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

摘要

Propagation of a two-photon pulse in a waveguide coupled to a two-levelsystem (TLS) is studied. The pulse is formed by two spatially separatedidentical wavepackets. A set of equations governing the dynamics of the photondistribution in the configuration-momentum space is derived and solved. It isshown that the distribution function can be negative that manifests itsquasiprobability nature. A spectrum of the reflected light is found to benarrower than that of the transmitted light that features a pronouncedfiltering effect. Average numbers of the transmitted and reflected photons andtheir variances are shown to be dependent not only on the pulse widths and thelight-TLS interaction but also on the pulse separation that can serve as aneffective controlling parameter. Our approach is generalized for the case of ann-photon Fock state.