Experimental simulation of solid-state phenomena using photonic lattices
Abstract
The propagation of light waves across a periodic array of evanescently coupled optical
waveguides can be described by a Schr¨odinger-like equation for a particle in a periodic
potential. This mapping allows us to investigate the dynamics of electrons in a
crystalline solid using an artificial crystal of optical waveguides, known as a photonic
lattice. The unique capabilities of ultrafast laser inscription enable us to design, fabricate
and precisely control various properties of a photonic lattice. Here, we focus on the
experimental construction of the Hamiltonians associated with various complex quantum
systems using engineered photonic lattices, and then measure the time evolution of
a given input state. In this photonic platform, we experimentally observe various single
particle effects known from solid-state physics, such as the localised states associated
with flat-band lattice geometries, localised Wannier-Stark states, photon-assisted tunnelling
and the anomalous topological edge modes in slowly-driven lattices. Specific
phenomena associated with particle interactions, such as the dynamics of two interacting
particles in a one-dimensional lattice with static and sinusoidally driven Hubbard
Hamiltonian, is also investigated. The experimental results presented here will be of interest
to a large community, including physicists working on photonics, quantum optics,
cold atomic gases, and condensed-matter physics.