Analytical approach to semiconductor Bloch equations

TL;DR

This paper introduces an analytical method for solving semiconductor Bloch equations by using correlated exciton pairs, simplifying calculations and revealing physics that are obscured in traditional numerical approaches.

Contribution

It develops an analytical approach based on composite-exciton many-body theory to address limitations of conventional semiconductor Bloch equations.

Findings

Analytical expressions for polarization dynamics are derived.

Coulomb interactions between virtual excitons are characterized.

Fermion exchange effects dominate at large detuning.

Abstract

Although semiconductor Bloch equations have been widely used for decades to address ultrafast optical phenomena in semiconductors, they have a few important drawbacks: (i) Coulomb terms between free electron-hole pairs require Hartree-Fock treatment which, in its usual form, preserves excitonic poles but loses biexcitonic resonances. (ii) Solving the resulting coupled differential equations imposes heavy numerics which completely hide the physics. This can be completely avoided if, instead of free electron-hole pairs, we use correlated pairs, i.e., excitons. Their interactions are easy to handle through the recently constructed composite-exciton many-body theory, which allows us to \emph{analytically} obtain the time evolution of the polarization induced by a laser pulse. This polarization comes from Coulomb interactions between virtual excitons, but also from Coulomb-free fermion exchanges, which are dominant at large detuning.