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

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 2pi/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, alphaabs(omegap;omega), of optical interband transitions invoked by the monochromatic probe laser fp(t) with the frequency omegap are calculated, where the spectra are not only linear in fp(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 alpha_abs⁰(omegap;omega)[proportional][partial-derivative]alphaabs(omegap;omega)/[partial-derivative]omegap 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 Jomega (with J a nonzero integer). This anomaly also shows the unusual time dependence in the dual-time optical susceptibility associated with alpha_abs⁰(omegap;omega). Moreover, the possibility of existence of the negative absorption in the more realistic excitonic spectra is speculated