Dynamic quasi-energy-band modulation and exciton effects in biased superlattices driven by a two-color far-infrared field: Disappearance of dynamic localization

Abstract

A theoretical study of the optical and electronic properties of semiconductor superlattices in ac-dc fields, termed the dynamic Wannier-Stark ladder (DWSL), is done. The biased superlattices are driven by two far-infrared fields with different frequencies and relative phase of $\ensuremath{\delta}.$ Here, the frequency of the first laser is equal to the Bloch frequency ${\ensuremath{\omega}}_{B}$ of the system under study, while that of the second laser is equal to $2{\ensuremath{\omega}}_{B}.$ Quasienergies of the DWSL are calculated based on the Floquet theorem, and the associated linear photoabsorption spectra are evaluated. For $\ensuremath{\delta}=0,$ a gourd-shaped quasi-energy structure characteristic of both dynamic localization (DL) and delocalization (DDL), similar to the usual DWSL driven by a single laser, appears. By changing the ratio of the two laser strengths, however, the width of the quasi-energy band and the locations of both DL and DDL vary noticeably. As for $\ensuremath{\delta}\ensuremath{\ne}0,$ on the other hand, band collapse and the associated DL do not necessarily follow. In fact, DL vanishes and the quasi-energy degeneracy is lifted in a certain range of $\ensuremath{\delta}.$ Just DDL remains over the entire range of the laser strength, eventually resulting in a plateaulike band structure in the linear absorption spectra. The basic physics underlying this phenomenon, which can be readily interpreted in terms of a closed analytical expression, is that all quasi-energies for given crystal momenta are out of phase with each other as a function of laser strength without converging to a single point of energy. This is a feature of this DWSL which sharply distinguishes it from a conventional DWSL generated using a single laser to drive it. Furthermore, an exciton effect is incorporated with the above noninteracting problem, so that exciton dressed states are formed. It is found that this effect gives rise to more involved quasi-energy structures and a more pronounced release of the energy degeneracy of DL, leading again to the formation of a band structure in the absorption spectra. These are exclusively due to unevenly spaced exciton energy levels.