Diamond Lamb wave resonators (LWRs) protected by a phononic band gap can enable a new technology platform for controlling interactions between spin qubits and single phonons and for using phonons to mediate coherent coupling between distant spin qubits. A LWR has the simple geometry of a thin elastic plate with free boundaries. The mechanical clamping or tethering loss of the compression modes in a LWR can be eliminated by shielding the mechanical modes with a phononic band gap. In this regime, mechanical damping is primarily due to intrinsic materials loss. Here, we report the fabrication and experimental demonstration of diamond LWRs that feature a GHz fundamental compression mode with a linewidth less than 100 Hz at a temperature near 7 K, corresponding to a Q-factor exceeding 10 million [1]. The ultrasmall linewidth achieved is one order of magnitude smaller than that of the state-of-the-art silicon GHz nanomechanical resonators obtained at similar or even lower temperatures, indicating ultrasmall intrinsic mechanical loss of diamond.

The nearly ideal protection provided by the phononic band gap also makes it difficult to excite and detect the compressional mechanical modes in a LWR. To overcome this difficulty, we have developed an all-optical approach, exciting compression modes with the temporally modulated optical gradient force of a sharply focused laser beam and probing the induced vibrations via strain coupling to a silicon vacancy (SiV) center. A resonant optical gradient force can effectively drive the fundamental compression mode, leading to strong phonon sidebands in the optical excitation spectrum of the SiV center. Vibrations as small as picometer are detected through sideband optical interferometry as well as sideband optical transitions.

The ultracoherent GHz nanomechanical resonator and its coupling to long-lived spin qubits in diamond should enable us to reach the quantum regime in spin-mechanics, opening a new path to developing spin-based quantum computers.

[1] Xinzhu Li, Ignas Lekavicius, Jens Noeckel, and Hailin Wang, “Ultracoherent Gigahertz Diamond Spin-Mechanical Lamb Wave Resonators,” Nano Letters 24, 10995 (2024).