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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Displaced Fock states and photon correlations in Glauber-Fock photonic lattices

Robert Keil, Armando Pérez-Leija, Felix Dreisow, Matthias Heinrich, H. M. Moya-Cessa, Stefan Nolte, Demetrios N. Christodoulides, Alexander Szameit

Published May 1, 2011• 0 citations
Publisher

Abstract

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〉.

DOI
10.1109/cleoe.2011.5943394

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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〉.
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.
Abstract The main objective of this work is to investigate, analyze and examine in detail the behavior of quantum light in a photonic lattice having a square root law distribution for the coupling constant known as a Glauber-Fock photonic lattice. We investigate the light dynamics for both small and large size lattices for the case of spatially extended path entangled input state. We also study the squeezed state inputs, where we focus on finite size lattices. We analyze in detail the behavior of the non-classical features such as squeezing and photon correlations at the output of the system. The results and findings show the transport and revival of these features as non-classical light propagates across the waveguide array. Our findings should have applications in the areas of photonic quantum information processing and simulation and are implementable with current technology.
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.
Abstract We report the study of non-classical light in a photonic lattice having a parabolic coupling distribution, also known as a J x photonic lattice. We focus on a two-photon Fock state, a two-photon N 00 N state, a single-mode squeezed state and a coherent state as inputs to the lattice. We investigate the possibility of a perfect transfer of the mean photon number as well as the quantum state from one waveguide mode to another. We study photon–photon correlation for the two-photon N 00 N state. For the single-mode squeezed state we perform a detailed study of the evolution of the squeezing factor and entanglement between the waveguide modes. Our findings suggest a perfect transfer of the average photon number in all cases and a perfect transfer of the quantum state in the cases of the two-photon Fock state and the two-photon N 00 N state only, but not in the cases of the squeezed and coherent states. Our results should have applications in the physical implementation of photonic continuous-variable quantum-information processing.