arXiv subjects

Ángel S. Sanz

Publications and source records attributed to Ángel S. Sanz.

10 recordsLinked to original sources

arXiv2026

Decoherence in matter-wave Talbot interference: A hydrodynamic probability-flow analysis

We investigate the suppression of matter-wave Talbot interference under environmentally induced decoherence. The system is modeled as an atomic beam diffracted by a periodic grating whose transverse dynamics is described within the paraxial approximation. Environmental coupling is introduced through an effective open-system model that exponentially damps spatial coherences between diffracted components, allowing a continuous interpolation between the coherent Talbot regime and the incoherent far-field diffraction limit. In addition to the usual intensity and transverse-momentum distributions, we analyze the local probability flow associated with the diffracted matter wave. The corresponding Bohmian, or hydrodynamic, representation is used here as a diagnostic tool fully equivalent to the standard quantum description, with no additional assumptions beyond the probability current of the paraxial wave field. In the present Talbot geometry, this analysis shows how decoherence progressively suppresses the carpet structure and smooths the transverse-momentum distribution, while the flow may remain organized into channels determined by the grating periodicity. The results illustrate, in a periodic matter-wave Talbot geometry, that the loss of visible interference and the degradation of the grating-defined flow-domain organization need not occur simultaneously. In particular, flux-channel structures can persist in parameter regimes where multislit interference features have already been strongly reduced. This distinction provides a local characterization of decoherence in matter-wave Talbot interferometry and complements previous trajectory-based analyses of coherence loss in simpler interference and confined geometries.

quant-ph↗

arXiv2026

Hidden transverse-flow topology in partially coherent structured light

Partial coherence is commonly viewed as a mechanism that reduces contrast or smooths intensity structure. Here we show that it can also encode hidden transverse-flow topology. Starting from the cross-spectral density, we formulate a generalized transverse flux, an effective velocity field, and the associated flux trajectories for quasi-monochromatic partially coherent paraxial beams. This construction converts two-point correlation phases into local transport information and reduces to the usual coherent energy-flow picture in the single-mode limit. Because the generalized flux is obtained through a local differential operation on the cross-spectral density, the proposed trajectories can, in principle, be reconstructed from measurements of the complex second-order coherence function, without requiring direct measurement of individual optical paths. Two analytical beam families expose this hidden topology. In twisted Gaussian Schell-model beams, a Gaussian intensity hides a distributed rotational flow with nonzero vorticity. In Laguerre-Christoffel-Darboux beams, sources with identical intensity profiles can have different flux topology, producing either spiral or purely radial trajectories. Thus, intensity and coherence magnitude do not exhaust the physical information contained in the cross-spectral density: partial coherence can reorganize the hidden topology of transverse optical transport.

physics.optics↗

arXiv2026

A geometrical-optics analogy for gravitational lensing using axicon-type lenses

Gravitational lensing is often introduced through the bending of light by mass, but its geometrical nature can be difficult to visualize without invoking the full machinery of general relativity. We present a geometrical-optics analogy in which selected lensing-like image morphologies are generated by ray tracing through axicon-type lenses. In contrast with analogies based on a spatially varying refractive index, the present model uses optical elements with a constant refractive index; the redistribution of rays is produced by the geometry of the refracting surfaces. After deriving the ray-tracing equations for a general two-surface axicon, we apply the model to conical and exponential profiles. Axially symmetric configurations generate ring-like images, misaligned incidence produces partial arcs, and broken axial symmetry leads to four-image patterns reminiscent of an Einstein cross. The model is not intended as a physical substitute for a relativistic lens equation, but as a computational and pedagogical tool for exploring how surface geometry and symmetry control ray deflection, redistribution, and image multiplicity.

gr-qc↗

arXiv2026

Nonlinear Schrödinger equations: Symmetries, superposition, and classicality from a Bohmian perspective

Interference is commonly regarded as the most direct manifestation of the superposition principle. This association is natural for the linear Schrödinger equation, where coherent alternatives combine at the level of probability amplitudes. However, the situation becomes less transparent when nonlinear couplings are present, or when the field is only partially coherent. In this work, we argue that a more robust organizing principle is provided by the local flow generated by phase variations. In this sense, phase-induced flow acts as a unifying mechanism for interference-like dynamics in nonlinear and partially coherent Schrödinger systems. The discussion is developed from a hydrodynamic, or Bohmian, perspective, understood here as a practical probing tool rather than as an additional ontology. Three representative situations are considered: interfering Bose--Einstein condensates described by the Gross--Pitaevskii equation, nonlinear Schrödinger dynamics obtained by modifying the quantum-potential contribution, and partially coherent Airy beams described through their cross-spectral density. Although these systems differ in physical origin and mathematical implementation, they share a common dynamical structure: density-related observables are shaped by velocity fields determined by phase, or ensemble-phase, information. From this viewpoint, interference-like traits, localization, self-acceleration and coherence loss can be interpreted in terms of the preservation, deformation or breaking of the symmetries displayed by the underlying flow. This provides a compact way of connecting interference, nonlinear dynamics, classicality, coherence loss, and structured-light propagation within a single trajectory-based framework.

quant-ph↗

arXiv2026

Effective skyrmion number for mixed polarization states of light

Polarization skyrmions are usually characterized through a unit Stokes vector field, which defines a map from the transverse plane to the Poincaré (Bloch) sphere and allows one to assign a skyrmion number under appropriate boundary conditions. This description assumes complete polarization. In many optical situations, however, the local polarization state is partially polarized and is therefore described by a spectral polarization matrix rather than by a single Jones vector. We formulate a density-matrix-based effective extension of the skyrmion-number construction for statistically stationary, quasi-monochromatic paraxial fields in terms of the normalized spectral polarization matrix. Its eigenvectors define two orthogonal polarization eigenstates, corresponding to antipodal points on the sphere, while the eigenvalue imbalance is fixed by the local degree of polarization $P({\bf r})$. Averaging the opposite skyrmion-density contributions of these two eigenpolarizations leads to an effective skyrmion number in which the usual pure-state density is weighted by $P({\bf r})$. The resulting quantity reduces to the conventional skyrmion number for fully polarized fields and vanishes in locally unpolarized regions. In general it is not an integer topological invariant; rather, it is an integrated effective measure, constructed from local Stokes parameters, of the skyrmionic content associated with the polarized part of a mixed optical field. We illustrate the construction with an analytic Gaussian-beam example in which a degree-one polarization texture is combined with a radially varying degree of polarization.

physics.optics↗

arXiv2026

Wavelet-based multiresolution analysis of quantum fractals in confined dynamics

Fractal structures naturally emerge in quantum systems whose initial states exhibit spatial discontinuities, a phenomenon first identified by Berry in the paradigmatic case of a particle confined in an infinite potential well. While previous analyses of quantum fractals have mainly relied on spectral decompositions and geometric scaling arguments, their quantitative characterization often depends on scale choices and truncation effects. Here we present a wavelet-based multiresolution framework that enables a direct and assumption-free quantification of quantum fractality. Fractal dimensions are extracted from the scale-dependent distribution of wavelet energies, without invoking prior power-law hypotheses. The method is applied to space and time quantum fractals arising in confined dynamics, as well as to dynamical curves generated by the associated quantum probability flux. These flux-driven trajectories provide a natural space--time parametrization of the underlying fractal structure and yield scaling properties fully consistent with Berry's predictions for space--time fractals. The resulting fractal dimensions are shown to be robust with respect to the choice of wavelet family, numerical cutoffs, and system parameters. Beyond validating earlier conjectures, the present framework offers a unified and computationally efficient tool for the multiscale analysis of quantum fractality in confined and interference-driven quantum dynamics. That is, it provides an operational, scale-adaptive criterion that unifies the characterization of space, time, and space--time quantum fractals within a single, hypothesis-free approach.

quant-ph↗

arXiv2025

Tailored Hotspots from Airy-Based Surface Plasmon Polaritons

Surface plasmons have attracted growing interest from the photonics community due to their inherent ability to controllably confine light below the diffraction limit and their direct application in trapping and transporting matter at the nanoscale. This method, known as plasmonic tweezers, employs confined fields generated by either localized plasmons or surface plasmon polaritons (SPP), which originate in the vicinity of nanostructure-based traps or across structureless platforms, respectively. Herein, we present a new theoretical method for generating intense light hotspots and engineering their features by overlapping Airy SPPs (ASPP) at a smooth dielectric-metal interface. We coherently add pairs of Hermite-Gauss modes that belong to a novel complete basis set of finite-energy ASPPs, which yield highly confined plasmonic hotspots ($\approx λ$/10) without the need of using any nanostructured platform. Mode order and relative spacing parameters can be used to tailor the intensity and quality factor of said hotspots, largely outperforming their Gaussian-only-based counterparts. Our method opens a promising venue to confine light at the nanoscale using ASPP-based structured light, which helps to advance the development of structureless plasmonic tweezers and holds promising potential for its application in optical signal processing and plasmonic circuitry.

physics.optics↗

arXiv2024

Exploring the nonclassical dynamics of the "classical" Schrödinger equation

The introduction of nonlinearities in the Schrödinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear effects induced by subtracting a term proportional to Bohm's quantum potential to the usual (linear) Schrödinger equation, which generates the so-called "classical" Schrödinger equation. Although a simple nonlinear transformation allows us to recover the well-known classical Hamilton-Jacobi equation, by combining a series of analytical results (in the limiting cases) and simulations (whenever the analytical treatment is unaffordable), we find an analytical explanation to why the dynamics in the nonlinear "classical" regime is still strongly nonclassical. This is even more evident by establishing a one-to-one comparison between the Bohmian trajectories associated with the corresponding wave function and the classical trajectories that one should obtain. Based on these observations, it is clear that the transition to a fully classical regime requires extra conditions in order to remove any trace of coherence, which is the truly distinctive trait of quantum mechanics. This behavior is investigated in three paradigmatic cases, namely, the dispersion of a free propagating localized particle, the harmonic oscillator, and a simplified version of Young's two-slit experiment.

quant-ph↗

arXiv2022

Analysis of the gradual transition from the near to the far field in single-slit diffraction

In Optics it is common to split up the formal analysis of diffraction according to two convenient approximations, in the near and far fields (also known as the Fresnel and Fraunhofer regimes, respectively). Within this scenario, geometrical optics, the optics describing the light phenomena observable in our everyday life, is introduced as the short-wavelength limit of near-field phenomena, assuming that the typical size of the aperture (or obstacle) that light is incident on is much larger than the light wavelength. With the purpose to provide an alternative view on how geometrical optics fits within the context of the diffraction theory, particularly how it emerges, the transition from the near to the far field is revisited here both analytically and numerically. Accordingly, first this transition is investigated in the case of Gaussian beam diffraction, since its full analyticity paves the way for a better understanding of the paradigmatic (and typical) case of diffraction by sharp-edged single slits. This latter case is then tackled both analytically, by means of some insightful approximations and guesses, and numerically. As it is shown, this analysis makes explicit the influence of the various parameters involved in diffraction processes, such as the typical size of the input (diffracted) wave or its wavelength, or the distance between the input and output planes. Moreover, analytical expressions have been determined for the critical turnover value of the slit width that separates typical Fraunhofer diffraction regimes from the behaviors eventually leading to the geometrical optics limit, finding a good agreement with both numerically simulated results and experimental data extracted from the literature.

physics.class-ph↗

arXiv2021

Taming singularities of the quantum Fisher information

Quantum Fisher information matrices (QFIMs) are fundamental to estimation theory: they encode the ultimate limit for the sensitivity with which a set of parameters can be estimated using a given probe. Since the limit invokes the inverse of a QFIM, an immediate question is what to do with singular QFIMs. Moreover, the QFIM may be discontinuous, forcing one away from the paradigm of regular statistical models. These questions of nonregular quantum statistical models are present in both single- and multiparameter estimation. Geometrically, singular QFIMs occur when the curvature of the metric vanishes in one or more directions in the space of probability distributions, while QFIMs have discontinuities when the density matrix has parameter-dependent rank. We present a nuanced discussion of how to deal with each of these scenarios, stressing the physical implications of singular QFIMs and the ensuing ramifications for quantum metrology.

quant-ph↗