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    Nuclear spins interact weakly with their environment. In particular, they are generally insensitive to mechanical vibrations. Here, we successfully demonstrate the coherent coupling of mechanics to a single nuclear spin. This coupling is mediated by a silicon vacancy (SiV) centre in diamond, taking advantage of its large strain susceptibility and hyperfine interaction with nuclear spins. Importantly, we demonstrate that the nuclear spin retains its excellent coherence properties even in the presence of this coupling. This provides a way to leverage nuclear spins as quantum memories for mechanical systems in the quantum regime. 
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  5. Integrating solid-state quantum emitters with photonic circuits is essential for realizing large-scale quantum photonic processors. Negatively charged tin-vacancy (SnV−) centers in diamond have emerged as promising candidates for quantum emitters because of their excellent optical and spin properties, including narrow-linewidth emission and long spin coherence times. SnV− centers need to be incorporated in optical waveguides for efficient onchip routing of the photons they generate. However, such integration has yet to be realized. In this Letter, we demonstrate the coupling of SnV− centers to a nanophotonic waveguide. We realize this device by leveraging our recently developed shallow ion implantation and growth method for the generation of high-quality SnV− centers and the advanced quasi-isotropic diamond fabrication technique. We confirm the compatibility and robustness of these techniques through successful coupling of narrow-linewidth SnV− centers (as narrow as 36 ± 2 MHz) to the diamond waveguide. Furthermore, we investigate the stability of waveguide-coupled SnV− centers under resonant excitation. Our results are an important step toward SnV−-based on-chip spin-photon interfaces, single-photon nonlinearity, and photon-mediated spin interactions. 
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  6. Color centers in solids, such as the nitrogen-vacancy center in diamond, offer well-protected and well-controlled localized electron spins that can be employed in various quantum technologies. Moreover, the long coherence time of the surrounding spinful nuclei can enable a robust quantum register controlled through the color center.We design pulse sequence protocols that drive the electron spin to generate robust entangling gates with these nuclear memory qubits.We find that compared to using Carr-Purcell-Meiboom-Gill (CPMG) alone, Uhrig decoupling sequence and hybrid protocols composed of CPMG and Uhrig sequences improve these entangling gates in terms of fidelity, spin control range, and spin selectivity. We provide analytical expressions for the sequence protocols and also show numerically the efficacy of our method on nitrogen-vacancy centers in diamond. Our results are broadly applicable to color centers weakly coupled to a small number of nuclear spin qubits. 
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