We control the electronic structure of the silicon-vacancy (SiV) color-center in diamond by changing its static strain environment with a nano-electro-mechanical system. This allows deterministic and local tuning of SiV optical and spin transition frequencies over a wide range, an essential step towards multi-qubit networks. In the process, we infer the strain Hamiltonian of the SiV revealing large strain susceptibilities of order 1 PHz/strain for the electronic orbital states. We identify regimes where the spin-orbit interaction results in a large strain suseptibility of order 100 THz/strain for spin transitions, and propose an experiment where the SiV spin is strongly coupled to a nanomechanical resonator.arXiv:1801.09833v2 [quant-ph]

Single-crystal diamond, with its unique optical, mechanical and thermal properties, has emerged as a promising material with applications in classical and quantum optics. However, the lack of heteroepitaxial growth and scalable fabrication techniques remains the major limiting factors preventing more wide-spread development and application of diamond photonics. In this work, we overcome this difficulty by adapting angled-etching techniques, previously developed for realization of diamond nanomechanical resonators, to fabricate racetrack resonators and photonic crystal cavities in bulk single-crystal diamond. Our devices feature large optical quality factors, in excess of 10 5 , and operate over a wide wavelength range, spanning visible and telecom. These newly developed high-Q diamond optical nanocavities open the door for a wealth of applications, ranging from nonlinear optics and chemical sensing, to quantum information processing and cavity optomechanics.

We propose and analyze a novel realization of a solid-state quantum network, where separated silicon-vacancy centers are coupled via the phonon modes of a quasi-one-dimensional diamond waveguide. In our approach, quantum states encoded in long-lived electronic spin states can be converted into propagating phonon wave packets and be reabsorbed efficiently by a distant defect center. Our analysis shows that under realistic conditions, this approach enables the implementation of high-fidelity, scalable quantum communication protocols within chip-scale spin-qubit networks. Apart from quantum information processing, this setup constitutes a novel waveguide QED platform, where strong-coupling effects between solid-state defects and individual propagating phonons can be explored at the quantum level.

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GUIDED ACOUSTIC PHONON MODES IN DIAMOND OPTOMECHANICAL CRYSTALSTo supplement our discussion of the guided acoustic phonon modes supported by diamond optomechanical crystals (OMCs), we present normalized displacement profiles of the nominal unit cell at the Γ (kx = 0) and X (kx = π/a) points of its mechanical bandstructure (originally displayed in Figure 1(c) of the main text). Figures S1 and S2 reveal the guided acoustic modes categorized by even (solid black lines) and odd (dashed blue lines) vector symmetries about the y-axis, respectively, with displacement profiles originating from the indicated band edges shown as insets (three dimensional, top down and cross-section views included). Note, the unit cell lattice constant in the displacement profiles is displayed between the (hx, n, hy, n) and (hx, n+1, hy, n+1) center points, in order to clearly reveal displacement components within the air holes. Mechanical simulations included here and throughout the main text use the full anisotropic elasticity matrix of diamond [1], where (C11, C12, C44) = (1076, 125, 578) GPa. However, due to considerations expanded upon in section 5 of this supplementary material, devices characterized in this work were ultimately fabricated with their x-axis oriented with the in-plane [110] crystallographic direction. Thus, a rotated version of the anisotropic elasticity matrix ensured proper device orientation in our simulations, with guided mode propagation along the x-axis aligned with the [110] crystallographic direction, with the z-axis aligned with [001]. Only a small (< 10 %) change in the guided mode frequencies was observed between simulations with unit cell x-axis alignment to the [100] and [110] in plane crystal directions.While the mechanical bandstructures reveal a rich library of guided acoustic modes in the few to 16 GHz frequency range, only guided modes originating from y-symmetric bands ultimately couple to the optical cavity [2]. Additionally, modes originating from the Γ-point ensure large optomechanical coupling rates in the final design [3]. With this in mind, two modes from the Γ-point of ysymmetric bands enable design of diamond OMCs with large single-photon optomechanical coupling rates, go. Specifically, the Γ-point modes from the 4 th and 7 th y-symmetric bands, referred to as the "flapping" and "swelling" modes, respectively, were both investigated. OPTIMIZED DIAMOND OPTOMECHANICAL CRYSTAL DESIGNAs discussed in the main text, the final diamond OMC design relies on transitioning from a "mirror" region formed by the base unit cell in Figure 1(a) to a "defect" cell, which localizes the target