# Photon pair generation in a lossy microring resonator. I. Theory

## TL;DR

This paper develops a theoretical model for entangled photon pair generation in lossy microring resonators, incorporating multiple round trips and nonlinear processes, and compares it to previous models.

## Contribution

It introduces a generalized input-output formalism that accounts for circulation effects in lossy microring resonators for photon pair generation.

## Key findings

- Derived biphoton state considering cavity losses and circulation.
- Calculated generation, coincidence-to-accidental, and heralding efficiencies.
- Compared generalized model results with standard Langevin formalism.

## Abstract

We investigate entangled photon pair generation in a lossy microring resonator using an input-output formalism based on the work of Raymer and McKinstrie (Phys. Rev. A 88, 043819 (2013)) and Alsing, et al. (Phys. Rev. A 95, 053828 (2017)) that incorporates circulation factors that account for the multiple round trips of the fields within the cavity. We consider the nonlinear processes of spontaneous parametric down conversion and spontaneous four wave mixing, and we compute the generated biphoton signal-idler state from a single bus microring resonator, along with the generation, coincidence-to-accidental, and heralding efficiency rates. We compare these generalized results to those obtained by previous works employing the standard Langevin input-output formalism.