Strongly Driven Quantum Wells: An Analytical Solution to the Time-Dependent Schrödinger Equation

An analytical solution is found for the lowest Floquet state in a single quantum well which is strongly driven by an external laser field of form $\mathrm{eFz}\cos \omega t$. The spectral weights of the photon sidebands vary in a highly nonlinear fashion with $F$, exhibiting strong quenchings close to roots of the Bessel functions $J_n(k_{0}eF/m{\omega }^2)$, where $n$ is the sideband index and $k_0$ is the wave vector of the centerband resonance. The ${\omega }^{-2\mathrm{}}$ scaling behavior of the roots is qualitatively different from the ${\omega }^{-1\mathrm{}}$ dependence found in the coherent miniband transport in superlattices.