  We explore the possibility of engineering quantum states of a charged
mechanical oscillator by coupling it to a stream of atoms in superpositions of
high-lying Rydberg states. Our scheme relies on the driving of a two-phonon
resonance within the oscillator by coupling it to an atomic two-photon
transition. This approach effectuates a controllable open system dynamics on
the oscillator that permits the dissipative creation of squeezed and other
non-classical states which are central to applications such as sensing and
metrology or for studies of fundamental questions concerning the boundary
between classical and quantum mechanical descriptions of macroscopic objects.
We show that these features are robust to thermal noise arising from a coupling
of the oscillator with the environment. Finally, we assess the feasibility of
the scheme finding that the required coupling strengths are challenging to
achieve with current state-of-the-art technology.
