Two-site Bose-Hubbard model in waveguides (Vol. 42, No. 2)

Light transport in waveguide lattices has provided over the past decade a test bench to visualize the classical analogues of a wide variety of coherent single-particle quantum phenomena generally encountered in condensed matter or matter wave systems. Since photons in linear optical structures do not interact, it is a common belief that the use of photonics as a model system for quantum physics carries the intrinsic drawback of being limited to visualize single-particle phenomena, missing the possibility to simulate the richer physics of interacting many-particle systems.

In this paper, the author has now pushed the realm of quantum-optical analogies beyond the single-particle phenomena, demonstrating that linear photonics can provide an accessible laboratory system to visualize in a purely classical setting the very basic dynamical aspects embodied in the physics of interacting quantum particles. In particular, a classical realization of the famous Bose-Hubbard Hamiltonian, which provides a paradigmatic model to describe the physics of strongly interacting bosons, has been theoretically proposed for light transport in engineered waveguide lattices. The author has shown that spatial propagation of light waves along the photonic crystal structure mimics in the Fock space the temporal dynamics of ultracold bosonic atoms trapped in a double-well potential, the so-called bosonic junction. While for ultracold atoms the full multi-particle dynamics is typically not accessible, the present work proposes a new route to simulate the Bose-Hubbard model which overcomes such a limitation, thus opening a new route to the realization of classical simulators of many-particle quantum physics.