Recently, waveguide lattices with non-uniform tunneling have been explored due to their myriad tunable properties, many of which arise from the extended nature of their eigenstates. Here, we investigate the dynamics, localization, and parity- and time-reversal-(PT) symmetry breaking in lattices with only localized eigenstates. We propose three families of tunneling profiles that lead to qualitatively different single-particle time evolution, and show that the effects of weak disorder contain signatures of the localized or extended nature of clean-lattice eigenstates. Our results suggest that waveguide lattices with only localized eigenstates will exhibit a wide array of phenomena that are absent in traditional systems.

http://arxiv.org/abs/1108.1402
Optics (physics.optics); Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)