Exact Dynamics and Bloch Oscillations in a Non Hermitian Zigzag Glauber Fock Lattice

The discrete dynamics of a one-dimensional non-hermitian zigzag waveguide array is studied theoretically. This system is characterized by unbalanced left/right nearest-neighbor hopping and reciprocal second-neighbor interactions in both hopping directions. The interplay between the unbalanced hopping amplitudes and the waveguide setup results in Non-Hermitian Bloch oscillations, where energy transport is either amplified or dissipated at specific locations, depending on the relative strengths of the left and right hopping terms. We demonstrate that by applying an appropriate non-unitary transformation, the original system can be mapped into an equivalent reciprocalwaveguide with Hermitian dynamics. This transformation allows us to derive a closed-form analytic solution, which is then compared with the numerical solution of the system.