Ardiley Torres Avelar

We study stationary, spatially localized modes in linearly coupled optical waveguides governed by coupled nonlinear Schrödinger equations with asymmetric defocusing Kerr nonlinearities. A waveguide with spatially inhomogeneous nonlinearity supports self-trapped states, whereas a homogeneous defocusing waveguide cannot localize on its own. We show that linear coupling induces localization in the nonlocalizing guide. Fundamental and excited stationary modes are computed, and their existence, power asymmetry, and stability are analyzed as functions of the coupling strength and nonlinearity. Dynamical simulations reveal stable ground and first excited states, whereas higher-order modes are unstable. These results demonstrate coupling-induced spatial localization in defocusing nonlinear waveguide systems.

In this work, we propose a quantum key distribution protocol using the polarization and transverse spatial degrees of freedom of single photons. We show that the protocol is secure and easy to implement experimentally, thus being able to be used in investigations on optical communication. In addition, we show that the information transmitted between two separate parties is always greater than the information retained by a eavesdropper. In this way, it is always possible to employ classical error correction and privacy amplification to minimize eavesdropper information.

The causality issues concerning the localization of relativistic quantum systems, as evidenced by Hegerfeld's paradox, are addressed through a proper-time relativistic formalism of single-particle operators. Starting from the premise that physical variables associated with the proper-time gauge have a prominent role in the specification of position, since they do not depend on classical parameters connected to an external observer, we obtain a single-particle formalism in which localization is described by explicitly covariant four-vector operators associated with POVM measurements parametrized by the system's proper time. Among the consequences of this result, we emphasize that physically acceptable states are necessarily associated with the existence of a temporal uncertainty and their proper-time evolution is not subject to the causality violation predicted by Hegerfeldt.

Von Zuben [J. Math. Phys. 41, 6093 (2000)] proposed a resolution to spatial localization problems related to Hegerfeldt’s paradox. To do so, he applied Dirac’s formalism to a free spinless massive particle to introduce a new perspective in which this paradox could be interpreted as an apparent phenomenon. However, although being a physically interesting proposal, here we show that its main result was obtained using an incomplete basis for the physical Hilbert space, the correction of which invalidates the proposed resolution.