Soliton trains and vortex streets as a form of Cerenkov radiation in trapped Bose-Einstein condensates

We numerically study the nucleation of gray solitons and vortex-antivortex pairs created by a moving impurity in, respectively, 1D and 2D Bose-Einstein condensates (BECs) confined by a parabolic potential. The simulations emulate the motion of a localized laser-beam spot through the trapped condensate. Our results for the 1D case indicate that, due to the inhomogeneity of the BEC density, the critical speed for nucleation, as a function of the condensate density displays two distinct dependences. In particular, the square root of the critical density for nucleation as a function of speed displays two different linear regimes corresponding to small and large velocities. Effectively, the emission of gray solitons and vortex-antivortex pairs occurs for any velocity of the impurity, as any given velocity will be supercritical in a region with a sufficiently small density. At longer times, the first nucleation is followed by generation of an array of solitons in 1D ("soliton train") or vortex pairs in 2D ("vortex street") by the moving object.