Microwave cavities are commonly used in many experiments, including optomechanics, magnetic field sensing, magnomechanics, and circuit quantum electrodynamics. Noise, such as variations in the magnetic field or mechanical vibrations, can cause fluctuations of the natural frequency of the cavity, creating challenges in operating them in experiments. To overcome these challenges, we demonstrate a dynamic feedback system implemented by the locking of a microwave drive to the noisy cavity. A homodyne-interferometer scheme monitors the cavity resonance fluctuations due to low-frequency noise, which is mitigated by frequency modulating the microwave generator. The feedback has a bandwidth of 400 Hz, with a reduction of cavity fluctuations by 85% integrating up to a bandwidth of 2 kHz. Moreover, the cavity resonance frequency fluctuations are reduced by 73%. This scheme can be scaled to enable multitone experiments locked to the same feedback signal. As a demonstration, we apply the feedback to an optomechanical experiment and implement a cavity-locked multitone mechanical measurement. As low-frequency cavity frequency noise can be a limiting factor in many experiments, the multitone microwave locking technique presented here is expected to be relevant for a wide range of microwave-cavity experiments. @en

The radiation pressurelike coupling between magnons and phonons in magnets can modify the phonon frequency (magnomechanical spring effect) and decay rate (magnomechanical decay) via dynamical backaction. Such effects have been recently observed by coupling the uniform magnon mode of a magnetic sphere (the Kittel mode) to a microwave cavity. In particular, the ability to evade backaction effects was demonstrated [C. A. Potts, Phys. Rev. B 107, L140405 (2023)10.1103/PhysRevB.107.L140405], a requisite for applications such as magnomechanical-based thermometry. However, deviations were observed from the predicted magnomechanical decay rate within the standard theoretical model. In this work, we account for these deviations by considering corrections due to (i) magnetic Kerr nonlinearities and (ii) the coupling of phonons to additional magnon modes. Provided that such additional modes couple weakly to the driven cavity, our model yields a correction proportional to the average Kittel magnon mode occupation. We focus our results on magnetic spheres, where we show that the magnetostatic Walker modes couple to the relevant mechanical modes as efficiently as the Kittel mode. Our model yields excellent agreement with the experimental data. @en

We demonstrate electromechanical coupling between a superfluid mechanical mode and a microwave mode formed by a patterned microfluidic chip and a 3D cavity. The electric field of the chip-cavity microwave resonator can be used to both drive and detect the motion of a pure superflow Helmholtz mode, which is dictated by geometric confinement. The coupling is characterized using a coherent measurement technique developed for measuring weak couplings deep in the sideband unresolved regime. The technique is based on two-probe optomechanically induced transparency/amplification using amplitude modulation. Instead of measuring two probe tones separately, they are interfered to retain only a signal coherent with the mechanical motion. With this method, we measure a vacuum electromechanical coupling strength of g 0 = 2 p × 23.3 µ Hz, three orders of magnitude larger than previous superfluid electromechanical experiments.@en