Analytical approach to semiconductor Bloch equations

¹  Institut des NanoSciences de Paris, Université Pierre et Marie Curie, CNRS, Campus Boucicaut 140 rue de Lourmel, 75015 Paris, EU
²  NanoScience Technology Center and Department of Physics, University of Central Florida 12424 Research Parkway Suite 400, Orlando, FL 32826, USA

Corresponding author: Monique.Combescot@insp.jussieu.fr

Received: 10 July 2009
Accepted: 16 November 2009

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 a Hartree-Fock treatment which, in its usual form, preserves excitonic poles but loses biexcitonic resonances. ii) The resulting coupled differential equations impose 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-boson many-body theory. This allows us to obtain the time evolution of the polarization induced by a laser pulse analytically. Polarization is shown to come from Coulomb interactions between virtual excitons, but also from Coulomb-free fermion exchanges, these being dominant at large detuning.