Dynamics of a Schrödinger cat state in a photonic waveguide array

We report the study of the dynamics of a Schrödinger cat state (SCS) in a photonic lattice, in which two different types of coupling functions between the waveguides are considered: a constant coupling and a parabolic coupling. In addition, we investigate the inclusion of defects in the constant coupling function condition for one or three waveguides. In our study, we evaluate the average number of photons per waveguide and the fidelity in order to determine the distribution of light in the lattice for each coupling function and to find conditions to reach a perfect state transfer (PST). In the case of constant coupling, it is not possible to obtain a PST since the state distributes over all the lattice, with the inclusion of defects serving as a control mechanism in this process. In the case of parabolic coupling, we observe PST when the lattice is composed of an odd number of coupled waveguides, while, for an even number of coupled waveguides, we observe that by varying the phase of the SCS, different values of the fidelity can be obtained. Interestingly, in this last case, it is possible to achieve values of the fidelity closer to one by choosing a phase of π and a small average number of photons.