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Next-generation gravitational wave observatories are expected to use cryogenically cooled, pendulum-suspended 200 kg test mass mirrors from a crystalline material such as crystalline silicon. During operation of the observatories, these mirrors undergo heating due to the absorption of laser radiation of up to a watt. Low noise cooling techniques need to be developed. Low-pressure helium exchange gas at 5 K might contribute to the challenging task. Here, we report the measurement of the helium accommodation coefficient $\alpha(11\,\mathrm{K} 0.7$ for temperatures < 20 K, which increases the cooling power compared to recently used assumptions. The idea of free molecular flow helium gas cooling is thus supported and might find application in some observatory concepts., Comment: 12 pages, 5 figures

Recent years have seen a rapid reduction in the intrinsic loss of nanomechanical resonators (i.e., chip-scale mechanical oscillators). As a result, these devices become increasingly sensitive to the friction exerted by smallest amounts of gas. Here, we present the pressure-dependency of a nanomechanical trampoline resonator's quality factor $Q$ over ten decades, from $10^{-7}$ to $10^{3}\,\mathrm{mbar}$. We find that the measured behavior is well-described by a model combining analytical and numerical components for molecular and viscous flow, respectively. This model relies exclusively on design and typical material parameters, together with measured values of intrinsic resonance frequency $f_\mathrm{in}$ and quality factor $Q_\mathrm{in}$. Measuring $f_\mathrm{in}$ and $Q_\mathrm{in}$ at a pressure $<\!10^{-7}\,\mathrm{mbar}$ self-calibrates our sensor over its entire measurement range. For a trampoline's fundamental out-of-plane vibrational mode, the resulting deviation between measured and simulated pressure dependencies of the quality factor and resonance frequency is within $15\,\%$ and $4\,\%$, respectively. The resulting error for pressure values inferred from quality factor and frequency measurements is $<10\,\%$, for pressures between $\sim 10^{-6}$ and $\sim 10^{-1}\,\mathrm{mbar}$, and $<25\,\%$ for the complete 10-decade measurement range. Exceptions are two outliers with increased measurement errors, which might be related to the limited accuracy of our commercial pressure gauge. Based on investigations with helium, we demonstrate the potential for extending this sensing capability to other gases, thereby highlighting the practical use of our sensor.

Recent observations made with Advanced LIGO and Advanced Virgo have initiated the era of gravitational-wave astronomy. The number of events detected by these "2nd Generation" (2G) ground-based observatories is partially limited by noise arising from temperature-induced position fluctuations of the test mass mirror surfaces used for probing spacetime dynamics. The design of next-generation gravitational-wave observatories addresses this limitation by using cryogenically cooled test masses; current approaches for continuously removing heat (resulting from absorbed laser light) rely on heat extraction via black-body radiation or conduction through suspension fibres. As a complementing approach for extracting heat during observational runs, we investigate cooling via helium gas impinging on the test mass in free molecular flow. We establish a relation between cooling power and corresponding displacement noise, based on analytical models, which we compare to numerical simulations. Applying this theoretical framework with regard to the conceptual design of the Einstein Telescope (ET), we find a cooling power of 10 mW at 18 K for a gas pressure that exceeds the ET design strain noise goal by at most a factor of $\sim 3$ in the signal frequency band from 3 to 11 Hz. A cooling power of 100 mW at 18 K corresponds to a gas pressure that exceeds the ET design strain noise goal by at most a factor of $\sim 11$ in the band from 1 to 28 Hz.

We introduce a passively-aligned, flexure-tuned cavity optomechanical system in which a membrane is positioned microns from one end mirror of a Fabry-Perot optical cavity. By displacing the membrane through gentle flexure of its silicon supporting frame (i.e., to ~80 m radius of curvature (ROC)), we gain access to the full range of available optomechanical couplings, finding also that the optical spectrum exhibits none of the abrupt discontinuities normally found in "membrane-in-the-middle" (MIM) systems. More aggressive flexure (3 m ROC) enables >15 microns membrane travel, milliradian tilt tuning, and a wavelength-scale (1.64 $\pm$ 0.78 microns) membrane-mirror separation. We also provide a complete set of analytical expressions for this system's leading-order dispersive and dissipative optomechanical couplings. Notably, this system can potentially generate orders of magnitude larger linear dissipative or quadratic dispersive strong coupling parameters than is possible with a MIM system. Additionally, it can generate the same purely quadratic dispersive coupling as a MIM system, but with significantly suppressed linear dissipative back-action (and force noise)., Comment: 24 pages, 3 figures

We demonstrate a high-Q ($>5 \times 10^{6}$) swept-frequency membrane mechanical resonator achieving octave resonance tuning via an integrated heater and an unprecedented acceleration noise floor below 1 $\mu$g Hz$^{-1/2}$ for frequencies above 50 kHz. This device is compatible with established batch fabrication techniques, and its optical readout is compatible with low-coherence light sources (e.g., a monochromatic light-emitting diode). The device can also be mechanically stabilized (or driven) with the same light source via bolometric optomechanics, and we demonstrate laser cooling from room temperature to 10 K. Finally, this method of frequency tuning is well-suited to fundamental studies of mechanical dissipation; in particular, we recover the dissipation spectra of many modes, identifying material damping and coupling to substrate resonances as the dominant loss mechanisms., Comment: 7 pages, 4 figures

We present a robust sideband laser locking technique that is ideally suited for applications requiring low probe power and heterodyne readout. By feeding back to a high-bandwidth voltage controlled oscillator, we lock a first-order phase-modulation sideband to a table-top high-finesse Fabry-Perot cavity, achieving a feedback bandwidth of 3.5 MHz with a single integrator, limited fundamentally by the signal delay. The directly measured transfer function of the closed feedback loop agrees with a model assuming ideal system components, and from this we suggest a modified design that should realistically achieve a bandwidth exceeding 6 MHz with a near-causally limited feedback gain of $4\times 10^7$ at 1 kHz. The off-resonance optical carrier is used for alignment-free heterodyne readout, alleviating the need for a second laser or additional optical modulators., Comment: 7 pages, 3 figures

By patterning a freestanding dielectric membrane into a photonic crystal reflector (PCR), it is possible to resonantly enhance its normal-incidence reflectivity, thereby realizing a thin, single-material mirror. In many PCR applications, the operating wavelength (e.g. that of a low-noise laser or emitter) is not tunable, imposing tolerances on crystal geometry that are not reliably achieved with standard nanolithography. Here we present a gentle technique to finely tune the resonant wavelength of a SiN PCR using iterative hydrofluoric acid etches. With little optimization, we achieve a 57-nm-thin photonic crystal having an operating wavelength within 0.15 nm (0.04 resonance linewidths) of our target (1550 nm). Our thin structure exhibits a broader and less pronounced transmission dip than is predicted by plane wave simulations, and we identify two effects leading to these discrepancies, both related to the divergence angle of a collimated laser beam. To overcome this limitation in future devices, we distill a series of simulations into a set of general design considerations for realizing robust, high-reflectivity resonances., Comment: 6 pages, 3 figures, 1 table

In force sensing, optomechanics, and quantum motion experiments, it is typically advantageous to create lightweight, compliant mechanical elements with the lowest possible force noise. Here we report wafer-scale batch fabrication and characterization of high-aspect-ratio, nanogram-scale Si$_3$N$_4$ "trampolines" having quality factors above $4 \times 10^7$ and ringdown times exceeding five minutes (1 mHz linewidth). We measure a thermally limited force noise sensitivity of 16.2$\pm$0.8 aN/Hz$^{1/2}$ at room temperature, with a spring constant ($\sim$1 N/m) 2-5 orders of magnitude larger than those of competing technologies. We also characterize the suitability of these devices for high-finesse cavity readout and optomechanics applications, finding no evidence of surface or bulk optical losses from the processed nitride in a cavity achieving finesse 40,000. These parameters provide access to a single-photon cooperativity $C_0 \sim 8$ in the resolved-sideband limit, wherein a variety of outstanding optomechanics goals become feasible., Comment: 8 pages, 4 figures, 1 table

Optically levitated mechanical sensors promise isolation from thermal noise far beyond what is possible using flexible materials alone. One way to access this potential is to apply a strong optical trap to a minimally supported mechanical element, thereby increasing its quality factor $Q_m$. Current schemes, however, require prohibitively high laser power ($\sim10$ W), and the $Q_m$ enhancement is ultimately limited to a factor of $\sim$ 50 by hybridization between the trapped mode and the dissipative modes of the supporting structure. Here we propose a levitation scheme taking full advantage of an optical resonator to reduce the circulating power requirements by many orders of magnitude. Applying this scheme to the case of a dielectric disk in a Fabry-Perot cavity, we find a tilt-based tuning mechanism for optimizing both center-of-mass and torsional mode traps. Notably, the two modes are trapped with comparable efficiency, and we estimate that a 10-micron-diameter, 100-nm-thick Si disc could be trapped to a frequency of $\sim$ 10 MHz with only $30$ mW circulating in a cavity of (modest) finesse 1500. Finally, we simulate the effect such a strong trap would have on a realistic doubly-tethered disc. Of central importance, we find torsional motion is comparatively immune to $Q_m$-limiting hybridization, allowing a $Q_m$ enhancement factor of $\sim$ 1500. This opens the possibility of realizing a laser-tuned 10 MHz mechanical system with a quality factor of order a billion., Comment: 10 pages, 6 figures