Comments on polaron–phonon scattering theory

Nikolay N. Bogolubov, Nikolay N. Bogolubov

M. Kh. Kharrasov, И. Р. Кызыргулов, А. Т. Хусаинов

The Hubbard model augmented by the Holstein interaction of localized electrons and optical dispersionless phonons is reduced (with the help of a canonical transformation) to a model, in which there occur jumps of polarons and scattering on “impurity” scatterers, which are accompanied by jumps and scatterings of an unlimited number of phonons. This circumstance and the fact that there is a strong on-site interaction of electrons inherent in the Hubbard model, lead to the need for the formulation of a new theory of the phenomenon and the use of a diagrammatic technique. A theory of perturbations in disorder for electrons moving in the random field of “impurity” scatterers has been developed. A collective mode of the phonon cloud surrounding a polaron has been found and the influence of the processes of scattering of this mode on the energy spectrum of both localized and delocalized polarons has been established. The motion of the delocalized polarons related to their scattering is described in the approximation of chain diagrams, in which the manyparticle irreducible Green’s functions of the polaron are ignored. The electron-energy spectrum obtained consists of four subbands.

Kaushik Roy‐Choudhury, Stephen Hughes

We present a polaronic quantum optics approach for modelling electron-phonon scattering in semiconductor cavity-QED structures containing quantum dots. We demonstrate several applications of the theory and connect to a number of recent experiments.

Nikolay N. Bogolubov, Nikolay N. Bogolubov

Jan-Philipp Christ, Pit Bermes, Fabian Grusdt

We consider the ground-state properties of a lattice Bose polaron, a quasiparticle arising from the interaction between an impurity confined to an optical lattice and a surrounding homogeneous Bose-Einstein condensate hosting phononic modes. We present an extension of Wegner's and Wilson's flow equation approach, the operator-valued-flow-equation approach, which allows us to calculate the renormalized dispersion of the polaron and assess the role of two-phonon scattering processes on the dispersion. The results obtained in this way are compared to a variational mean-field approach, which will allow us to demonstrate that the flow equations behave correctly at weak coupling. We find that in certain impurity phonon interaction regimes the shape of the dispersion is significantly altered by the inclusion of two-phonon scattering events as opposed to only single-phonon scattering events. Moreover, our results predict that a polaronic bound state may emerge, which is not present in Fröhlich-type models that only consider single-phonon scattering events.

G. O. Balabanyan