Photonics West 2011 Classical-quantum analogies: SU(1,1) and Glauber photonic lattices Héctor Moya-Cessa Instituto Nacional de Astrofísica, Optica y Electrónica.

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Presentation transcript:

Photonics West 2011 Classical-quantum analogies: SU(1,1) and Glauber photonic lattices Héctor Moya-Cessa Instituto Nacional de Astrofísica, Optica y Electrónica Tonantzintla, Pue. Mexico

Bessel states as nonlinear coherent states Infinite waveguides array: fibers A. L. Jones, JOSA 55, (1965) Weak coupling, interaction only with nearest neighbor: Photonics West 2011

Waveguide number A beam injected into one of the waveguides in the array spreads to the rest of them by wave coupling. Discrete Diffraction This phenomenon has been referred to as DISCRETE DIFFRACTION H.S Eisenberg et al, PRL 81, 3383 (1998) Photonics West 2011

Schrödinger-like equation

Photonics West 2011

see Arfken

Photonics West 2011

Optics Communications (2011) f(n)

SU(1,1) algebra Photonics West 2011

Classical time dependent HO Ermakov-Lewis invariant Ermakov equation Lewis, PRL (1967). Optical realization of a quantum invariant

Photonics West 2011 Squeezing & Displacement Translation to quantum H. Moya-Cessa and M. Fernández Guasti PHYSICS LETTERS A 311, 1 (2003).

Photonics West 2011 Time dependence now as a factor

Photonics West 2011 Paraxial wave equation Suponemos ahora dos medios GRIN pegados GRaded INdex referring to an optical material with refractive index in the form of a parabolic curve, decreasing from the center towards the cladding.

Photonics West 2011

H. MOYA-CESSA, M. Fernández Guasti, V.M. Arrizon and S. Chávez-Cerda, Opt. Lett. 34, No. 9, (2009), “OPTICAL REALIZATION OF QUANTUM MECHANICAL INVARIANTS.”