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We propose an efficient scheme for generating spin-squeezed states at steady state in a spinmechanical hybrid system, where an ensemble of SiV centers are coupled to a strongly damped nanomechanical resonator. We show that, there exists a collective steady state in the system, which is exactly formed by the collective spin states plus the zero excitation state of the mechanical mode. The generation of the steady spin-squeezed state is based on a dissipative quantum dynamical process in which the mechanical dissipation plays a positive role but without destroying the target state. We demonstrate that the spin-squeezed steady state can be deterministically prepared via dissipative means, with the optimal spin squeezing up to 4/N in the ideal case, where N is the number of spins. This work provides a promising platform for quantum information processing and quantum metrology.

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Spin-mechanical hybrid systems have been widely used in quantum information processing. However, the spin-mechanical interaction is generally weak, making it a critical challenge to enhance the spin-mechanical interaction into the strong coupling or even ultra-strong coupling regime. Here, we propose a protocol that can significantly enhance the spin-mechanical coupling strength with a diamond spin vacancy and a levitated micromagnet. A driving electrical current is used to modulate the mechanical motion of the levitated micromagnet, which induces a two-phonon drive and can exponentially enhance the spin-phonon and phonon-medicated spin-spin coupling strengths. Furthermore, a high fidelity Schrödinger cat state and an unconventional 2-qubit geometric phase gate with high fidelity and faster gate speed can be achieved using this hybrid system. This protocol provides a promising platform for quantum information processing with NV spins coupled to levitated micromagnets.

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