Fractional Schrödinger equation in optics

Area of Science:

• Quantum mechanics
• Optics
• Mathematical physics

Background:

• The standard Schrödinger equation describes quantum mechanical systems.
• Fractional Schrödinger equations extend quantum mechanics using Levy flights instead of Brownian trajectories in Feynman path integrals.
• Optical systems offer potential platforms for simulating quantum phenomena.

Purpose of the Study:

• To propose an optical realization of the space-fractional Schrödinger equation.
• To demonstrate a laser implementation of the fractional quantum harmonic oscillator.

Main Methods:

• Utilizing transverse light dynamics within aspherical optical cavities.
• Employing off-axis longitudinal pumping in a laser system.
• Investigating the generation of dual Airy beams.

Main Results:

• Successful proposal for an optical system simulating the fractional Schrödinger equation.
• Demonstration of a laser setup for the fractional quantum harmonic oscillator.
• Selective generation of dual Airy beams achieved through controlled pumping.

Conclusions:

• Optical cavities provide a viable platform for exploring fractional quantum mechanics.
• The proposed laser implementation offers a novel method for studying fractional quantum phenomena.
• Dual Airy beam generation highlights the practical applications of this optical realization.