A Quantum Walk Model for Describing the Energy Transfer of a Dressed Photon
(Submitted on 2 September 2021, Uploaded on 3 September 2021)
keywords: dressed photon, phonon, quantum walk, dissipation
This paper presents a quantum walk (QW) model for describing the spatio-temporal behavior of dressed photons (DPs). A three-row vector is used to simultaneously deal with two counter-travelling DPs and a phonon for deriving the probability amplitude of a dressed-photon–phonon (DPP). As the first step, an infinite-sized two-dimensional lattice is assumed to derive spatio-temporal difference equations for this amplitude. Subsequently, a finite-sized two-dimensional lattice is used to install a singularity that serves as an output port. Spatio-temporal difference equations are derived to describe the behavior of the DPP not only inside, but also at the borders and at the corners of the lattice. As the next step, a three-dimensional model is introduced for a more realistic comparison with experimental results. Eighteen combined paths of the DP hopping in the forward-upper and backward-lower directions are regarded as modes 1-18. It is found to be sufficient to study the spatio-temporal behavior of mode 1. Three-dimensional cubes used for this model are transformed to two-dimensional right triangles, and spatio-temporal difference equations are successfully derived.
The copyright holder for this preprint is the author. It is made available under a CC-BY-NC-ND 4.0 International license.
Research Origin for Dressed Photon,3-13-19 Moriya-cho, Kanagawa-ku, Yokohama, Kanagawa 221-0022 Japan