Exponentially complex nonseparable states in planar arrays of nonlinearly coupled one-dimensional elastic waveguides

Externally driven parallel arrays of elastic waveguides inelastically coupled along their length are shown to support inelastic modes that span exponentially complex Hilbert spaces. The nonlinear coupling takes the form of power functions of the relative displacement between waveguides. First order perturbation theory is employed to obtained closed form solutions for the contribution of nonlinearity to the displacement field in the form of nonseparable superpositions of product states of plane waves. When the system is dissipative, the coefficients of the superposition of product states are complex and can be varied by controlling the characteristics of the way the array is driven externally. The entropy of ‘entanglement’ of these nonseparable superpositions of product states is calculated from the complex amplitudes through the density matrix. Navigation of the exponentially complex Hilbert space of product states enables manipulation of the degree of nonseparability of the superpositions.