arXiv subjects

Julio C. Gutierrez-Vega

Publications and source records attributed to Julio C. Gutierrez-Vega.

4 recordsLinked to original sources

arXiv2024

Solutions of the Lippmann-Schwinger equation for confocal parabolic billiards

We present analytical and numerical solutions of the Lippmann-Schwinger equation for the scattered wavefunctions generated by confocal parabolic billiards and parabolic segments with various $δ$-type potential-strength functions. The analytical expressions are expressed as summations of products of parabolic cylinder functions $D_m$. We numerically investigate the resonances and tunneling in the confocal parabolic billiards by employing an accurate boundary wall method that provides a complete inside-outside picture. The criterion for discretizing the parabolic sides of the billiard is explained in detail. We discuss the phenomenon of transparency at certain eigenenergies.

quant-ph↗

arXiv2024

Quantum states resembling classical periodic trajectories in mesoscopic elliptic billiards

A quantum wave function with localization on classical periodic orbits in a mesoscopic elliptic billiard has been achieved by appropriately superposing nearly degenerate eigenstates expressed as products of Mathieu functions. We analyze and discuss the rotational and librational regimes of motion in the elliptic billiard. Simplified line equations corresponding to the classical trajectories can be extracted from the quantum state as an integral equation involving angular Mathieu functions. The phase factors appearing in the integrals are connected to the classical initial positions and velocity components. We analyze the probability current density, the phase maps, and the vortex distributions of the periodic orbit quantum states for both rotational and librational motions; furthermore, they may represent traveling and standing trajectories inside the elliptic billiard.

nlin.CD↗

arXiv2018

Rigorous analytical formula for freeform singlet lens design free of spherical aberration

An analytical closed-form formula for the design of freeform lenses free of spherical aberration is presented. Given the equation of the freeform input surface, the formula gives the equation of the second surface in order to correct the spherical aberration. The derivation is based on the formal application of the variational Fermat principle under the standard geometrical optics approximation.

physics.optics↗

arXiv2013

Observation of non-diffracting behavior at the single-photon level

We demonstrate the generation of non-diffracting heralded single photons, i.e. which are characterized by a single-photon transverse intensity distribution which remains essentially unchanged over a significant propagation distance. For this purpose we have relied on the process of spontaneous parametric downconversion (SPDC) for the generation of signal and idler photon pairs, where our SPDC crystal is pumped by a Bessel-Gauss (BG) beam. Our experiment shows that the well-understood non-diffracting behavior of a BG beam may be directly mapped to the signal-mode, single photons heralded by the detection of a single idler photon. In our experiment, the heralded single photon is thus arranged to be non-diffracting without the need for projecting its single-photon transverse amplitude, post-generation, in any manner.

quant-ph↗