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Title: Quantum dynamics of the relative phase in second-harmonic generation
Author: Delgado, J.
Luis, A.
Sanchez-Soto, L.L.
Klimov, Andrei B.
Issue Date: 2000
Abstract: We present a comprehensive and self-consistent theory of the relative phase between fundamental and harmonic modes in the nonlinear process of second-harmonic generation. We introduce an adequate polar decomposition of the field amplitudes that leads to a truly Hermitian relative-phase operator, whose eigenstates correctly describe the phase properties of the fields. We find the probability distribution for the relative phase and, by using a numerical diagonalization of the interaction Hamiltonian, we study its time evolution. This evolution shows quite different asymptotic behaviours for long times depending on the total number of quanta.
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