Probing the ladder spectrum arising from motion in a 2-D lattice driven by the in-plane constant force

The coherent interband dynamics of optically excited two-dimensional lateral surface superlattices driven by an in-plane static electric field has been investigated. The linear absorption, the spectrally-resolved pump-probe four-wave mixing signals and spatial coherent wavepacket evolution in the time-domain are obtained. When the rational condition $E_x/E_y=p/q$, with $p,q$ prime to each other, is fullfilled, it is found that $p$ peaks appear within the frequency interval $\omega_{Bx}=eE_xa/\hbar$ in both linear absorption and degenerate four-wave mixing signals. The coherent time evolution of the electron-hole pair wavepacket is that of a breathing mode, with the period $2\pi p/\omega_{Bx}$, These findings are consistent with the recent spectral results (Phys. Rev. Lett. {\bf 86}, 3116), hence providing a method for probing the coherent dynamics of quantum particles in 2D lattices.