Quantum trajectories for a system interacting with environment in n-photon state

Anita Dąbrowska, Gniewomir Sarbicki, Dariusz Chruściński

Published 2018-08-22Version 1

We derive stochastic master equation for a quantum system interacting with an environment prepared in a continuous-mode $n$-photon state. To determine the conditional evolution of the quantum system depending on the continuous in time measurements of the output field we apply the model of repeated interactions and measurements with the environment given as an infinite chain of harmonic oscillators which do not interact between themselves and they are prepared initially in an entangled state being a discrete analogue of a continuous-mode $n$-photon state. We derive the continuous in time conditional evolution of the quantum system starting from determination of discrete in time recurrence equations. We present not only the quantum trajectories but also the analytical formulas for the whole statistics of the output photons and the solution to the master equation. The solution in the continuous case is represented by a simple diagrammatic technique with very transparent "Feynmann rules". This technique considerably simplifies the structure of the solution and enables one to find physical interpretation for the solution in terms of a few elementary processes.