Phase-space distribution functions for photon propagation in waveguides coupled to a qubit

摘要

We investigate propagation of few-photon pulses in waveguides coupled to a two-level system by means of thenmethod of distribution functions in coordinate-momentum space that provides a detailed description of photonnsystems. We find that the distribution function of the transmitted pulse can be negative for the nonclassicalninput (i.e., single-photon Fock state). This reveals the quasiprobability nature of photon distribution. Analyticalnexpressions for photon densities in the momentum space as well as in the coordinate space are obtained for thenmentioned single-photon Gaussian input. We also study the evolution of the multimode coherent-state input fornan arbitrary photon number. Time-dependent differential equations describing average densities and fluctuationsnof outgoing photons are derived and solved. The influence of the number of input photons, pulse width, andnradiation-atom interaction strength on the statistical properties of the fluctuations is investigated.