In real-time quantum feedback protocols, the record of a continuous measurement is used to stabilize a desired quantum state. Recent years have seen successful applications of these protocols in a variety of well-isolated micro-systems, including microwave photons and superconducting qubits. However, stabilizing the quantum state of a tangibly massive object, such as a mechanical oscillator, remains very challenging: the main obstacle is environmental decoherence, which places stringent requirements on the timescale in which the state must be measured. Here we describe a position sensor that is capable of resolving the zero-point motion of a solid-state, 4.3-megahertz nanomechanical oscillator in the timescale of its thermal decoherence, a basic requirement for real-time (Markovian) quantum feedback control tasks, such as ground-state preparation. The sensor is based on evanescent optomechanical coupling to a high-Q microcavity, and achieves an imprecision four orders of magnitude below that at the standard quantum limit for a weak continuous position measurement--a 100-fold improvement over previous reports--while maintaining an imprecision-back-action product that is within a factor of five of the Heisenberg uncertainty limit. As a demonstration of its utility, we use the measurement as an error signal with which to feedback cool the oscillator. Using radiation pressure as an actuator, the oscillator is cold damped with high efficiency: from a cryogenic-bath temperature of 4.4 kelvin to an effective value of 1.1 ± 0.1 millikelvin, corresponding to a mean phonon number of 5.3 ± 0.6 (that is, a ground-state probability of 16 per cent). Our results set a new benchmark for the performance of a linear position sensor, and signal the emergence of mechanical oscillators as practical subjects for measurement-based quantum control.

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 correlations between imprecision and back-action are a hallmark of continuous linear measurements. Here we study how measurement-based feedback can be used to improve the visibility of quantum correlations due to the interaction of a laser field with a nano-optomechanical system. Back-action imparted by the meter laser, due to radiation pressure quantum fluctuations, gives rise to correlations between its phase and amplitude quadratures. These quantum correlations are observed in the experiment both as squeezing of the meter field fluctuations below the vacuum level in a homodyne measurement, and as sideband asymmetry in a heterodyne measurement, demonstrating the common origin of both phenomena. We show that quantum feedback, i.e. feedback that suppresses measurement back-action, can be used to increase the visibility of the sideband asymmetry ratio. In contrast, by operating the feedback loop in the regime of noise squashing, where the in-loop photocurrent variance is reduced below the vacuum level, the visibility of the sideband asymmetry is reduced. This is due to feedback back-action arising from vacuum noise in the homodyne detector. These experiments demonstrate the possibility, as well as the fundamental limits of measurement-based feedback as a tool to manipulate quantum correlations. arXiv:1602.05942v2 [quant-ph]

High-stress SiN nanoresonators have become an attractive choice for electro- and optomechanical devices. Membrane resonators can achieve quality factor (Q)-frequency (f) products exceeding 10 Hz, enabling (in principle) quantum coherent operation at room temperature. String-like beam resonators possess smaller Q × f products; however, on account of their significantly lower mass and mode density, they remain a canonical choice for precision force, mass, and charge sensing, and have recently enabled Heisenberg-limited position measurements at cryogenic temperatures. Here we explore two techniques to enhance the Q of a nanomechanical beam. The techniques relate to two main loss mechanisms: internal loss, which dominates for high aspect ratios and f ≲ 100 MHz, and radiation loss, which dominates for low aspect ratios and f ≳ 100 MHz. First, we show that by embedding a nanobeam in a 1D phononic crystal (PnC), it is possible to localize its flexural motion and shield it against radiation loss. Using this method, we realize f > 100 MHz modes with Q ≈ 10, consistent with internal loss and contrasting sharply with unshielded beams of similar dimensions. We then study the Q × f product of high-order modes of millimeter-long nanobeams. Taking advantage of the mode-shape dependence of stress-induced "loss dilution", we realize a f ≈ 4 MHz mode with Q × f ≈ 9 × 10 Hz. Our results complement recent work on PnC-based "soft-clamping" of nanomembranes, in which mode localization is used to enhance loss dilution. Combining these strategies should enable ultra-low-mass nanobeam oscillators that operate deep in the quantum coherent regime at room temperature.

Mechanical resonators with high quality factors are of relevance in precision experiments, ranging from gravitational wave detection and force sensing to quantum optomechanics. Beams and membranes are well known to exhibit flexural modes with enhanced quality factors when subjected to tensile stress. The mechanism for this enhancement has been a subject of debate, but is typically attributed to elastic energy being "diluted" by a lossless potential. Here we clarify the origin of the lossless potential to be the combination of tension and geometric nonlinearity of strain. We present a general theory of dissipation dilution that is applicable to arbitrary resonator geometries and discuss why this effect is particularly strong for flexural modes of nanomechanical structures with high aspect ratios. Applying the theory to a non-uniform doubly clamped beam, we show analytically how dissipation dilution can be enhanced by modifying the beam shape to implement "soft clamping", thin clamping and geometric strain engineering, and derive the ultimate limit for dissipation dilution. arXiv:1807.07086v1 [physics.app-ph]