  The collective dynamics of a dipolar fermionic quantum gas confined in a
one-dimensional double-well superlattice is explored. The fermionic gas resides
in a paramagnetic-like ground state in the weak interaction regime, upon which
a new type of collective dynamics is found when applying a local perturbation.
This dynamics is composed of the local tunneling of fermions in separate
supercells, and is a pure quantum effect, with no classical counterpart. Due to
the presence of the dipolar interactions the local tunneling transports through
the entire superlattice, giving rise to a collective dynamics. A well-defined
momentum-energy dispersion relation is identified in the ab-initio simulations
demonstrating the phonon-like behavior. The phonon-like characteristic is also
confirmed by an analytical description of the dynamics within a semiclassical
picture.
