Polariton-polariton scattering in microcavities: A microscopic theory

TL;DR

This paper develops a microscopic fermionic approach to analyze polariton-polariton scattering in microcavities, revealing bosonic stimulation effects and additional scattering contributions due to exciton saturation.

Contribution

It introduces a transparent fermionic derivation of polariton scattering, demonstrating bosonic stimulation and exciton saturation effects within a unified framework.

Findings

Bosonic stimulation of scattering is confirmed in the fermionic approach.

An additional scattering contribution from exciton oscillator strength saturation is identified.

Polariton scattering with opposite spins mainly involves dark excitonic states.

Abstract

We apply the fermion commutation technique for composite bosons to polariton-polariton scattering in semiconductor planar microcavities. Derivations are presented in a simple and physically transparent fashion. A procedure of orthogonolization of the initial and final two-exciton state wavefunctions is used to calculate the effective scattering matrix elements and the scattering rates. We show how the bosonic stimulation of the scattering appears in this full fermionic approach whose equivalence to the bosonization method is thus demonstrated in the regime of low exciton density. We find an additional contribution to polariton-polariton scattering due to the exciton oscillator strength saturation, which we analyze as well. We present a theory of the polariton-polariton scattering with opposite spin orientations and show that this scattering process takes place mainly via dark excitonic states. Analytical estimations of the effective scattering amplitudes are given.