Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices

TL;DR

This paper demonstrates a classical analogue of displaced Fock states using Glauber-Fock photonic lattices, revealing new quantum correlations and position-dependent effects that could enable advanced quantum random walk implementations.

Contribution

It introduces a classical analogue for displaced Fock states in Glauber-Fock lattices and uncovers position-dependent quantum correlations due to non-uniform coupling.

Findings

Classical analogue of displaced Fock states observed in photonic lattices

Discovery of position-dependent quantum correlations in Glauber-Fock lattices

Potential for implementing quantum random walks with additional degrees of freedom

Abstract

Coherent states and their generalisations, displaced Fock states, are of fundamental importance to quantum optics. Here we present a direct observation of a classical analogue for the emergence of these states from the eigenstates of the harmonic oscillator. To this end, the light propagation in a Glauber-Fock waveguide lattice serves as equivalent for the displacement of Fock states in phase space. Theoretical calculations and analogue classical experiments show that the square-root distribution of the coupling parameter in such lattices supports a new family of intriguing quantum correlations not encountered in uniform arrays. Due to the broken shift-invariance of the lattice, these correlations strongly depend on the transverse position. Consequently, quantum random walks with this extra degree of freedom may be realised in Glauber-Fock lattices.