Nondegenerate parametric amplification in superlattice and the limits of strong and weak dissipation

Abstract

We develop a semiclassical theory of the nondegenerate parametric amplification in a single miniband of superlattice. We present the formulas describing absorption and gain of signal and idler fields in superlattice and analyze the limiting cases of strong and weak dissipation. We show how the well-known Manley-Rowe relations arise in the tight-binding lattice in the weak dissipation limit. Our results can be applied to an amplification of THz signals in semiconductor superlattices and a control of nonlinear transport of cold atoms in optical lattices.Comment: Submitted to Proceedings of 32nd International Workshop on Condensed Matter Theories (birth centenary of L D Landau), Loughborough, UK, 13-18 August 2008, International Journal of Modern Physics B, 11 page