Effects of Rashba spin-orbit coupling, Zeeman splitting and gyrotropy in   two-dimensional cavity polaritons under the influence of the Landau   quantization
  GaAs-type quantum wells (QWs) with p-type valence band embedded into the resonators. The Landau quantization of the electrons and heavy-holes (hh) was investigated taking into account the Rashba spin-orbit coupling with third-order chirality terms for hh and with nonparabolicity terms in their dispersion low including the Zeeman splitting (ZS) effects. The exact solutions for the eigenfunctions and eigenenergies were obtained using the Rashba method [1]. We derive in the second quantization representation the Hamiltonians describing the Coulomb electron-electron and the electron-radiation interactions and determine the magnetoexciton energy branches and the magnetoexciton-photon interaction. The fifth order dispersion equation describing the energy spectrum of the cavity magnetoexciton-polariton is investigated. It takes into account the interaction of the cavity photons with two dipole-active and with two quadrupole-active 2D magnetoexciton energy branches. The cavity photons have the circular polarizations oriented along their wave vectors, which has the quantized longitudinal component. The selection rules of the exciton-photon interaction is expressed through the scalar products of the two-types circular polarizations and it is related with the numbers of the LQ levels of electrons and heavy-holes. It is shown that the Rabi frequency of the polariton branches and the magnetoexciton oscillator strength increase in dependence on the magnetic field strength. The optical gyrotropy effects may be revealed if changing the sign of the photon circular polarization at a given sign of the wave vector longitudinal projection or equivalently changing the sign of the longitudinal projection at the same selected light circular polarization. 
Sveatoslav A. Moskalenko, Igor V. Podlesny, Evgheni V. Dumanov and   Michael A. Liberman
cond-mat.quant-gas