We propose a scheme to implement Heisenberg-limited spin squeezing in a hybrid cavity optomechanical-spin system. In our system, $N$ two-level systems are coupled via Tavis-Cummings interactions to a mechanical resonator (MR) in a standard optomechanical setup. Within the dispersive coupling regime, adiabatic elimination of the optical mode induces a squeezing effect on the MR, which in the squeezed representation effectively transforms the collective spin operators into a Bogoliubov form. Under large-detuning conditions, the phonon mode mediates interactions among the Bogoliubov collective spins, thereby enabling versatile squeezing schemes including the two-axis twisting (TAT) protocol. In particular, with a phonon-induced auxiliary collective spin term, our protocol exhibits more robust squeezing against dissipation, outperforming the standard TAT protocol. Furthermore, both analysis and numerical simulations show that the maximum squeezing degree asymptotically converges to a constant as $N$ increases, which implies that the metrological precision asymptotically approaches the standard quantum limit without parameter optimization. Nevertheless, in parameter optimization we extract scaling relations of the optimal squeezing which surpass existing schemes in the literature. Moreover, the optimization can also lead to a considerable reduction of the preparation time for the optimal squeezing. Our work may provide insights into dissipation effects in spin squeezing and offer a potential route for high-precision quantum metrology in many-body systems.

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• Open quantum systems & decoherence
• Optomechanics
• Quantum metrology
• Quantum protocols