Filtering of matter wave vibrational states via spatial adiabatic passage

We propose here to make use of the spatial adiabatic passage technique, i.e., the matter wave analogue of the well known stimulated Raman adiabatic passage technique. We discuss the filtering of the vibrational states of a cold atom in an optical trap, by chaining this trap with two empty ones and controlling adiabatically the tunnelling. Matter wave filtering is performed by selectively transferring the population of the highest populated vibrational state to the most distant trap while the population of the rest of the states remains in the initial trap.