Separability and Nonseparability of Elastic States in Arrays of One-Dimensional Elastic Waveguides

Abstract

We show that the directional projection of longitudinal waves propagating in a parallel array of N elastically coupled waveguides can be described by a nonlinear Dirac-like equation in a 2 N dimensional exponential space. This space spans the tensor product Hilbert space of the two-dimensional subspaces of N uncoupled waveguides grounded elastically to a rigid substrate (called φ -bits). The superposition of directional states of a φ -bit is analogous to that of a quantum spin. We can construct tensor product states of the elastically coupled system that are nonseparable on the basis of tensor product states of N φ -bits. We propose a system of coupled waveguides in a ring configuration that supports these nonseparable states.