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Frontiers in Optics

Simulating Quantum Mechanics with Light: The Quantum Pendulum Via Mathieu Beams

Enrique J. Galvez, Fabio J. Auccapuclla, Yingsi Qin, Kristina L. Wittler

Published Jan 1, 2019• 0 citations
Publisher

Abstract

We simulate the nonlinear quantum pendulum using non-diffracting solutions of the 2-dimensional Helmholtz equation in elliptical coordinates. Stationary and wavepacket Mathieu spatial modes are in quantitative agreement with the quantum probabilities.
DOI
10.1364/fio.2019.jw3a.117

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Parallels between the Helmholtz and Schrodinger equations can be exploited for using light beams to investigate quantum problems. We present the study of a type of non-diffracting beams known as pendulum beams, where the optical modes satisfy a form of the Helmholtz equation that is identical to the Schrodinger equation for the mechanical pendulum. We prepared optical beams in the corresponding eigenmodes and made measurements of their Fourier spectrum. We find remarkable quantitative agreement between the measured angular spectrum and the quantum mechanical probabilities.