Ground-state selection as a four-wave-mixing process

We study nonlinear relaxation of the excited state in a system with two levels and a continuum. The process is first simulated in a one-dimensional waveguide array described by the discrete nonlinear Schrodinger equation. The results are interpreted in terms of degenerate four-wave mixing between the eigenmodes and diffraction properties of the array. We also show analytically that the role of the continuum can be played by a third bound state, with linear loss that replaces the diffraction in the continuum. This model enables derivation of the energy transfer rate and other parameters of the process.