Coherent states and their generalisations, displaced Fock states, are offundamental importance to quantum optics. Here we present a direct observationof a classical analogue for the emergence of these states from the eigenstatesof the harmonic oscillator. To this end, the light propagation in aGlauber-Fock waveguide lattice serves as equivalent for the displacement ofFock states in phase space. Theoretical calculations and analogue classicalexperiments show that the square-root distribution of the coupling parameter insuch lattices supports a new family of intriguing quantum correlations notencountered in uniform arrays. Due to the broken shift-invariance of thelattice, these correlations strongly depend on the transverse position.Consequently, quantum random walks with this extra degree of freedom may berealised in Glauber-Fock lattices.
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