Phonon lasers, which exploit coherent amplifications of phonons, are a means to explore nonlinear phononics, image nanomaterial structures and operate phononic devices. Recently, a phonon laser governed by dispersive optomechanical coupling has been demonstrated by levitating a nanosphere in an optical tweezer. Such levitated optomechanical devices, with minimal noise in high vacuum, can allow flexible control of large-mass objects without any internal discrete energy levels. However, it is challenging to achieve phonon lasing with levitated microscale objects because optical scattering losses are much larger than at the nanoscale. Here we report a nonlinear multi-frequency phonon laser with a micro-size sphere, which is governed by dissipative coupling. The active gain provided by a Yb³⁺-doped system plays a key role. It achieves three orders of magnitude for the amplitude of the fundamental-mode phonon lasing, compared with the passive device. In addition, nonlinear mechanical harmonics can emerge spontaneously above the lasing threshold. Furthermore, we observe coherent correlations of phonons for both the fundamental mode and its harmonics. Our work drives the field of levitated optomechanics into a regime where it becomes feasible to engineer collective motional properties of typical micro-size objects.

The comagnetometer has been one of the most sensitive devices with which to test new physics related to spin-dependent interactions, but the comagnetometers based on overlapping ensembles of multiple spin species usually suffer from systematic errors due to magnetic field gradients. Here, we propose a comagnetometer based on the Zeeman transitions of the dual hyperfine levels in ground-state ${}^{87}\mathrm{Rb}$ atoms, which shows nearly negligible sensitivity to variations of laser power and frequency, magnetic field, and magnetic field gradients. We measured the hypothetical spin-dependent gravitational energy of the proton with the comagnetometer, which is smaller than $4\times {10}^{-18}\mathrm{eV}$, comparable to the most stringent existing constraint. Through optimizing the system parameters such as cell temperature, laser power, amplitude of driving magnetic field, as well as choosing better current source, it is possible to improve the sensitivity of the comagnetometer further.

The presence of a magnetic field gradient in a sample cell containing spin-polarized ¹²⁹Xe atoms will cause an increased relaxation rate. We measured the transverse spin relaxation time of ¹²⁹Xe verse the applied magnetic field gradient and the cell temperature. We then compared the different transverse spin relaxation behavior of dual isotopes of xenon (¹²⁹Xe and ¹³¹Xe) due to magnetic field gradient in the same cell. The experiment results show the residual magnetic field gradient can be measured and compensated by applying a negative magnetic gradient in the sample cell. The transverse spin relaxation time of ¹²⁹Xe could be increased 2–7 times longer when applying an appropriate magnetic field gradient. The experiment results can also be used to determine the diffusion constant of ¹²⁹Xe in H₂ and N₂ to be 0.4 ± 0.26 cm²/sec and 0.12 ± 0.02 cm²/sec. The results are close with theoretical calculation.

The cylindrical resonator gyroscope (CRG) is a typical Coriolis vibratory gyroscope whose performance is determined by the Q factor and frequency mismatch of the cylindrical resonator. Enhancing the Q factor is crucial for improving the rate sensitivity and noise performance of the CRG. In this paper, for the first time, a monolithic cylindrical fused silica resonator with a Q factor approaching 8 × 10⁵ (ring-down time over 1 min) is reported. The resonator is made of fused silica with low internal friction and high isotropy, with a diameter of 25 mm and a center frequency of 3974.35 Hz. The structure of the resonator is first briefly introduced, and then the experimental non-contact characterization method is presented. In addition, the post-fabrication experimental procedure of Q factor improvement, including chemical and thermal treatment, is demonstrated. The Q factor improvement by both treatments is compared and the primary loss mechanism is analyzed. To the best of our knowledge, the work presented in this paper represents the highest reported Q factor for a cylindrical resonator. The proposed monolithic cylindrical fused silica resonator may enable high performance inertial sensing with standard manufacturing process and simple post-fabrication treatment.

The hemispherical resonator gyroscope (HRG) has attracted the interest of the world inertial navigation community because of its exceptional performance, ultra-high reliability and its potential to be miniaturized. These devices achieve their best performance when the differences in the frequencies of the two degenerate working modes are eliminated. Mechanical treatment, laser ablation, ion-beams etching, etc., have all been applied for the frequency tuning of resonators, however, they either require costly equipment and procedures, or alter the quality factors of the resonators significantly. In this paper, we experimentally investigated for the first time the use of a chemical etching procedure to decrease the frequency splits of hemispherical resonators. We provide a theoretical analysis of the chemical etching procedure, as well as the relation between frequency splits and mass errors. Then we demonstrate that the frequency split could be decreased to below 0.05 Hz by the proposed chemical etching procedure. Results also showed that the chemical etching method caused no damage to the quality factors. Compared with other tuning methods, the chemical etching method is convenient to implement, requiring less time and labor input. It can be regarded as an effective trimming method for obtaining medium accuracy hemispherical resonator gyroscopes.

Phonon lasers, as mechanical analogues of optical lasers, are unique tools for not only fundamental studies of the emerging field of phononics but also diverse applications such as deep-ocean monitoring, force sensing, and biomedical ultrasonics. Recently, nonlinear phonon-lasing effects were observed in an opto-levitated micro-sphere, i.e., the spontaneous emerging of weak signals of high-order phonon harmonics in the phonon lasing regime. However, both the strengths and the quality factors of the emerging phonon harmonics are very poor, thus severely hindering their potential applications in making and utilizing nonlinear phonon-laser devices. Here we show that, by applying a single-colour electronic injection to this levitated system, giant enhancement can be achieved for all higher-order phonon harmonics, with more than 3 orders enhanced brightness and 5 orders narrowed linewidth. Such an electronically-enhanced phonon laser is also far more stable, with frequency stability extended from a dozen of minutes to over 1 h. More importantly, higher-order phonon correlations, as an essential lasing feature, are confirmed to be enhanced by the electronic injection as well, which as far as we know, has not been reported in previous works using this technique. This work, providing much stronger and better-quality signals of coherent phonon harmonics, is a key step towards controlling and utilizing nonlinear phonon lasers for applications such as phonon frequency combs, broadband phonon sensors, and ultrasonic bio-medical diagnosis.