Abstract

The evolution of an excitation propagating through a discrete lattice shows common features regardless of the physical nature of the underlying system. Provided that a linearly growing potential is applied Bloch oscillations are observed in semiconductor superlattices,¹ in Bose condensates trapped in optical potentials,² on molecular chains³ or in optical waveguide arrays⁴ etc. These systems have in common that their eigensolutions are localized and that the corresponding eigenvalues are evenly spaced (Wannier-Stark states).⁵ Therefore every excitation results in a periodic motion (Bloch oscillations). Until know exact expressions for higher dimensional lattices have only been found for the simple cubic case without diagonal interaction, which separates into orthogonal 1D systems.

© 1999 Optical Society of America