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

The incorporation paths of Be in GaAs nanowires grown by the Ga-assisted method in molecular beam epitaxy have been investigated by electrical measurements of nanowires with different doping profiles. We find that Be atoms incorporate preferentially via the nanowire side facets, while the incorporation path through the Ga droplet is negligible. We also show that Be can diffuse into the volume of the nanowire giving an alternative incorporation path. This work is an important step towards controlled doping of nanowires and will serve as a help for designing future devices based on nanowires.

We image and characterize the mechanical modes of a 2D drum resonator made of hBN suspended over a high-stress Si3N4 membrane. Our measurements demonstrate hybridization between various modes of the hBN resonator and those of the Si3N4 membrane. The measured resonance frequencies and spatial profiles of the modes are consistent with finite-element simulations based on idealized geometry. Spectra of the thermal motion reveal that, depending on the degree of hybridization with modes of the heavier and higher-quality-factor Si3N4 membrane, the quality factors and the motional mass of the hBN drum modes can be shifted by orders of magnitude. This effect could be exploited to engineer hybrid drum/membrane modes that combine the low motional mass of 2D materials with the high quality factor of Si3N4 membranes for optomechanical or sensing applications.

We realize mirror templates on the tips of optical fibers using a single-shot CO 2 laser ablation procedure. We perform a systematic study of the influence of the pulse power, pulse duration, and laser spot size on the radius of curvature, depth, and diameter of the mirror templates. We find that these geometrical characteristics can be tuned to a larger extent than has been previously reported, and notably observe that compound convex-concave shapes can be obtained. This detailed investigation should help further the understanding of the physics of CO 2 laser ablation processes and help improve current models. We additionally identify regimes of ablation parameters that lead to mirror templates with favorable geometries for use in cavity quantum electrodynamics and optomechanics.

We describe an apparatus for the implementation of hybrid optomechanical systems at 4 K. The platform is based on a high-finesse, micrometer-scale fiber Fabry–Perot cavity, which can be widely tuned using piezoelectric positioners. A mechanical resonator can be positioned within the cavity in the object-in-the-middle configuration by a second set of positioners. A high level of stability is achieved without sacrificing either performance or tunability, through the combination of a stiff mechanical design, passive vibration isolation, and an active Pound–Drever–Hall feedback lock incorporating a reconfigurable digital filter. The stability of the cavity length is demonstrated to be better than a few picometers over many hours both at room temperature and at 4 K.