Engineering impurity Bell states through coupling with a quantum bath

We theoretically demonstrate the feasibility of creating Bell states in multicomponent ultracold atomic gases by solely using the ability to control the interparticle interactions via Feshbach resonances. For this we consider two distinguishable impurities immersed in an atomic background cloud of a few bosons, with the entire system being confined in a one-dimensional harmonic trap. By analyzing the numerically obtained ground states we demonstrate that the two impurities can form spatially entangled bipolaron states due to mediated interactions from the bosonic bath. Our analysis is based on calculating the correlations between the two impurities in a two-mode basis, which is experimentally accessible by measuring the particle positions in the left or right sides of the trap. While interspecies interactions are crucial in order to create the strongly entangled impurity states, they can also inhibit correlations depending on the ordering of the impurities and three-body impurity-bath correlations. We show how these drawbacks can be mitigated by manipulating the properties of the bath, namely its size, mass, and intraspecies interactions, allowing one to create impurity Bell states over a wide range of impurity-impurity interactions.