Many fields interaction: Beam splitters and waveguide arrays

Authors

  • R. Mar-Sarao,

    1. INAOE, Instituto Nacional de Astrofísica, Óptica y Electrónica, Apdo. Postal 51 y 216, 72000, Puebla, Pue., Mexico
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  • F. Soto-Eguibar,

    1. INAOE, Instituto Nacional de Astrofísica, Óptica y Electrónica, Apdo. Postal 51 y 216, 72000, Puebla, Pue., Mexico
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  • H. Moya-Cessa

    Corresponding author
    1. INAOE, Instituto Nacional de Astrofísica, Óptica y Electrónica, Apdo. Postal 51 y 216, 72000, Puebla, Pue., Mexico
    • INAOE, Instituto Nacional de Astrofísica, Óptica y Electrónica, Apdo. Postal 51 y 216, 72000, Puebla, Pue., Mexico
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    • Phone: +52 222 266 3100, Fax: +52 222 247 2940


Abstract

We study the interaction of many fields. We obtain an effective Hamiltonian for this system by using a method recently introduced that produces a small rotation to the Hamiltonian that allows to neglect some terms in the rotated Hamiltonian. We show that coherent states remain coherent under the action of a quadratic Hamiltonian and by solving the eigenvalue and eigenvector problem for tridiagonal matrices we also show that a system of n interacting harmonic oscillators, initially in coherent states, remain coherent during the interaction.

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