  We investigate the physics of a Tomonaga-Luttinger liquid of spin-polarized
fermions superimposed on an ion chain. This compound system features
(attractive) long-range interspecies interactions. By means of density matrix
renormalization group techniques we compute the Tomonaga-Luttinger-liquid
parameter and speed of sound as a function of the relative atom/ion density and
the two quantum defect parameters, namely, the even and odd short-range phases
which characterize the short-range part of the atom-ion polarization potential.
The presence of ions is found to allow critical tuning of the atom-atom
interaction, and the properties of the system are found to depend significantly
on the short-range phases due to the atom-ion interaction. These latter
dependencies can be controlled, for instance, by manipulating the ions'
internal state. This allows modification of the static properties of the
quantum liquid via external driving of the ionic impurities.
