arXiv subjects

Jefferson Delgado-Quesada

Publications and source records attributed to Jefferson Delgado-Quesada.

3 recordsLinked to original sources

arXiv2026

Transport regimes of biphoton-state quantum walks in ordered and disordered arrays of nonlinear waveguides

A quantum walk in an ordered medium exhibits ballistic propagation. A related process is the driven quantum walk, in which the number of walkers varies along the propagation. In this work, we show that a driven quantum walk of biphoton states in an array of nonlinear waveguides does not propagate ballistically, but instead presents two transport regimes: superballistic and superdiffusive. We also study the effects of off-diagonal and diagonal disorder. In addition to the observation of Anderson localization, both types of disorder lead to the disappearance of the superballistic regime.

quant-ph↗

arXiv2025

Analytic solution to degenerate biphoton states generated in arrays of nonlinear waveguides

The arrays of nonlinear waveguides are a powerful integrated photonics platform for studying and manipulating quantum states of light. Also, they are a valuable resource for various quantum technologies. In this work, we employed a supermode approach to obtain an analytic solution to the evolution of degenerate biphoton states in arrays of nonlinear waveguides. The solution accounts for arrays of an arbitrary number of waveguides and coupling profiles. In addition, it provides an explicit analytic expression without the need of computationally-expensive steps. Actually, it only relies on the calculation of the eigenvalues and eigenvectors of the coupling matrix. In general, this needs to be performed numerically, but there are relevant instances in which analytic expressions are available. Thus, in certain cases, the procedure proposed here does not require the use of any numerical method. We analyze the general properties of the solution and show some application examples. Particularly, simple solutions that can be obtained by special symmetric injection profiles, the results for small arrays, and the properties of the propagation when only the center waveguide is pumped in a symmetric odd array. In addition, we present a proof-of-principle example on how to use the analytic solution to tackle inversion problems. That is, obtaining the initial conditions required to achieve a desired quantum state -- which is a valuable technological application. A relevant aspect of the method presented here is its scalability for large arrays due to the lack of resource-intensive steps -- both for the direct and inverse problems.

quant-ph↗

arXiv2025

Impacto del desorden en los estados cuánticos de dos fotones generados en arreglos de guías de onda no lineales

In an array of nonlinear waveguides, quantum states can be generated from classical states through spontaneous parametric down-conversion of photons. This work simulates and analyzes the effect of disorder on light propagation and its quantum correlations, implementing disorder in three system parameters: coupling, injection amplitude, and injection phase. It is determined that when light is injected into only one waveguide, disorder in the coupling increases localization and reduces dispersion. Moreover, in this case, propagation tends to remain ballistic, a characteristic feature of waveguide arrays. Conversely, disorder in the injection amplitude and phase tends to delocalize the wave function, with the latter having a more pronounced effect. Finally, it is observed that quantum correlations, obtained from the correlation matrix, are robust in the presence of disorder, particularly the null elements. -- En un arreglo de guías de onda no lineales se pueden generar estados cuánticos a partir de estados clásicos mediante la conversión paramétrica descendente espontánea de fotones. En este trabajo se simula y analiza el efecto del desorden en la propagación de la luz y sus correlaciones cuánticas, implementando desorden en tres perfiles del sistema: acoplamiento, amplitud de inyección y fase de inyección. Se determina que, cuando se inyecta solamente una guía de onda, el desorden en el acoplamiento aumenta la localización y disminuye la dispersión. Además, en este caso se preserva la propagación con tendencia a ser balística, lo cual es característico de arreglos de guías de onda. Contrariamente, el desorden en la amplitud y fase de inyección tienden a deslocalizar la función de onda, siendo el efecto mayor en el último caso. Finalmente, se observa que las correlaciones cuánticas, obtenidas a partir de la matriz de correlación, son robustas ante la presencia de desorden, en particular los elementos nulos.

quant-ph↗