Strong coupling between a single nitrogen-vacancy spin and the rotational mode of diamonds levitating in an ion trap

A scheme for strong coupling between a single atomic spin and the rotational mode of levitating nanoparticles is proposed. The idea is based on spin readout of nitrogen-vacancy centers embedded in aspherical nanodiamonds levitating in an ion trap. We show that the asymmetry of the diamond induces a rotational confinement in the ion trap. Using a weak homogeneous magnetic field and a strong microwave driving we then demonstrate that the spin of the nitrogen-vacancy center can be strongly coupled to the rotational mode of the diamond.

Figure 1

(a) Schematics showing a prolate nanodiamond levitating in a needle Paul trap. The spin of a nitrogen-vacancy (NV) center inside the diamond senses the rotation of the particle in the presence of a transverse $B$ field. (b) Harmonic potential energy as a function of the angle $\varphi$ between the particle and the main trap axis, with rotational frequency ${\omega }_{\varphi }$. (c) NV center ground-state level shifts in the presence of a transverse magnetic field. The arrow shows the microwave driving with detuning $\mathrm{\Delta }$ from the $|g\rangle$ to the $|d\rangle$ transition.

Figure 2

(a) Level diagram and coupling between dressed spin states with rotational phonon numbers $N+1$ and $N$. (b) Coupling rate as a function of the $B$ field and $\mathrm{\Psi }/\pi$ for ${\omega }_{\varphi }/\left(2\pi \right)=5$ MHz and a 20-nm-diameter prolate particle. Solid, dashed, and dotted black lines are the $\psi$ parameter under resonant conditions as a function of the $B$ field for Rabi frequencies of 250, 500, and 1000 MHz, respectively.

Figure 3

Shapes of the proposed asymetric particles: (a) oblate ellipsoid, (b) prolate ellipsoid, and (c) composite particle formed by a diamond sphere deposited on a thin disk, approximated by an oblate ellipsoid.

Figure 4

Coupling rate ${\tilde{\lambda }}_{\varphi }$ for nanodiamonds of different shapes (a) with radius $b=20$ nm for prolate and oblate ellipsoids with rotational confinement ${\omega }_{\varphi }=5$ MHz and (b) with $b=80$ nm and rotational confinement ${\omega }_{\varphi }=0.5$ MHz. The microwave is set at resonance with a varying Rabi frequency and the magnetic field is tuned to obtain resonant conditions. For example, at ${\mathrm{\Omega }}_R/2\pi =500$ MHz we have $B\sim 30$ mT. The aspect ratio of the proposed particles is $a/b=2.5$ for all particles and $c/b=1/8$ and $1/16$ for the composite 20- and 10-nm disks, respectively. The coupling rate with a zero-mass disk (i.e., for a sphere) is plotted as a limit for such particles (trace iv).