Designing bound states in a band as a model for a quantum network

We provide a model of a one dimensional quantum network, in the framework of a lattice using von Neumann and Wigner's idea of bound states in a continuum. The localized states acting as qubits are created by a controlled deformation of a periodic potential using supersymmetric quantum mechanics. These wave functions lie at the band edges and are defects in a lattice. We propose that these defect states, with atoms trapped in them, can be realized in an optical lattice and can act as a model for a quantum network.