Optical potentials using resonance states in Supersymmetric Quantum Mechanics

TL;DR

This paper develops a method to construct complex optical potentials using resonance states in supersymmetric quantum mechanics, enabling the design of devices that refract and absorb light while preserving spectral properties.

Contribution

It introduces a novel approach to generate optical potentials via Darboux-deformations with resonance states, expanding the toolkit for quantum and optical device modeling.

Findings

Resonance states are quantized in the constructed potentials.

Wave-functions behave as bounded states when parity symmetry is broken.

The method is demonstrated on the radial square well example.

Abstract

Complex potentials are constructed as Darboux-deformations of short range, radial nonsingular potentials. They behave as optical devices which both refracts and absorbs light waves. The deformation preserves the initial spectrum of energies and it is implemented by means of a Gamow-Siegert function (resonance state). As straightforward example, the method is applied to the radial square well. Analytical derivations of the involved resonances show that they are `quantized' while the corresponding wave-functions are shown to behave as bounded states under the broken of parity symmetry of the related one-dimensional problem.