Nonlinear interference of matter waves in supersonic BEC flows through non-uniform channels

Abstract

The interference pattern generated by the interaction of two 1D rarefaction waves (RWs) was studied in [1]. However, only numerical solutions was presented. This problem can be solved analytically using the methods from [2] where the 1D dispersive shock wave (DSW) - RW interaction has analytical results. We propose a 2D analogue of this problem providing analytical and numerical results. To this end, we consider a hypersonic Bose-Einstein condensate (BEC) flow through a non-uniform channel, where the Mach number is M>>1. In this scenario, considering that we have uniform flow (with constant density and velocity at infinity) studied in the framework of the 2D defocusing nonlinear Schroedinger (NLS) equation, it is expected the formation of two 2D RWs and their interference would result in the formation of a 2D DSW or two 2D DSWs separated by a nonmodulated periodic solution. Using the piston approximation this problem can be asymptotically reduced to 1D and then the 1D analytical results can be compared with full unsteady 2D numerical simulations. Other channel configurations could be considered later as well as vortex formation due to the RW interference for smaller oncoming BEC velocities. (AU)