Manifestation of anomalous Floquet states with longevity in dynamic fractional Stark ladder with high AC electric fields

We examine a resonance structure of Floquet state in dynamic fractional Stark ladder (DFSL) realized in biased semiconductor superlattices driven by a terahertz cw laser on the basis of the R-matrix Floquet theory. To do this, we calculate an excess density of state ${\rho }^{(ex)}(E)$ corresponding to lifetime of the Floquet state with a fractional matching ratio $\eta$, where $\eta$ is the ratio of a Bloch frequency ${\mathrm{\Omega }}_B$ to a laser frequency $\omega$, namely, $\eta ={\mathrm{\Omega }}_B\mathrm{/}\omega$. The results for $\eta =3\mathrm{/}2$ demonstrate the appearance of discernibly large peaks associated with Floquet states with longevity in a region of relatively high laser-intensity. The underlying physics is discussed in terms of an analytical expression of ${\rho }^{(ex)}(E)$ and the associated Green function in which ponderomotive couplings are included in a non-perturbative way.