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An experimentally feasible scheme for preparing the squeezed spin states in a novel spin–mechanical hybrid system is studied. The setup under consideration is realized by a single‐crystal diamond waveguide with negatively charged silicon‐vacancy (SiV) centers embedded. After studying the strain couplings between the SiV spins and the propagating phonon modes, analyses show that long‐range spin–spin interactions can be achieved under large detuning condition. Modeled as an effective one‐axis twisting Hamiltonian, these nonlinear spin–spin couplings can steer the system to the squeezed spin states in the practical situations. This proposal may have interesting applications in high‐precision metrology and quantum information processing. [ABSTRACT FROM AUTHOR]

A new kind of spin coherent state called a Z3-graded spin coherent state is constructed by using the complex solution of the equation q3 = 1. We explicitly find three kinds of Z3-graded spin coherent states. The associated coherent property and spin squeezing are also examined. [ABSTRACT FROM AUTHOR]