0000000000075579
AUTHOR
Miguel ÁNgel García-march
Photonic Nambu-Goldstone bosons
We study numerically the spatial dynamics of light in periodic square lattices in the presence of a Kerr term, emphasizing the peculiarities stemming from the nonlinearity. We find that, under rather general circumstances, the phase pattern of the stable ground state depends on the character of the nonlinearity: the phase is spatially uniform if it is defocusing whereas in the focusing case, it presents a chess board pattern, with a difference of $\pi$ between neighboring sites. We show that the lowest lying perturbative excitations can be described as perturbations of the phase and that finite-sized structures can act as tunable metawaveguides for them. The tuning is made by varying the in…
Single trajectory characterization via machine learning
[EN] In order to study transport in complex environments, it is extremely important to determine the physical mechanism underlying diffusion and precisely characterize its nature and parameters. Often, this task is strongly impacted by data consisting of trajectories with short length (either due to brief recordings or previous trajectory segmentation) and limited localization precision. In this paper, we propose a machine learning method based on a random forest architecture, which is able to associate single trajectories to the underlying diffusion mechanism with high accuracy. In addition, the algorithm is able to determine the anomalous exponent with a small error, thus inherently provi…
Supersolid Behavior of Light
We will show how light can form stationary structures on dielectric periodic media such that their dynamics present simultaneous features of spatial long range order and superfluidity. This phenomenon is normally referred to as supersolidity.
Topological charge selection rule for phase singularities
We present a study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.
Introductory Quantum Physics Courses using a LabVIEW multimedia module
We present the development of a LabVIEW multimedia module for introductory Quantum Physics courses and our experience in the use of this application as an educational tool in learning methodologies. The program solves the Time Dependent Schrodinger Equation for arbitrary potentials. We describe the numerical method used for solving this equation, as well as some mathematical tools employed to reduce the calculation time and to obtain more accurate results. As an illustration, we present the evolution of a wave packet for three different potentials: the repulsive barrier potential, the repulsive step potential, and the harmonic oscillator. This application has been successfully integrated in…
A topological charge selection rule for phase singularities
We present a study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified.
Symmetry, winding number, and topological charge of vortex solitons in discrete-symmetry media
[EN] We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schrodinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance
Graded-index optical fiber emulator of an interacting three-atom system: illumination control of particle statistics and classical non-separability
[EN] We show that a system of three trapped ultracold and strongly interacting atoms in one-dimension can be emulated using an optical fiber with a graded-index profile and thin metallic slabs. While the wave-nature of single quantum particles leads to direct and well known analogies with classical optics, for interacting many-particle systems with unrestricted statistics such analoga are not straightforward. Here we study the symmetries present in the fiber eigenstates by using discrete group theory and show that, by spatially modulating the incident field, one can select the atomic statistics, i.e., emulate a system of three bosons, fermions or two bosons or fermions plus an additional di…
Vorticity cutoff in nonlinear photonic crystals
Using group theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition needed is that the non-linearity term exclusively depends on the modulus of the field. In the particular case of 2D periodic systems, such as nonlinear photonic crystals or Bose-Einstein condensates in periodic potentials, it is shown that the realization of discrete symmetry forbids the existence of symmetric vortex solutions with vorticity higher than two.
Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media
We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we…