Fast-Forward Problem in Microscopic and Macroscopic Quantum Mechanics

Abstract

We showed the way to speed up the time-evolution of a wave function (WF), i.e. to fast-forward the WF in microscopic and macroscopic quantum mechanics, by controlling the driving potential with resultant regulation of the additional phase of the WF, so that a target state is obtained in a shorter time (Phys. Rev. A 78:062108, 2008). We first presented a general framework of the fast-forwarding of WF in quantum mechanics and provided an example of the fast-forward of WF in two-dimensional (2-d) free space. Then the framework of the fast-forward was extended to macroscopic quantum mechanics described by the nonlinear Schrödinger equation. We showed the fast-forward of (1) transport of Bose Einstein condensates trapped by a moving 2-d harmonic potential and (2) propagation of a soliton both in free space and through a potential barrier (macroscopic quantum tunnelling).