Periodic State Revivals in Commensurate Waveguide Arrays

Emerging optical and quantum computers require hardware capable of coherent transport of and operations on quantum states. Here, we investigate finite optical waveguide arrays with linear coupling as means of efficient and compact coherent state transfer. Coherent transfer with periodic state revivals is enabled by engineering coupling coefficients between neighbouring waveguides to yield commensurate eigenvalue spectrum. Particular cases of finite arrays have been actively studied to achieve the perfect state transfer by mirroring the input into the output state. We explore a much wider scope of coherent propagation and revivals of both the state amplitude and phase. We analytically solve the inverse eigenvalue problem to find the corresponding array coupling coefficients and use them to construct optical waveguide arrays that support full state revivals. We present analytical solutions for general arrays with 4 and 5 waveguides and for symmetric arrays with 7 and 9 waveguides. These solutions include previously proposed families of solutions based on equidistance between eigenvalues