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 (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.

Optical waveguide arrays: quantum effects and PT symmetry breaking

“…However, panels (b) and (d) show that the intensity correlation function g(r) = g(−r) cannot distinguish between the two. Thus, symmetry properties of the disorder-induced spectrum are reflected in the disorder-averaged intensity correlation function, and not the on-site or off-diagonal nature of disorder [67]. These results also suggest that although intensity distribution, or intensity correlation function is insensitive to the disorder distribution function, higher order intensity correlations may encode signatures of different disorder distributions that have zero mean and identical variance [16,66].…”

“…However, panels (b) and (d) show that the intensity correlation function g(r) = g(−r) cannot distinguish between the two. Thus, symmetry properties of the disorder-induced spectrum are reflected in the disorder-averaged intensity correlation function, and not the on-site or off-diagonal nature of disorder [60].…”

“…The bottom panel (α = 2) shows a qualitatively similar result. Thus, a position-dependent, parity-symmetric tunneling in a finite array of waveguides leads to effective localization at two waveguide locations, even if the initial wave packet is introduced in a single waveguide [67].…”

Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization

“…Therefore, its non-unitary time evolution has bounded intensity oscillations and at long times Jt 1, it leads to a quasi steady-state intensity profile I d (k) with constant total intensity ∑ k I d (k) > 1. 4,30 When γ > γ min , for a fraction of the M 1 disorder realizations, the system is in the PT -broken phase where the total intensity increases exponentially with time as does the intensity in the neighborhood of the gain site m 0 . As a result, the disorder-averaged intensity I d (k,t) develops a peak at the gain site m 0 whose weight increases with time.…”

“…A straightforward way to salvage the fragile PT -symmetric phase is to require a PT -symmetric disorder. 30 However, this approach imposes highly non-local correlations on the randomness and is therefore difficult to implement, even with an engineered disorder. Thus questions about localization and PT -symmetry breaking in a disordered PT -symmetric system appear moot.…”