Classical and quantum models for phase imprinting

We investigate theoretically the generation of a persistent current in a Bose-Einstein condensate in a toroidal trap by means of phase imprinting. The phase-imprinting potential must be periodic around the torus, and will have parts that accelerate atoms in the direction opposite to the intended flow. We study the evolution of the average momentum and the momentum spread under a two-slope model potential numerically by using the Gross-Pitaevskii equation, and also in a simple classical-mechanics analogy. Because of the inevitable pollution caused by the opposite slopes of the potential, it is not possible to generate a pure persistent current. The same caveat presumably applies to vortices in higher-dimensional systems.