Disorder effects in tunable waveguide arrays with parity-symmetric tunneling

Abstract: We investigate the effects of disorder on single particle time-evolution and two-particle correlations in an array of evanescently coupled waveguides with position-dependent tunneling rates. In the clean limit, the energy spectrum of such an array is widely tunable. In the presence of a Hermitian on-site or tunneling disorder, we find that the localization of a wave packet is highly sensitive to this energy spectrum. In particular, for an input confined to a single waveguide, we show that the fraction of light localized to the original waveguide depends on the tunneling profile. We compare the two-particle intensity correlations in the presence of Hermitian, tunneling disorder and non-Hermitian, parity-and-time-reversal ($\mathcal{PT}$) symmetric, on-site potential disorder. We show the two-particle correlation function in both cases is qualitatively similar, since both disorders preserve the particle-hole symmetric nature of the energy spectrum.