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Many fields interaction: Beam splitters and waveguide arrays
Author(s) -
MarSarao R.,
SotoEguibar F.,
MoyaCessa H.
Publication year - 2011
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.201000147
Subject(s) - hamiltonian (control theory) , physics , tridiagonal matrix , eigenvalues and eigenvectors , coherent states , harmonic oscillator , quantum mechanics , quadratic equation , classical mechanics , mathematics , quantum , geometry , mathematical optimization
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.