From a posteriori to a priori solutions for a two-level system interacting with a single-photon wavepacket

TL;DR

This paper derives analytical formulas for the states of a two-level atom interacting with a single-photon wavepacket, linking quantum trajectories to photon detection processes and providing key statistical measures.

Contribution

It introduces new analytical expressions for the a priori and a posteriori states of the system, connecting quantum trajectories with photon detection statistics.

Findings

Formulas for conditional and unconditional states derived

Expressions for mean photon detection number and timing provided

Links between quantum trajectories and detection processes established

Abstract

We present the analytical formulas for the conditional and unconditional states of a two-level atom interacting with a single-photon wavepacket. We express the a priori state of the system by means of the quantum trajectories related to the process of detection of photons in the output field. We give the formulas for the mean number of photons detected up to the given time and we derive the expressions for the mean time of detection of the photons.