  Nonclassical states of macroscopic objects are promising for ultrasensitive
metrology as well as testing quantum mechanics. In this work, we investigate
dissipative mechanical quantum state engineering in an optically levitated
nanodiamond. First, we study single-mode mechanical squeezed states by
magnetically coupling the mechanical motion to a dressed three-level system
provided by a Nitrogen-vacancy center in the nanoparticle. Quantum coherence
between the dressed levels is created via microwave fields to induce a
two-phonon transition, which results in mechanical squeezing. Remarkably, we
find that in ultrahigh vacuum quantum squeezing is achievable at room
temperature with feedback cooling. For moderate vacuum, quantum squeezing is
possible with cryogenic temperature. Second, we present a setup for two
mechanical modes coupled to the dressed three levels, which results in two-mode
squeezing analogous to the mechanism of the single-mode case. In contrast to
previous works, our study provides a deterministic method for engineering
macroscopic squeezed states without the requirement for a cavity.
