Resonant mode conversions and Rabi oscillations in a fractional Schr dinger equation

In a theoretical and numerical analysis, we report resonant mode conversions and Rabi oscillations in the fractional Schrödinger equation through the longitudinal modulation of the transverse potential. As specific systems of interest, we select eigenmodes of the transverse Gaussian and periodic potentials. In the Gaussian potential, we find that an increasing number of eigenmodes can be supported as the Lévy index α is reduced from 2 to 1, and that the conversion distance between the first and third eigenmodes first decreases and then increases. In the periodic potential, we obtain a cascade conversion between the neighboring eigenmodes because the parity of eigenmodes remains the same. We also find that the conversion distances between the first and second eigenmodes, as well as between the second and third eigenmodes, decrease monotonously, while that between the first and third eigenmodes first decreases and then increases with increasing α. In addition, we find that for a certain α, these conversion distances can be equal to each other.