Abstract

Restricting the dimensionality of many-body systems can not only lead to new and interesting physics, but often allows for simpler theoretical treatment or even exactly solvable models. This possibility of detailed understanding in turn creates opportunities to develop engineering schemes to test new concepts and ideas. Here we will show how a simple mathematical model of a one-dimensional split trap can be used to describe the realistic properties of a gas of ultracold, neutral bosons in the presence of an impurity, for example an ion. Within this exact mdel we can then calculate the full RSPDM for samples with a medium number of particles and find that the coherence is an oscillating function of the particle number. From this we will present a model for entanglement between spatial modes in a cold gas and how it can be interpreted as a consequence of spatial coherence. While for ideal gases temperature and external trapping are the only control parameters, we will show that in strongly correlated systems the amount of entanglement present can be engineered by controlling the inter-particle interaction.