Nonlinear Response of Virtual Excitations in Semiconductor Superlattices

Abstract

There is currently a lot of interest in ultrafast modulation of optical properties of semiconductors by radiation in the transparency region.1,2 This has been stimulated by the development of ultrashort pulses, and the subsequent discovery of the Dynamical Stark Effect in semiconductor quantum wells.3 The Dynamical Stark Effect is a frequency shift of the absorption of a weak test beam in a sample illuminated by a strong pump beam with frequency below the exciton resonance. The changes in the absorption spectrum instantaneously follow the presence of the pump field. The pump field induces virtual transitions from valence to conduction states creating virtual electron-hole pairs. The time spent by electrons in the conduction band is inversely proportional to the degree of detuning of the pump frequency from the band gap. Electrons and holes are strongly correlated because of many-body effects. This results in vertex (excitonic) and self-energy (band-filling) effects. The effect of the short, strong pulse is to induce both changes in the occupation of valence and conduction states and macroscopic polarization. The presence of polarization is the main difference from the usual case of an electron-hole plasma in quasiequilibrium created by strong and long resonant pulses. In such situations the pump field enters only via changes in the density of carriers. The current investigations4–13 focused on the linear response of the semiconductor-pump-field system, measured via absorption of a weak test beam. Here we describe the nonlinear response of the semiconductor-pump-field system to the test field.