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Frontiers in Optics

Simulating Quantum Wavepackets with Non-Diffracting Pendulum Beams

Enrique J. Galvez, Jake M. Freedman, Anupama Motee

Published Jan 1, 2020• 0 citations
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Abstract

Exploiting similarities between the Schrödinger and Helmholtz equations we prepare optical beams that simulate quantum solutions of the simple mechanical pendulum. We did laboratory investigations of optical patterns that correlated with the probabilities in the quantum pendulum. Coherent superpositions of modes simulated quantum wavepackets in the linear-harmonic-oscillator and nonlinear-Mathieu regimes.

DOI
10.1364/fio.2020.fw5b.3

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Exploiting similarities between the Schrödinger and Helmholtz equations we prepare optical beams that simulate quantum solutions of the simple mechanical pendulum. We did laboratory investigations of optical patterns that correlated with the probabilities in the quantum pendulum. Coherent superpositions of modes simulated quantum wavepackets in the linear-harmonic-oscillator and nonlinear-Mathieu regimes.
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.
We suggest that propagation of nonclassical light in lattices of optical waveguides can provide a laboratory tool to simulate quantum decoherence phenomena with high non-Markovian features. As examples, we study decoherence of optical Schrödinger cats in a lattice that mimics a dissipative quantum harmonic oscillator coupled to a quantum bath, showing fractional decoherence in the strong coupling regime, and Bloch oscillations of optical Schrödinger cats, where damped revivals of the coherence can be observed.
We suggest that propagation of nonclassical light in lattices of optical waveguides can provide a laboratory tool to simulate quantum decoherence phenomena with high non-Markovian features. As examples, we study decoherence of optical Schrödinger cats in a lattice that mimics a dissipative quantum harmonic oscillator coupled to a quantum bath, showing fractional decoherence in the strong coupling regime, and Bloch oscillations of optical Schrödinger cats, where damped revivals of the coherence can be observed.