Exact dynamics of finite Glauber-Fock photonic lattices

2011/08/31 by B. M. Rodríguez-Lara · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Combinatorics #Eigenvalues and eigenvectors #Fock space #Fock state #Glauber #Hamiltonian (control theory) #Hermite polynomials #Lambda #Lattice (music) #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Optical Network Technologies #Physics #Quantum mechanics #Scattering #Spectral line #quant-ph

paper · pdf · doi:10.1103/physreva.84.053845

published as Phys. Rev. A 84, 053845 (2011) [6 pages] · 6 pages, 8 figures

openalex publication_date 2011/11/23 · arxiv created 2011/11/24 · arxiv updated 2011/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The dynamics of Glauber-Fock lattice of size N is given through exact diagonalization of the corresponding Hamiltonian; the spectra \ensuremathλ_k is given as the roots of the Nth Hermite polynomial, H_N(\ensuremathλ_k/√(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 \ensuremathλ_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.

Citations

• Realization of Quantum Walks with Negligible Decoherence in Waveguide Lattices
• Nonexponential Decay Via Tunneling in Tight-Binding Lattices and the Optical Zeno Effect
• Special Functions and Their Applications

Cited by

• A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices