Photon distribution function for propagation of two-photon pulses in waveguide-qubit systems

TL;DR

This paper investigates how two-photon pulses propagate in a waveguide coupled to a two-level system, revealing quasiprobability features, filtering effects, and control parameters affecting photon transmission and reflection.

Contribution

It introduces a set of equations for photon distribution in waveguide-TLS systems and generalizes the approach to n-photon Fock states, highlighting new control mechanisms.

Findings

Photon distribution function can be negative, indicating quasiprobability.

Reflected light spectrum is narrower than transmitted, showing filtering.

Pulse separation influences photon transmission and reflection, enabling control.

Abstract

Propagation of a two-photon pulse in a waveguide coupled to a two-level system (TLS) is studied. The pulse is formed by two spatially separated identical wavepackets. A set of equations governing the dynamics of the photon distribution in the configuration-momentum space is derived and solved. It is shown that the distribution function can be negative that manifests its quasiprobability nature. A spectrum of the reflected light is found to be narrower than that of the transmitted light that features a pronounced filtering effect. Average numbers of the transmitted and reflected photons and their variances are shown to be dependent not only on the pulse widths and the light-TLS interaction but also on the pulse separation that can serve as an effective controlling parameter. Our approach is generalized for the case of an n-photon Fock state.