Figure 1

(a) A nanodiamond with a NV center is optically trapped in vacuum with spin-mechanical coupling enabled through a nearby magnetic tip and optomechanical coupling through a cavity around. (b) The atomic structure (left) and the level diagram (right) in the ground-state manifold for a NV center in the nanodiamond.Reuse & Permissions

Figure 2

Fidelity of creating the phonon number superposition state ${\left(\right|0\rangle }_m+{i|1\rangle }_m)/\sqrt{2}$ by coherent-state transfer between the NV spin and the mechanical mode. Fidelities higher than 99% can be achieved. (a) The peak fidelity as a function of the parameter $s={\omega }_m/\lambda$. (b) The fidelity as a function of the interaction time for two different parameters ($s=6.3,10$).Reuse & Permissions

Figure 3

(a) A nanodiamond with $d=30$ nm is confined tightly by a 100 kHz frequency optical tweezer in a magnetic field with a large gradient $G=4\times {10}^4$ T/m. Its NV center is prepared in a state $|0\rangle$. (b) The power of the optical tweezer is suddenly reduced to 20 kHz, and the NV center is changed to a superposition state $\left(\right|+1\rangle +|-1\rangle )/\sqrt{2}$, while the magnetic gradient is the same. As a result, the trap centers for different electron spins are separated. (c) The nanodiamond changes into a spatial superposition state as the state evolves in time. (d) and (e) show the time evolution of the probability distribution of the nanodiamond after the trapping frequency and the NV center state are suddenly changed. The mechanical state is initially (d) ${|0\rangle }_{m,100\mathtt{kHz}}$ or (e) ${|1\rangle }_{m,100\mathtt{kHz}}$ in the high-frequency trap. $a_2=\sqrt{\hslash /2m{\omega }_{m2}}=0.092$ nm and $T_2=50\mu$s.Reuse & Permissions

Figure 4

(a) Maximum spatial separation $D_m$ of the superposition state as a function of trap frequency ${\omega }_{m2}$ when the magnetic gradient is ${10}^5$ T/m. (b) Maximum spatial separation $D_m$ as a function of the magnetic gradient $G$ when the trapping frequency is 1 kHz. Macroscopic superposition states with separation larger than the size of the particle can be achieved with a moderate magnetic gradient.Reuse & Permissions

Figure 5

Spatial interference patterns for a 30 nm nanodiamond after 10 ms of free expansion. The nanodiamond is initially prepared in the vacuum state ${|0\rangle }_m$ or the one-phonon state ${|1\rangle }_m$ of a 20 kHz trap. The magnetic gradient is $3\times {10}^4$ T/m. Before the trap is turned off, the center of mass of the nanodiamond is prepared in (a) $|{\psi }_{+}{\rangle }_0$, (b) $|{\psi }_{+}{\rangle }_1$, (c) $|{\psi }_{-}{\rangle }_0$, and (d) $|{\psi }_{-}{\rangle }_1$.Reuse & Permissions

Figure 6

Spatial interference patterns for a 30 nm nanodiamond after 10 ms of free expansion. The magnetic gradient is $3\times {10}^4$ T/m. The nanodiamond is initially prepared in the thermal state of a 20 kHz trap. Before the trap is turned off, the center of mass of the nanodiamond is prepared in the spatial quantum superposition state with initial thermal phonon number $\langle n_m\rangle =0,0.01,0.1$.Reuse & Permissions