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
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