Two-dimensional cavity polaritons under the influence of strong perpendicular magnetic and electric fields

Abstract

The properties of two-dimensional (2D) cavity polaritons subjected to the action of strong perpendicular magnetic and electric fields giving rise to the Landau quantization (LQ) of the 2D electrons and holes accompanied by the Rashba spin-orbit coupling (RSOC) and by the Zeeman splitting (ZS) have been investigated. A strong magnetic field, where the electron and the hole cyclotron energy frequencies are greater than the binding energy of the 2D Wannier-Mott excitons, completely reconstructs it transforming into a magnetoexciton, the structure of which is determined by the Lorentz force rather than by the Coulomb electronhole (eh) interaction. We predict drastic changes in the optical properties of the cavity polaritons including those in the state of Bose-Einstein condensation. The main of them is the existence of a multitude of the polariton energy levels closely adjacent on the energy scale, their origin being related with the LQ of the electrons and holes. Most of these levels exhibit nonmonotonous dependences on magnetic field strength B with overlapping and intersections. More so, the selection rules for the band-to-band optical quantum transitions, as well as the quantum transitions from the ground state of the crystal to the magnetoexciton states, essentially depend on numbers ne and nh of the LQ levels of the eh pair forming the magnetoexciton. By slowly changing the external magnetic and electric fields, it is possible to change the lowest polariton energy level, its oscillator strength, the probability of the quantum transition, and the Rabi frequency of the polariton dispersion law. They depend on the relation between numbers ne and nh and can lead to dipole-active, quadrupole-active, or forbidden optical transitions. Our results are based on the exact solutions for the eigenfunctions and the eigenvalues of the Pauli-type Hamilonian with third order chirality terms and a nonparabolic dispersion law for heavy-holes and with first order chirality terms for electrons. They were obtained using the method proposed by Rashba [1]. We expect that these results will also determine the collective behavior of the cavity polaritons, for example, in the GaAs-type quantum wells embedded into a microcavity, which have recently revealed the phenomenon of the Bose-Einstein condensation in the state of the thermodynamic quasi-equilibrium but in the absence of a strong perpendicular magnetic field.