Fractional Schrödinger equation in optics

2015/01/09 by Stefano Longhi · 6 citations
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Orbital Angular Momentum in Optics #Quantum chaos and dynamical systems #physics.optics #quant-ph

paper · pdf · doi:10.1364/ol.40.001117

published as Opt. Lett. 40, 1117 (2015) · 5 pages, 3 figures

arxiv created 2015/01/09 · openalex publication_date 2015/03/12 · arxiv updated 2016/03/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31

Abstract

In quantum mechanics, the space-fractional Schrödinger equation provides a natural extension of the standard Schrödinger equation when the Brownian trajectories in Feynman path integrals are replaced by Levy flights. Here an optical realization of the fractional Schrödinger equation, based on transverse light dynamics in aspherical optical cavities, is proposed. As an example a laser implementation of the fractional quantum harmonic oscillator is presented, in which dual Airy beams can be selectively generated under off-axis longitudinal pumping.

Citations

• Making sense of non-Hermitian Hamiltonians
• Resonant Modes in a Maser Interferometer
• Some solutions to the space fractional Schrödinger equation using momentum representation method

Cited by

• Spectral and Dynamical Properties of the Fractional Nonlinear Schrödinger Equation under Harmonic Confinement
• Properties of the Katugampola fractional derivative with potential application in quantum mechanics
• PT symmetry in a fractional Schrödinger equation
• Optical realization of the dissipative quantum oscillator
• Self-accelerating beam dynamics in the space fractional Schrödinger equation
• The most general form of deformation of the Heisenberg algebra from the generalized uncertainty principle

Related

• Fractional Classical Mechanics
• Stabilization of Axisymmetric Airy Beams by Means of Diffraction and Nonlinearity Management in Two-Dimensional Fractional Nonlinear Schrödinger Equations
• Fractional Quantum Mechanics
• Time Fractional Schroödinger Equation
• Fractional Nonlinear Schrodinger Equation Revisited