Critical tuning of Luttinger liquid interactions through control of ion impurities

Introducing ionic impurities into a Luttinger liquid (LL) of neutral atoms modifies the effective atom-atom interaction. By tuning characteristic parameters of the system, namely the short range phases of the atom-ion polarization potential and the relative density of atoms and ions, we show that the effective interaction of the LL can be tuned across a wide spectrum of values. Remarkably, the introduction of ions allows an interaction which is initially attractive to become effectively repulsive. We demonstrate this by finding the ground state of an atom-ion system using DMRG and extracting the LL parameter and the speed of sound. The LL theory models the low-energy physics of a gas of cold atoms in a one-dimensional trap, and thus these results are experimentally relevant for the recent advances in bringing different atomic species together in hybrid quantum systems.