Classical simulation of the Hubbard-Holstein dynamics with optical waveguide lattices

TL;DR

This paper presents a classical optical waveguide setup that simulates the quantum dynamics of the Hubbard-Holstein model, allowing visualization of complex electron-phonon interactions through light propagation patterns.

Contribution

It introduces a novel photonic analog simulator that maps quantum electron-phonon dynamics into classical light transport in engineered waveguides, enabling direct visualization of quantum phenomena.

Findings

Periodic self-imaging of light correlates with Holstein polaron dynamics.

Simulation captures strong correlation effects in the Hubbard-Holstein model.

Visualization of generalized Bloch oscillations in a photonic system.

Abstract

A classical analog simulator of the two-site Hubbard-Holstein model, describing the dynamics of two correlated electrons coupled with local phonons, is proposed based on light transport in engineered optical waveguide arrays. Our photonic analog simulator enables to map the temporal dynamics of the quantum system in Fock space into spatial propagation of classical light waves in the evanescently-coupled waveguides of the array. In particular, in the strong correlation regime the periodic temporal dynamics, related to the excitation of Holstein polarons with equal energy spacing, can be visualized as a periodic self-imaging phenomenon of the light beam along the waveguide array and explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight-binding lattice.