Excitons and Microcavity Polaritons in Coupled Quantum Wells
We have recently developed an accurate theory of excitons in coupled quantum wells (CQWs) in an applied electric field.
The optical properties of such CQW structures have been the subject of intensive studies by several groups around the world. In a CQW, the electron (hole) wave function is distributed between two wells. Applying an external electric field one can change the electron tunelling through the barrier. Thus the exciton and polariton properties are efficiently tunable by changing the electric field. They show remarkable anticrossing behaviour and redistribution of the dipole moment.
Our approach is based on expanding the exciton wave function into electron-hole pair states and solving a radial matrix Schroedinger equation in the real space. The calculated exciton energies and wave functions are then used in the nonlocal dielectric constant contributing to the Maxwell equation which we solve using the scattering matrix method.
The exciton ground state experiences a crossover as the electric field increases, changing from direct to indirect exciton. This is well seen in the absorption spectrum of a symmetric 8-4-8nm AlGaAs CQW. At the same time, the brightest excited state remains almost unchanged in a wide range of applied voltages, since this state is Coulomb decoupled from the ground state. Such a bright decoupled state is absent in the spectrum of an asymmetric CQW structure which being placed inside a microcavity turns out to be a more suitable for having control over strong exciton-photon coupling.
To demonstrate the tunable light-matter coupling, we study a system of 4 asymmetric InGaAs CQWs inside a microcavity. Excitonic states are optically coupled to the cavity mode producing exciton polaritons. Reflectivity spectra show in electric field multiple avoided crossings demonstrating strong exciton-photon coupling and its efficient on/off switching using the applied voltage.
At normal incidence, the cavity mode is weakly coupled to exciton states: the red vertical line (bare cavity mode) almost coincide with the narrow line (polariton mode). At non-normal incidence (35 degrees) the cavity mode is in resonance with both direct and indirect (ground and excited) exciton states producing 3 distinct polariton lines in the absorption.
Remarkably, the ground polariton state is a combination of the cavity mode, bright direct exciton and dark indirect exciton. The latter has a large electric dipolar moment which is responsible for the exciton dipole-dipole repulsion. The fraction of the indirect exciton changes with the applied voltage. Thus, by simply changing the electric field one can effectively manipulate the interaction between microcavity polaritons.
We have provided freely available on-line software, which calculates the exciton energies, wave functions, oscillator strength and absorption spectrum in different CQWs in an applied electric field. The software has been developed by Kanchana Sivalertporn and Roger Philp.
- Sivalertporn, K. et al. 2012. Direct and indirect excitons in semiconductor coupled quantum wells in an applied electric field. Physical Review B: Condensed Matter and Materials Physics 85 (4) 45207. (10.1103/PhysRevB.85.045207)