2011
DOI: 10.1103/physreva.84.053845
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Exact dynamics of finite Glauber-Fock photonic lattices

Abstract: The dynamics of Glauber-Fock lattice of size N is given through exact diagonalization of the corresponding Hamiltonian; the spectra {λ k } is given as the roots of the N -th Hermite polynomial, HN (λ 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 {λ k }, oscillatory behavior with highly localized spectra, that is, near complete re… Show more

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Cited by 28 publications
(44 citation statements)
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“…which, after complex conjugation, is identical to (29) and accepts a solution of the form E(z) = e iz(â † +â) E(0) that can be seen as a displaced superposition of Fock states; e.g. in the case of just E 0 = 1 and all other field amplitudes equal to zero, the amplitude of the electric field at the nth waveguide will be equivalent to the complex conjugat of the nth amplitude of a coherent state with coherent parameter iz, E n (z) = n|z = e −z 2 /2 (iz) n / √ n!.…”
Section: A Displaced Number Statesmentioning
confidence: 99%
“…which, after complex conjugation, is identical to (29) and accepts a solution of the form E(z) = e iz(â † +â) E(0) that can be seen as a displaced superposition of Fock states; e.g. in the case of just E 0 = 1 and all other field amplitudes equal to zero, the amplitude of the electric field at the nth waveguide will be equivalent to the complex conjugat of the nth amplitude of a coherent state with coherent parameter iz, E n (z) = n|z = e −z 2 /2 (iz) n / √ n!.…”
Section: A Displaced Number Statesmentioning
confidence: 99%
“…Furthermore, using (17) it is straightforward to derive the two-photon correlation function Γ j,k r,s (nτ ) (12). The experimentally observable two-photon correlation function is shown in Fig.…”
Section: A Cylindrical Arraymentioning
confidence: 99%
“…Unlike normal Glauber-Fock lattices, in the present case we have an extra term (−1) m , which indicates that these lattices must be endowed with alternating positive and negative coupling coefficients apart from the square root law distribution [11,31].…”
Section: Fig 2: Evolution Of a Coherent State |β With Average Photmentioning
confidence: 99%