One-dimensional matter waves as a multi-state bit

We design a technique to control the position of a localized matter wave. Our system is composed by a two counter-phased periodic potentials and a third optical lattice which can be chosen to be either periodic or disordered. The only control needed on the system is a three-state switch that allows the instantaneous selection of the desired potential. We show that this framework is robust and the multi-state bit behavior can be observed under generic hypothesis.