# Quantum trajectories for propagating Fock states

## TL;DR

This paper develops quantum trajectory equations for systems probed by propagating Fock states of light, covering various detection schemes and generalizing to superpositions and mixtures, with illustrative examples.

## Contribution

It introduces a formalism for quantum trajectories with propagating Fock states, extending previous models to superpositions and mixtures of Fock states.

## Key findings

- Derived stochastic master equations for Fock state probes.
- Analyzed three detection schemes: photon counting, homodyne, heterodyne.
- Demonstrated formalism with multiple example scenarios.

## Abstract

We derive quantum trajectories (also known as stochastic master equations) that describe an arbitrary quantum system probed by a propagating wave packet of light prepared in a continuous-mode Fock state. We consider three detection schemes of the output light: photon counting, homodyne detection, and heterodyne detection. We generalize to input field states that are superpositions and or mixtures of Fock states and illustrate the formalism with several examples.