Coupling of nitrogen vacancy centers in nanodiamonds by means of phonons

Realising controlled quantum dynamics via the magnetic interactions between colour centers in diamond remains a challenge despite recent demonstrations for nanometer separated pairs. Here we propose to use the intrinsic acoustical phonons in diamond as a data bus for accomplishing this task. We show that for nanodiamonds the electron-phonon coupling can take significant values that together with mode frequencies in the THz range, can serve as a resource for conditional gate operations. Based on these results we analyze how to use this phonon-induced interaction for constructing quantum gates among the electron-spin triplet ground states, introducing the phonon dependence via Raman transitions. Combined with decoupling pulses this offers the possibility for creating entangled states within nanodiamonds on the scale of several tens of nanometers, a promising prerequisite for quantum sensing applications.