Quantum metrology uses quantum entanglement--correlations in the properties of microscopic systems--to improve the statistical precision of physical measurements. When measuring a signal, such as the phase shift of a light beam or an atomic state, a prominent limitation to achievable precision arises from the noise associated with the counting of uncorrelated probe particles. This noise, commonly referred to as shot noise or projection noise, gives rise to the standard quantum limit (SQL) to phase resolution. However, it can be mitigated down to the fundamental Heisenberg limit by entangling the probe particles. Despite considerable experimental progress in a variety of physical systems, a question that persists is whether these methods can achieve performance levels that compare favourably with optimized conventional (non-entangled) systems. Here we demonstrate an approach that achieves unprecedented levels of metrological improvement using half a million (87)Rb atoms in their 'clock' states. The ensemble is 20.1 ± 0.3 decibels (100-fold) spin-squeezed via an optical-cavity-based measurement. We directly resolve small microwave-induced rotations 18.5 ± 0.3 decibels (70-fold) beyond the SQL. The single-shot phase resolution of 147 microradians achieved by the apparatus is better than that achieved by the best engineered cold atom sensors despite lower atom numbers. We infer entanglement of more than 680 ± 35 particles in the atomic ensemble. Applications include atomic clocks, inertial sensors, and fundamental physics experiments such as tests of general relativity or searches for electron electric dipole moment. To this end, we demonstrate an atomic clock measurement with a quantum enhancement of 10.5 ± 0.3 decibels (11-fold), limited by the phase noise of our microwave source.

Extreme stresses can be produced in nanoscale structures; this feature has been used to realize enhanced materials properties, such as the high mobility of silicon in modern transistors. We show how nanoscale stress can be used to realize exceptionally low mechanical dissipation when combined with "soft-clamping"-a form of phononic engineering. Specifically, using a nonuniform phononic crystal pattern, we colocalize the strain and flexural motion of a free-standing silicon nitride nanobeam. Ringdown measurements at room temperature reveal string-like vibrational modes with quality () factors as high as 800 million and × frequency exceeding 10 hertz. These results illustrate a promising route for engineering ultracoherent nanomechanical devices.

Quantum metrology exploits entangled states of particles to improve sensing precision beyond the limit achievable with uncorrelated particles. All previous methods required detection noise levels below this standard quantum limit to realize the benefits of the intrinsic sensitivity provided by these states. We experimentally demonstrate a widely applicable method for entanglement-enhanced measurements without low-noise detection. The method involves an intermediate quantum phase magnification step that eases implementation complexity. We used it to perform squeezed-state metrology 8 decibels below the standard quantum limit with a detection system that has a noise floor 10 decibels above the standard quantum limit.

Low-loss photonic integrated circuits and microresonators have enabled a wide range of applications, such as narrow-linewidth lasers and chip-scale frequency combs. To translate these into a widespread technology, attaining ultralow optical losses with established foundry manufacturing is critical. Recent advances in integrated Si3N4 photonics have shown that ultralow-loss, dispersion-engineered microresonators with quality factors Q > 10 × 106 can be attained at die-level throughput. Yet, current fabrication techniques do not have sufficiently high yield and performance for existing and emerging applications, such as integrated travelling-wave parametric amplifiers that require meter-long photonic circuits. Here we demonstrate a fabrication technology that meets all requirements on wafer-level yield, performance and length scale. Photonic microresonators with a mean Q factor exceeding 30 × 106, corresponding to 1.0 dB m−1 optical loss, are obtained over full 4-inch wafers, as determined from a statistical analysis of tens of thousands of optical resonances, and confirmed via cavity ringdown with 19 ns photon storage time. The process operates over large areas with high yield, enabling 1-meter-long spiral waveguides with 2.4 dB m−1 loss in dies of only 5 × 5 mm2 size. Using a response measurement self-calibrated via the Kerr nonlinearity, we reveal that the intrinsic absorption-limited Q factor of our Si3N4 microresonators can exceed 2 × 108. This absorption loss is sufficiently low such that the Kerr nonlinearity dominates the microresonator’s response even in the audio frequency band. Transferring this Si3N4 technology to commercial foundries can significantly improve the performance and capabilities of integrated photonics.

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