On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

The small mass and high coherence of nanomechanical resonators render them the ultimate mechanical probe, with applications that range from protein mass spectrometry and magnetic resonance force microscopy to quantum optomechanics. A notorious challenge in these experiments is the thermomechanical noise related to the dissipation through internal or external loss channels. Here we introduce a novel approach to define the nanomechanical modes, which simultaneously provides a strong spatial confinement, full isolation from the substrate and dilution of the resonator material's intrinsic dissipation by five orders of magnitude. It is based on a phononic bandgap structure that localizes the mode but does not impose the boundary conditions of a rigid clamp. The reduced curvature in the highly tensioned silicon nitride resonator enables a mechanical Q > 108 at 1 MHz to yield the highest mechanical Qf products (>1014 Hz) yet reported at room temperature. The corresponding coherence times approach those of optically trapped dielectric particles. Extrapolation to 4.2 K predicts quanta per milliseconds heating rates, similar to those of trapped ions. Soft phononic clamping dilutes the intrinsic dissipation of a mechanical resonator's material by five orders of magnitude, enabling a record value of the product between frequency and quality factor at room temperature, and mechanical coherence times otherwise only available in optical or Paul traps.

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Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution.

Nanomechanical oscillators are at the heart of ultrasensitive detectors of force, mass and motion. As these detectors progress to even better sensitivity, they will encounter measurement limits imposed by the laws of quantum mechanics. If the imprecision of a measurement of the displacement of an oscillator is pushed below a scale set by the standard quantum limit, the measurement must perturb the motion of the oscillator by an amount larger than that scale. Here we show a displacement measurement with an imprecision below the standard quantum limit scale. We achieve this imprecision by measuring the motion of a nanomechanical oscillator with a nearly shot-noise limited microwave interferometer. As the interferometer is naturally operated at cryogenic temperatures, the thermal motion of the oscillator is minimized, yielding an excellent force detector with a sensitivity of 0.51 aN Hz(-1/2). This measurement is a critical step towards observing quantum behaviour in a mechanical object.

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Nanomechanical motion measured with an imprecision below the standard quantum limit

Controlling a quantum system by using observations of its dynamics is complicated by the backaction of the measurement process—that is, the unavoidable quantum disturbance caused by coupling the system to a measurement apparatus. An efficient measurement is one that maximizes the amount of information gained per disturbance incurred. Real-time feedback can then be used to cancel the backaction of the measurement and to control the evolution of the quantum state. Such measurement-based quantum control has been demonstrated in the clean settings of cavity and circuit quantum electrodynamics, but its application to motional degrees of freedom has remained elusive. Here we demonstrate measurement-based quantum control of the motion of a millimetre-sized membrane resonator. An optomechanical transducer resolves the zero-point motion of the resonator in a fraction of its millisecond-scale coherence time, with an overall measurement efficiency close to unity. An electronic feedback loop converts this position record to a force that cools the resonator mode to its quantum ground state (residual thermal occupation of about 0.29). This occupation is nine decibels below the quantum-backaction limit of sideband cooling and six orders of magnitude below the equilibrium occupation of the thermal environment. We thus realize a long-standing goal in the field, adding position and momentum to the degrees of freedom that are amenable to measurement-based quantum control, with potential applications in quantum information processing and gravitational-wave detectors.

Measurement-based quantum control of mechanical motion

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 ( Q ) factors as high as 800 million and Q × frequency exceeding 10 15 hertz. These results illustrate a promising route for engineering ultracoherent nanomechanical devices.

https://science.sciencemag.org/content/sci/360/6390/764.full.pdf

Elastic strain engineering for ultralow mechanical dissipation

Dielectric membranes with exceptional mechanical and optical properties present one of the most promising platforms in quantum opto-mechanics. The performance of stressed silicon nitride nanomembranes as mechanical resonators notoriously depends on how their frame is clamped to the sample mount, which in practice usually necessitates delicate, and difficult-to-reproduce mounting solutions. Here, we demonstrate that a phononic bandgap shield integrated in the membrane’s silicon frame eliminates this dependence, by suppressing dissipation through phonon tunneling. We dry-etch the membrane’s frame so that it assumes the form of a cm-sized bridge featuring a 1-dimensional periodic pattern, whose phononic density of states is tailored to exhibit one, or several, full band gaps around the membrane’s high-Q modes in the MHz-range. We quantify the effectiveness of this phononic bandgap shield by optical interferometry measuring both the suppressed transmission of vibrations, as well as the influence of frame clamping conditions on the membrane modes. We find suppressions up to 40 dB and, for three different realized phononic structures, consistently observe significant suppression of the dependence of the membrane’s modes on sample clamping—if the mode’s frequency lies in the bandgap. As a result, we achieve membrane mode quality factors of 5 × 106 with samples that are tightly bolted to the 8 K-cold finger of a cryostat. Q × f -products of 6 × 1012 Hz at 300 K and 14 × 1012 Hz at 8 K are observed, satisfying one of the main requirements for optical cooling of mechanical vibrations to their quantum ground-state.

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Demonstration of suppressed phonon tunneling losses in phononic bandgap shielded membrane resonators for high-Q optomechanics

We discuss several techniques based on laser-driven interferometers and cavities to measure nanomechanical motion. With increasing complexity, they achieve sensitivities reaching from thermal displacement amplitudes, typically at the picometer scale, all the way to the quantum regime, in which radiation pressure induces motion correlated with the quantum fluctuations of the probing light. We show that an imaging modality is readily provided by scanning laser interferometry, reaching a sensitivity on the order of $ 10\kern0.166667em \mathrm{fm}/{\mathrm{Hz}}^{1/2} $, and a transverse resolution down to $ 2\kern0.166667em \upmu \mathrm{m} $. We compare this approach with a less versatile, but faster (single-shot) dark-field imaging technique.

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Measuring and imaging nanomechanical motion with laser light

We realise a circular gray-field polariscope to image stress-induced birefringence in thin (submicron thick) silicon nitride (SiN) membranes and strings. This enables quantitative mapping of the orientation of principal stresses and stress anisotropy, complementary to, and in agreement with, finite element modeling (FEM). Furthermore, using a sample with a well known stress anisotropy, we extract a new value for the photoelastic (Brewster) coefficient of silicon nitride, $C \approx (3.4~\pm~0.1)\times~10^{-6}~\mathrm{MPa}^{-1}$. We explore possible applications of the method to analyse and quality-control stressed membranes with phononic crystal patterns

Polarimetric analysis of stress anisotropy in nanomechanical silicon nitride resonators

We realise a circular gray-field polariscope to image stress-induced birefringence in thin (sub-micron thick) silicon nitride membranes and strings. This enables quantitative mapping of the orientation of principal stresses and stress anisotropy, complementary to, and in agreement with, finite element modeling. Furthermore, using a sample with a well-known stress anisotropy, we extract a value for the photoelastic (Brewster) coefficient of silicon nitride, C ≈ (3.4 ± 0.1) × 10−6 MPa−1. We explore possible applications of the method to analyse and quality-control stressed membranes with phononic crystal patterns.

Andreas Barg

Papers

Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution.

Demonstration of suppressed phonon tunneling losses in phononic bandgap shielded membrane resonators for high-Q optomechanics

Measuring and imaging nanomechanical motion with laser light

Polarimetric analysis of stress anisotropy in nanomechanical silicon nitride resonators

Polarimetric analysis of stress anisotropy in nanomechanical silicon nitride resonators