# Quantum filtering for a two-level atom driven by two counter-propagating photons

## TL;DR

This paper develops quantum filtering equations for a two-level atom driven by two counter-propagating photons under continuous measurement, demonstrating how pulse shapes and coupling affect atomic excitation through simulations.

## Contribution

It introduces explicit quantum filtering equations for a two-level atom driven by two photons with different measurement setups, advancing quantum control techniques.

## Key findings

- Scaling relations between atom-photon coupling and pulse shape for excitation
- Explicit filtering equations for two measurement scenarios
- Simulations showing optimal excitation conditions

## Abstract

The purpose of this paper is to propose quantum filters for a two-level atom driven by two continuous-mode counter-propagating photons and under continuous measurements. Two scenarios of multiple measurements, 1) homodyne detection plus photodetection, and 2) two homodyne detections, are discussed. Filtering equations for both cases are derived explicitly. As demonstration, the two input photons with rising exponential and Gaussian pulse shapes are used to excite a two-level atom under two homodyne detection measurements. Simulations reveal scaling relations between atom-photon coupling and photonic pulse shape for maximum atomic excitation.