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Recently observed quantum emitters in hexagonal boron nitride (hBN) membraneshave a potential for achieving high accessibility and controllability thanks tothe lower spatial dimension. Moreover, these objects naturally have a highsensitivity to vibrations of the hosting membrane due to its low mass densityand high elasticity modulus. Here, we propose and analyze a spin-mechanicalsystem based on color centers in a suspended hBN mechanical resonator. Throughgroup theoretical analyses and ab-initio calculation of the electronic and spinproperties of such a system, we identify a spin doublet ground state anddemonstrate that a spin-motion interaction can be engineered which enablesground state cooling of the mechanical resonator. We also present a toolbox forinitialization, rotation, and readout of the defect spin qubit. As a result theproposed setup presents the possibility for studying a wide range of physics.To illustrate its assets, we show that a fast and noise resilient preparationof a multicomponent cat state and a squeezed state of the mechanical resonatoris possible; the latter is achieved by realizing the extremely detuned,ultrastrong coupling regime of the Rabi model, where a phonon superradiantphase transition is expected to occur.

Spin-Mechanical Scheme with Color Centers in Hexagonal Boron Nitride Membranes