Multiple Landau-Zener tunnelling in two weakly coupled waveguide arrays

A visual observation of multiple Landau-Zener transitions between different modes is theoretically proposed by using two weakly coupled waveguide arrays. Applying a small temperature gradient between the opposite corners of the sample it is possible to realize ordinary symmetric Landau-Zener tunnelling exchange between two modes. While increasing the temperature gradient more modes are involved in the tunnelling exchange and the picture becomes asymmetric even in the linear limit. We interpret this phenomenon via dynamics associated with Schr?dinger equation in double well potential and additional gradient potential along both dimensions.