

This paper models the initial stage of single photon detection using quantum networks of coupled states and structured continua, focusing on optimizing transmission functions for improved detection efficiency.

## Contribution

It introduces a generic quantum network framework to analyze and engineer the photon detection process before amplification, emphasizing transmission function optimization.

## Key findings

- Derived expressions for detection efficiency from transmission amplitude
- Identified parameter sets to maximize detection efficiency
- Analyzed various network configurations for tailored transmission functions

## Abstract

Single photon detection generally consists of several stages: the photon has to interact with one or more charged particles, its excitation energy will be converted into other forms of energy, and amplification to a macroscopic signal must occur, thus leading to a "click." We focus here on the part of the detection process before amplification (which we have studied in a separate publication). We discuss how networks consisting of coupled discrete quantum states and structured continua (e.g. band gaps) provide generic models for that first part of the detection process. The input to the network is a continuum (the continuum of single-photon states), the output is again a continuum describing the next irreversible step. The process of a single photon entering the network, its energy propagating through that network and finally exiting into another output continuum of modes can be described by a single dimensionless complex transmission amplitude, $T(\omega)$. We discuss how to obtain from $T(\omega)$ the photo detection efficiency, how to find sets of parameters that maximize this efficiency, as well as expressions for other input-independent quantities such as the frequency-dependent group delay and spectral bandwidth. We then study a variety of networks and discuss how to engineer different transmission functions $T(\omega)$ amenable to photo detection.