Quantum chaos with graphs: a silicon photonics plateform

TL;DR

This paper introduces a silicon photonics platform for studying quantum chaos using waveguide networks that emulate quantum graphs, demonstrating spectral statistics consistent with random matrix theory.

Contribution

The work experimentally implements quantum graphs in silicon photonics to explore spectral statistics and wavefunction patterns related to quantum chaos.

Findings

Spectral statistics of chaotic graphs match random matrix theory predictions.

Less chaotic graphs show deviations from random matrix theory.

Wavefunction patterns align with quantum ergodicity expectations.

Abstract

We provide a versatile plateform to investigate wave-particle duality. This photonic waveguide network implements quantum (wave) graphs as proposed in the seminal paper by Kottos \& Smilansky [PRL \textbf{85} 968 (2000)]. We experimentally demonstrated that the spectral statistics of a mixing (i.e. strongly chaotic) graph follows the predictions of random matrix theory, contrary to an ergodic (i.e. less chaotic) graph, in agreement with the Bohigas-Giannoni-Schmit conjecture [PRL \textbf{52} 1 (1984)]. This plateform also gives access to the wavefunction patterns, which are expected to verify the quantum ergodicity theorem.