Tunable waveguide lattices with nonuniform parity-symmetric tunneling

Abstract

We investigate the single-particle time evolution and two-particle quantum correlations in a one-dimensional $N$-site lattice with a site-dependent nearest-neighbor tunneling function ${t}_{\ensuremath{\alpha}}(k)={t}_{0}[k(N\ensuremath{-}k)]{}^{\ensuremath{\alpha}/2}$. Since the bandwidth and the energy-level spacings for such a lattice both depend upon $\ensuremath{\alpha}$, we show that the observable properties of a wave packet, such as its spread and the relative phases of its constituents, vary dramatically as $\ensuremath{\alpha}$ is varied from positive to negative values. We also find that the quantum correlations are exquisitely sensitive to the form of the tunneling function. Our results suggest that arrays of waveguides with position-dependent evanescent couplings will show rich dynamics with no counterpart in present-day, traditional systems.