Manipulation of quantum particles in rapidly oscillating potentials by inducing phase hops

Analytical calculations show that the mean motion of a quantum particle trapped by a rapidly oscillating potential can be significantly manipulated by inducing phase hops---i.e., by instantaneously changing the potential's phase. A phase hop can be visualized as being the result of a collision with an imaginary particle which can be controlled. Several phase hops can have accumulating effects on the particle's mean motion, even if they transform the particle's Hamiltonian into its initial one. The theoretical predictions are verified by numerical simulations for the one-dimensional Paul trap.