  We describe a hybrid quantum system composed of a micrometer-size carbon
nanotube (CNT) longitudinally coupled to a flux qubit. We demonstrate the
usefulness of this device for generating high-fidelity nonclassical states of
the CNT via dissipative quantum engineering. Sideband cooling of the CNT to its
ground state and generating a squeezed ground state, as a mechanical analogue
of the optical squeezed vacuum, are two additional examples of the dissipative
quantum engineering studied here. Moreover, we show how to generate a
long-lived macroscopically-distinct superposition (i.e., a Schr\"odinger
cat-like) state. This cat state can be trapped, under some conditions, in a
dark state, as can be verified by detecting the optical response of control
fields.
