Theory of coherent optical nonlinearities of intersubband transitions in semiconductor quantum wells

TL;DR

This paper models the coherent nonlinear optical response of electrons in semiconductor quantum wells near intersubband resonances, revealing intensity-dependent frequency shifts and discussing implications for quantum optics applications.

Contribution

It introduces a theoretical framework based on the Schrödinger-Poisson equation to analyze nonlinearities in intersubband transitions, including analytical interpretations and relevance to experimental phenomena.

Findings

Redshift of resonance frequency with increasing intensity

Suppression of depolarization shift at high intensities

Estimation of optical nonlinearity strength across mid-IR to THz

Abstract

We theoretically study the coherent nonlinear response of electrons confined in semiconductor quantum wells under the effect of an electromagnetic radiation close to resonance with an intersubband transition. Our approach is based on the time-dependent Schr\"odinger-Poisson equation stemming from a Hartree description of Coulomb-interacting electrons. This equation is solved by standard numerical tools and the results are interpreted in terms of approximated analytical formulas. For growing intensity, we observe a redshift of the effective resonance frequency due to the reduction of the electric dipole moment and the corresponding suppression of the depolarization shift. The competition between coherent nonlinearities and incoherent saturation effects is discussed. The strength of the resulting optical nonlinearity is estimated across different frequency ranges from mid-IR to THz with an eye to ongoing experiments on Bose-Einstein condensation of intersubband polaritons and to the speculative exploration of quantum optical phenomena such as single-photon emission in the mid-IR and THz windows.