The normal procedure for numerical simulation of exponentially correlated colored noise is superseded by the novel algorithm presented here. A differential algorithm is replaced by an integral algorithm which is faster, more accurate, and permits the use of longer step sizes.

Abstract. Over the last two decades, advances in fabrication have led to significant progress in creating patterned heterostructures that support either carriers, such as electrons or holes, with specific band structure or electromagnetic waves with a given mode structure and dispersion. In this article, we review the properties of light in coupled optical waveguides that support specific energy spectra, with or without the effects of disorder, that are well-described by a Hermitian tight-binding model. We show that with a judicious choice of the initial wave packet, this system displays the characteristics of a quantum particle, including transverse photonic transport and localization, and that of a classical particle. We extend the analysis to non-Hermitian, parity and time-reversal (PT ) symmetric Hamiltonians which physically represent waveguide arrays with spatially separated, balanced absorption or amplification. We show that coupled waveguides are an ideal candidate to simulate PT -symmetric Hamiltonians and the transition from a purely real energy spectrum to a spectrum with complex conjugate eigenvalues that occurs in them.

We propose a scheme for obtaining sub-Doppler resolution for one transition of an inhomogeneously broadened, three-level atomic system, by using an intense control field at the other transition. Analytical and numerical calculations are presented to delineate the mechanism responsible for this sub-Doppler resolution, and quantify the extent to which Doppler broadening can be reduced.

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 α (k) = t 0 [k(N − k)] α/2 . Since the bandwidth and the energy-level spacings for such a lattice both depend upon α, we show that the observable properties of a wave packet, such as its spread and the relative phases of its constituents, vary dramatically as α 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.