Probing the ladder spectrum arising from motion in a two-dimensional lattice driven by in-plane constant forces

The coherent interband dynamics of optically excited two-dimensional lateral surface superlattices (quantum-dot arrays), driven by an in-plane static electric field, has been investigated. Linear absorption and a spectrally resolved four-wave mixing signals are obtained. When the rational condition $E_x{/E}_y=p/q,$ with p and q prime to each other, is fulfilled, it is found that p peaks appear within the frequency interval ${\omega }_{\mathrm{Bx}}{=eE}_{x}a/ħ$ in both linear absorption and degenerate four-wave mixing signals with different time delays. These findings are consistent with the recent spectral results [Phys. Rev. Lett. 86, 3116 $\mathrm{}\left(2001\right)\mathrm{}]$, hence providing a method for probing the coherent dynamics of quantum particles in two-dimensional lattices.