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Journal of International Crisis and Risk Communication Research

Observation of Glauber-Fock dynamics in photonic lattices

Armando Pérez-Leija, Robert Keil, H. M. Moya-Cessa, Demetrios N. Christodoulides, Alexander Szameit

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We report the first observation of classical intensity distributions in optical arrays that are totally analogous to quantum coherent and displaced Fock states. Bloch-like oscillations and revivals are also predicted in such Glauber-Fock photonic lattices.
DOI
10.1364/qels.2011.qthd7

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The dynamics of Glauber-Fock lattice of size NNN is given through exact diagonalization of the corresponding Hamiltonian; the spectra ${{\ensuremath{\lambda}}_{k}}$ is given as the roots of the NNNth Hermite polynomial, ${H}_{N}({\ensuremath{\lambda}}_{k}/\sqrt{2})=0$, and the eigenstates are given in terms of Hermite polynomials evaluated at these roots. The exact dynamics is used to study coherent phenomena in discrete lattices. Due to the symmetry and spacing of the eigenvalues ${{\ensuremath{\lambda}}_{k}}$, oscillatory behavior is predicted with highly localized spectra, that is, near complete revivals of the photon number and partial recovery of the initial state at given waveguides.
Coherent states and their generalizations, 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. Because of 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 realized in Glauber-Fock lattices.
Here, we present the experimental analysis of light propagation in such Glauber Fock photonic lattices. The individual guides have been inscribed into fused silica employing femtosecond laser pulses and the desired coupling between the waveguides has been obtained by varying the inter-waveguide spacing accordingly. Figs. 1(a,c) show the calculated intensity evolution and experimental fluorescence images for an excitation of the first two guides, corresponding to a displacement of the Fock-states |0〉 and |1〉.