Newton's cradle analogue with Bose-Einstein condensates

We propose a possible experimental realization of a quantum analogue of Newton's cradle using a configuration which starts from a Bose-Einstein condensate. The system consists of atoms with two internal states trapped in a one-dimensional tube with a longitudinal optical lattice and maintained in a strong Tonks-Girardeau regime at maximal filling. In each site the wave-function is a superposition of the two atomic states and a disturbance of the wave-function propagates along the chain in analogy with the propagation of momentum in the classical Newton cradle. The quantum travelling signal is generally deteriorated by dispersion, which is large for a uniform chain and is known to be zero for a suitably engineered chain, but the latter is hardly realizable in practice. Starting from these opposite situations we show how the coherent behaviour can be enhanced with minimal experimental effort.