Interacting dynamic Wannier-Stark ladder driven by a periodic pulse train

Abstract

The electronic structures of the Floquet states of the dynamic Wannier-Stark ladder (DWSL) are examined, where the DWSL is formed by driving the biased superlattices (SLs) by the periodic pulse train (PPT) with the electric field $F(t)$---with time $t$---and the temporal period $2\ensuremath{\pi}∕\ensuremath{\omega}$. For a strong $F(t)$, interminiband interactions, namely, the ac-Zener tunneling (ac-ZT), are predominantly caused in the DWSL. Such a system is termed the interacting DWSL. In order to understand the details of the Floquet states and the modulation patterns by alteration of a couple of the PPT laser parameters, the linear absorption spectra, ${\ensuremath{\alpha}}_{\mathit{abs}}({\ensuremath{\omega}}_{p};\ensuremath{\omega})$, of optical interband transitions invoked by the monochromatic probe laser ${f}_{p}(t)$ with the frequency ${\ensuremath{\omega}}_{p}$ are calculated, where the spectra are not only linear in ${f}_{p}(t)$ but also nonlinear in $F(t)$. The exciton effect is not included for the sake of simplicity. For the PPT driving with unit-pulse shapes largely deviated from the square and saw-toothed profiles, the spectra show unexpected dent structures, differing a great deal from the corresponding ac-ZT-free spectra basically similar to those of the original SLs just showing the ascending steplike structure. To deepen the understanding of this anomaly, the spectra of ${\ensuremath{\alpha}}_{\mathit{abs}}^{0}({\ensuremath{\omega}}_{p};\ensuremath{\omega})\ensuremath{\propto}\ensuremath{\partial}{\ensuremath{\alpha}}_{\mathit{abs}}({\ensuremath{\omega}}_{p};\ensuremath{\omega})∕\ensuremath{\partial}{\ensuremath{\omega}}_{p}$ are also calculated, whereby the dent structures become spectral dips showing the negative absorption. It is found that such anomalous behavior is attributed to the ac-ZT between different minibands that accompanies emission/absorption of the nonzero net number of photons with $J\ensuremath{\omega}$ (with $J$ a nonzero integer). This anomaly also shows the unusual time dependence in the dual-time optical susceptibility associated with ${\ensuremath{\alpha}}_{\mathit{abs}}^{0}({\ensuremath{\omega}}_{p};\ensuremath{\omega})$. Moreover, the possibility of existence of the negative absorption in the more realistic excitonic spectra is speculated.