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Evidence of fluctuations in transport have long been predicted in 3 He. They are expected to contribute only within 100μK of T c and play a vital role in the theoretical modeling of ordering; they encode details about the Fermi liquid parameters, pairing symmetry, and scattering phase shifts. It is expected that they will be of crucial importance for transport probes of the topologically nontrivial features of superfluid 3 He under strong confinement. Here we characterize the temperature and pressure dependence of the fluctuation signature, by monitoring the quality factor of a quartz tuning fork oscillator. We have observed a fluctuation-driven reduction in the viscosity of bulk 3 He, finding data collapse consistent with the predicted theoretical behavior., (© 2023. Springer Nature Limited.)

Because of the extreme purity, lack of disorder, and complex order parameter, the first-order superfluid 3 He A-B transition is the leading model system for first order transitions in the early universe. Here we report on the path dependence of the supercooling of the A phase over a wide range of pressures below 29.3 bar at nearly zero magnetic field. The A phase can be cooled significantly below the thermodynamic A-B transition temperature. While the extent of supercooling is highly reproducible, it depends strongly upon the cooling trajectory: The metastability of the A phase is enhanced by transiting through regions where the A phase is more stable. We provide evidence that some of the additional supercooling is due to the elimination of B phase nucleation precursors formed upon passage through the superfluid transition. A greater understanding of the physics is essential before 3 He can be exploited to model transitions in the early universe., (© 2023. The Author(s).)

Superfluid 3 He, with unconventional spin-triplet p-wave pairing, provides a model system for topological superconductors, which have attracted significant interest through potential applications in topologically protected quantum computing. In topological insulators and quantum Hall systems, the surface/edge states, arising from bulk-surface correspondence and the momentum space topology of the band structure, are robust. Here we demonstrate that in topological superfluids and superconductors the surface Andreev bound states, which depend on the momentum space topology of the emergent order parameter, are fragile with respect to the details of surface scattering. We confine superfluid 3 He within a cavity of height D comparable to the Cooper pair diameter ξ 0 . We precisely determine the superfluid transition temperature T c and the suppression of the superfluid energy gap, for different scattering conditions tuned in situ, and compare to the predictions of quasiclassical theory. We discover that surface magnetic scattering leads to unexpectedly large suppression of T c , corresponding to an increased density of low energy bound states.

The investigation of transport properties in normal liquid helium-3 and its topological superfluid phases provides insights into related phenomena in electron fluids, topological materials, and putative topological superconductors. It relies on the measurement of mass, heat, and spin currents, due to system neutrality. Of particular interest is transport in strongly confining channels of height approaching the superfluid coherence length, to enhance the relative contribution of surface excitations, and suppress hydrodynamic counterflow. Here we report on the thermal conduction of helium-3 in a 1.1 μm high channel. In the normal state we observe a diffusive thermal conductivity that is approximately temperature independent, consistent with interference of bulk and boundary scattering. In the superfluid, the thermal conductivity is only weakly temperature dependent, requiring detailed theoretical analysis. An anomalous thermal response is detected in the superfluid which we propose arises from the emission of a flux of surface excitations from the channel.

In superfluid ^{3}He-B confined in a slab geometry, domain walls between regions of different order parameter orientation are predicted to be energetically stable. Formation of the spatially modulated superfluid stripe phase has been proposed. We confined ^{3}He in a 1.1  μm high microfluidic cavity and cooled it into the B phase at low pressure, where the stripe phase is predicted. We measured the surface-induced order parameter distortion with NMR, sensitive to the formation of domains. The results rule out the stripe phase, but are consistent with 2D modulated superfluid order.

We demonstrate the fabrication of ∼1.08 μm deep microfluidic cavities with characteristic size as large as 7 mm × 11 mm or 11 mm diameter, using a silicon-glass anodic bonding technique that does not require posts to act as separators to define cavity height. Since the phase diagram of 3 He is significantly altered under confinement, posts might act as pinning centers for phase boundaries. The previous generation of cavities relied on full wafer-bonding which is more prone to failure and requires dicing post-bonding, whereas these cavities are made by bonding a pre-cut piece of Hoya SD-2 glass to a patterned piece of silicon in which the cavity is defined by etching. Anodic bonding was carried out at 425 °C with 200 V, and we observe that pressurizing the cavity to failure (>30 bars pressure) results in glass breaking, rather than the glass-silicon bond separation. In this article, we discuss the detailed fabrication of the cavity, its edges, and details of the junction between the coin silver fill line and the silicon base of the cavity that enables a low internal-friction joint. This feature is important for mass coupling torsional oscillator experimental assays of the superfluid inertial contribution where a high quality factor (Q) improves frequency resolution. The surface preparation that yields well-characterized smooth surfaces to eliminate pinning sites, the use of transparent glass as a cover permitting optical access, low temperature capability, and attachment of pressure-capable ports for fluid access may be features that are important in other applications.

Advances in nanomechanics within recent years have demonstrated an always expanding range of devices, from top-down structures to appealing bottom-up MoS 2 and graphene membranes, used for both sensing and component-oriented applications. One of the main concerns in all of these devices is frequency noise, which ultimately limits their applicability. This issue has attracted a lot of attention recently, and the origin of this noise remains elusive to date. In this article we present a very simple technique to measure frequency noise in nonlinear mechanical devices, based on the presence of bistability. It is illustrated on silicon-nitride high-stress doubly clamped beams, in a cryogenic environment. We report on the same T/ f dependence of the frequency noise power spectra as reported in the literature. But we also find unexpected damping fluctuations, amplified in the vicinity of the bifurcation points; this effect is clearly distinct from already reported nonlinear dephasing and poses a fundamental limit on the measurement of bifurcation frequencies. The technique is further applied to the measurement of frequency noise as a function of mode number, within the same device. The relative frequency noise for the fundamental flexure δ f/ f 0 lies in the range 0.5-0.01 ppm (consistent with the literature for cryogenic MHz devices) and decreases with mode number in the range studied. The technique can be applied to any type of nanomechanical structure, enabling progress toward the understanding of intrinsic sources of noise in these devices.

We investigate the nonlinear mechanics of a bimetallic, optically absorbing SiN-Nb nanowire in the presence of incident laser light and a reflecting Si mirror. Situated in a standing wave of optical intensity and subject to photothermal forces, the nanowire undergoes self-induced oscillations at low incident light thresholds of <1 μW due to engineered strong temperature-position (T-z) coupling. Along with inducing self-oscillation, laser light causes large changes to the mechanical resonant frequency ω 0 and equilibrium position z 0 that cannot be neglected. We present experimental results and a theoretical model for the motion under laser illumination. In the model, we solve the governing nonlinear differential equations by perturbative means to show that self-oscillation amplitude is set by the competing effects of direct T-z coupling and 2ω 0 parametric excitation due to T-ω 0 coupling. We then study the linearized equations of motion to show that the optimal thermal time constant τ for photothermal feedback is τ → ∞ rather than the previously reported ω 0 τ = 1. Lastly, we demonstrate photothermal quality factor (Q) enhancement of driven motion as a means to counteract air damping. Understanding photothermal effects on nano- and micromechanical devices, as well as nonlinear aspects of optics-based motion detection, can enable new device applications as oscillators or other electronic elements with smaller device footprints and less stringent ambient vacuum requirements.

The influence of confinement on the phases of superfluid helium-3 is studied using the torsional pendulum method. We focus on the transition between the A and B phases, where the A phase is stabilized by confinement and a spatially modulated stripe phase is predicted at the A-B phase boundary. Here we discuss results from superfluid helium-3 contained in a single 1.08-μm-thick nanofluidic cavity incorporated into a high-precision torsion pendulum, and map the phase diagram between 0.1 and 5.6 bar. We observe only small supercooling of the A phase, in comparison to bulk or when confined in aerogel, with evidence for a non-monotonic pressure dependence. This suggests that an intrinsic B-phase nucleation mechanism operates under confinement. Both the phase diagram and the relative superfluid fraction of the A and B phases, show that strong coupling is present at all pressures, with implications for the stability of the stripe phase.

In bulk superfluid 3 He at zero magnetic field, two phases emerge with the B-phase stable everywhere except at high pressures and temperatures, where the A-phase is favoured. Aerogels with nanostructure smaller than the superfluid coherence length are the only means to introduce disorder into the superfluid. Here we use a torsion pendulum to study 3 He confined in an extremely anisotropic, nematically ordered aerogel consisting of ∼10 nm-thick alumina strands, spaced by ∼100 nm, and aligned parallel to the pendulum axis. Kinks in the development of the superfluid fraction (at various pressures) as the temperature is varied correspond to phase transitions. Two such transitions are seen in the superfluid state, and we identify the superfluid phase closest to T c at low pressure as the polar state, a phase that is not seen in bulk 3 He.

A major achievement of the past decade has been the realization of macroscopic quantum systems by exploiting the interactions between optical cavities and mechanical resonators. In these systems, phonons are coherently annihilated or created in exchange for photons. Similar phenomena have recently been observed through phonon-cavity coupling-energy exchange between the modes of a single system mediated by intrinsic material nonlinearity. This has so far been demonstrated primarily for bulk crystalline, high-quality-factor (Q > 10(5)) mechanical systems operated at cryogenic temperatures. Here, we propose graphene as an ideal candidate for the study of such nonlinear mechanics. The large elastic modulus of this material and capability for spatial symmetry breaking via electrostatic forces is expected to generate a wealth of nonlinear phenomena, including tunable intermodal coupling. We have fabricated circular graphene membranes and report strong phonon-cavity effects at room temperature, despite the modest Q factor (∼100) of this system. We observe both amplification into parametric instability (mechanical lasing) and the cooling of Brownian motion in the fundamental mode through excitation of cavity sidebands. Furthermore, we characterize the quenching of these parametric effects at large vibrational amplitudes, offering a window on the all-mechanical analogue of cavity optomechanics, where the observation of such effects has proven elusive.

We describe a simple and scalable method for the transfer of CVD graphene for the fabrication of field effect transistors. This is a dry process that uses a modified RCA-cleaning step to improve the surface quality. In contrast to conventional fabrication routes where lithographic steps are performed after the transfer, here graphene is transferred to a pre-patterned substrate. The resulting FET devices display nearly zero Dirac voltage, and the contact resistance between the graphene and metal contacts is on the order of 910 ± 340 Ω μm. This approach enables formation of conducting graphene channel lengths up to one millimeter. The resist-free transfer process provides a clean graphene surface that is promising for use in high sensitivity graphene FET biosensors.

A graphene channel field-effect biosensor is demonstrated for detecting the binding of double-stranded DNA and poly-l-lysine. Sensors consist of chemical vapor deposition graphene transferred using a clean, etchant-free transfer method. The presence of DNA and poly-l-lysine are detected by the conductance change of the graphene transistor. A readily measured shift in the Dirac voltage (the voltage at which the graphene's resistance peaks) is observed after the graphene channel is exposed to solutions containing DNA or poly-l-lysine. The 'Dirac voltage shift' is attributed to the binding/unbinding of charged molecules on the graphene surface. The polarity of the response changes to positive direction with poly-l-lysine and negative direction with DNA. This response results in detection limits of 8 pM for 48.5 kbp DNA and 11 pM for poly-l-lysine. The biosensors are easy to fabricate, reusable and are promising as sensors of a wide variety of charged biomolecules.

The B phase of superfluid 3He is a three-dimensional time-reversal invariant topological superfluid, predicted to support gapless Majorana surface states. We confine superfluid 3He into a thin nanofluidic slab geometry. In the presence of a weak symmetry-breaking magnetic field, we have observed two possible states of the confined 3He-B phase manifold, through the small tipping angle NMR response. Large tipping angle nonlinear NMR has allowed the identification of the order parameter of these states and enabled a measurement of the surface-induced gap distortion. The results for two different quasiparticle surface scattering boundary conditions are compared with the predictions of weak-coupling quasiclassical theory. We identify a textural domain wall between the two B phase states, the edge of which at the cavity surface is predicted to host gapless states, protected in the magnetic field.

High stress stoichiometric silicon nitride resonators, whose quality factors exceed one million, have shown promise for applications in sensing, signal processing, and optomechanics. Yet, electrical integration of the insulating silicon nitride resonators has been challenging, as depositing even a thin layer of metal degrades the quality factor significantly. In this work, we show that graphene used as a conductive coating for Si3N4 membranes reduces the quality factor by less than 30% on average, which is minimal when compared to the effect of conventional metallization layers such as chromium or aluminum. The electrical integration of Si3N4-Graphene (SiNG) heterostructure resonators is demonstrated with electrical readout and electrostatic tuning of the frequency by up to 0.3% per volt. These studies demonstrate the feasibility of hybrid graphene/nitride mechanical resonators in which the electrical properties of graphene are combined with the superior mechanical performance of silicon nitride.

The superfluid phases of helium-3 ((3)He) are predicted to be strongly influenced by mesoscopic confinement. However, mapping out the phase diagram in a confined geometry has been experimentally challenging. We confined a sample of (3)He within a nanofluidic cavity of precisely defined geometry, cooled it, and fingerprinted the order parameter using a sensitive nuclear magnetic resonance spectrometer. The measured suppression of the p-wave order parameter arising from surface scattering was consistent with the predictions of quasi-classical theory. Controlled confinement of nanofluidic samples provides a new laboratory for the study of topological superfluids and their surface- and edge-bound excitations.

Graphene's suite of useful properties makes it of interest for use in biosensors. However, graphene interacts strongly with hydrophobic components of biomolecules, potentially altering their conformation and disrupting their biological activity. We have immobilized the protein Concanavalin A onto a self-assembled monolayer of multivalent tripodal molecules on single-layer graphene. We used a quartz crystal microbalance (QCM) to show that tripod-bound Concanavalin A retains its affinity for polysaccharides containing α-D-glucopyrannosyl groups as well as for the α-D-mannopyranosyl groups located on the cell wall of Bacillus subtilis. QCM measurements on unfunctionalized graphene indicate that adsorption of Concanavalin A onto graphene is accompanied by near-complete loss of these functions, suggesting that interactions with the graphene surface induce deleterious structural changes to the protein. Given that Concanavalin A's tertiary structure is thought to be relatively robust, these results suggest that other proteins might also be denatured upon adsorption onto graphene, such that the graphene-biomolecule interface must be considered carefully. Multivalent tripodal binding groups address this challenge by anchoring proteins without loss of function and without disrupting graphene's desirable electronic structure.

By virtue of their low mass and stiffness, atomically thin mechanical resonators are attractive candidates for use in optomechanics. Here, we demonstrate photothermal back-action in a graphene mechanical resonator comprising one end of a Fabry-Perot cavity. As a demonstration of the utility of this effect, we show that a continuous wave laser can be used to cool a graphene vibrational mode or to power a graphene-based tunable frequency oscillator. Owing to graphene's high thermal conductivity and optical absorption, photothermal optomechanics is efficient in graphene and could ultimately enable laser cooling to the quantum ground state or applications such as photonic signal processing.

We present a simple micromanipulation technique to transfer suspended graphene flakes onto any substrate and to assemble them with small localized gates into mechanical resonators. The mechanical motion of the graphene is detected using an electrical, radio frequency (RF) reflection readout scheme where the time-varying graphene capacitor reflects a RF carrier at f = 5-6 GHz producing modulation sidebands at f ± f(m). A mechanical resonance frequency up to f(m) = 178 MHz is demonstrated. We find both hardening/softening Duffing effects on different samples and obtain a critical amplitude of ~40 pm for the onset of nonlinearity in graphene mechanical resonators. Measurements of the quality factor of the mechanical resonance as a function of dc bias voltage V(dc) indicates that dissipation due to motion-induced displacement currents in graphene electrode is important at high frequencies and large V(dc)., (© 2011 American Chemical Society)

Motivated by the recent prediction that uniaxially compressed aerogel can stabilize the anisotropic A phase over the isotropic B phase, we measure the pressure dependent superfluid fraction of (3)He entrained in 10% axially compressed, 98% porous aerogel. We observe that a broad region of the temperature-pressure phase diagram is occupied by the metastable A phase. The reappearance of the A phase on warming from the B phase, before superfluidity is extinguished at T(c), is in contrast to its absence in uncompressed aerogel. The phase diagram is modified from that of pure (3)He, with the disappearance of the polycritical point (PCP) and the appearance of a region of A phase extending below the PCP of bulk (3)He, even in zero applied magnetic field. The expected alignment of the A phase texture by compression is not observed., (© 2011 American Physical Society)

We discuss the mass transport of a degenerate Fermi liquid ^{3}He film over a rough surface, and the film momentum relaxation time, in the framework of theoretical predictions. In the mesoscopic regime, the anomalous temperature dependence of the relaxation time is explained in terms of the interference between elastic boundary scattering and inelastic quasiparticle-quasiparticle scattering within the film. We exploit a quasiclassical treatment of quantum size effects in the film in which the surface roughness, whose power spectrum is experimentally determined, is mapped into an effective disorder potential within a film of uniform thickness. Confirmation is provided by the introduction of elastic scattering centers within the film. The improved understanding of surface roughness scattering may impact on enhancing the conductivity in thin metallic films.

Graphene's unparalleled strength, stiffness, and low mass per unit area make it an ideal material for nanomechanical resonators, but its relatively low quality factor is an important drawback that has been difficult to overcome. Here, we use a simple procedure to fabricate circular mechanical resonators of various diameters from graphene grown by chemical vapor deposition. In addition to highly reproducible resonance frequencies and mode shapes, we observe a striking improvement of the membrane quality factor with increasing size. At room temperature, we observe quality factors as high as 2400 ± 300 for a resonator 22.5 μm in diameter, about an order of magnitude greater than previously observed quality factors for monolayer graphene. Measurements of quality factor as a function of modal frequency reveal little dependence of Q on frequency. These measurements shed light on the mechanisms behind dissipation in monolayer graphene resonators and demonstrate that the quality factor of graphene resonators relative to their thickness is among the highest of any mechanical resonator demonstrated to date.

Mechanical dissipation poses a ubiquitous challenge to the performance of nanomechanical devices. Here we analyze the support-induced dissipation of high-stress nanomechanical resonators. We develop a model for this loss mechanism and test it on Si(3)N(4) membranes with circular and square geometries. The measured Q values of different harmonics present a nonmonotonic behavior which is successfully explained. For azimuthal harmonics of the circular geometry we predict that destructive interference of the radiated waves leads to an exponential suppression of the clamping loss in the harmonic index. Our model can also be applied to graphene drums under high tension.

We fabricated large arrays of suspended, single-layer graphene membrane resonators using chemical vapor deposition (CVD) growth followed by patterning and transfer. We measure the resonators using both optical and electrical actuation and detection techniques. We find that the resonators can be modeled as flat membranes under tension, and that clamping the membranes on all sides improves agreement with our model and reduces the variation in frequency between identical resonators. The resonance frequency is tunable with both electrostatic gate voltage and temperature, and quality factors improve dramatically with cooling, reaching values up to 9000 at 10 K. These measurements show that it is possible to produce large arrays of CVD-grown graphene resonators with reproducible properties and the same excellent electrical and mechanical properties previously reported for exfoliated graphene.

Interferometric imaging of normal mode dynamics in electromechanical resonators, oscillating in the rf regime, is demonstrated by synchronous imaging with a pulsed nanosecond laser. Profiles of mechanical modes in suspended thin film structures and their equilibrium profiles are measured through all-optical Fabry-Perot reflectance fits to the temporal traces. As a proof of principle, the mode patterns of a microdrum silicon resonator are visualized, and the extracted vibration modes and equilibrium profile show good agreement with numerical estimations.

Nanomechanical resonators operating in vacuum are capable of detecting and weighing single biomolecules, but their application to the life sciences has been limited by viscous forces that impede their motion in liquid environments. A promising approach to avoid this problem, encapsulating the fluid within a mechanical resonator surrounded by vacuum, has not yet been tried with resonant sensors of mass less than approximately 100 ng, despite predictions that devices with smaller effective mass will have proportionally finer mass resolution. Here, we fabricate and evaluate the performance of doubly clamped beam resonators that contain filled nanofluidic channels and have masses of less than 100 pg. These nanochannel resonators operate at frequencies on the order of 25 MHz and when filled with fluid have quality factors as high as 800, 2 orders of magnitude higher than that of resonators of comparable size and frequency operating in fluid. Fluid density measurements reveal a mass responsivity of 100 Hz/fg and a noise equivalent mass of 2 fg. Our analysis suggests that realistic improvements in the quality factor and frequency stability of nanochannel resonators would render these devices capable of sensing attogram masses from liquid.

We demonstrate the use of anodic bonding to fabricate cells with characteristic size as large as 7 x 10 mm(2), with height of approximately 640 nm, and without any internal support structure. The cells were fabricated from Hoya SD-2 glass and silicon wafers, each with 3 mm thickness to maintain dimensional stability under internal pressure. Bonding was carried out at 350 degrees C and 450 V with an electrode structure that excluded the electric field from the open region. We detail fabrication and characterization steps and also discuss the design of the fill line for access to the cavity.

We report on a method to produce free-standing graphene sheets from epitaxial graphene on silicon carbide (SiC) substrate. Doubly clamped nanomechanical resonators with lengths up to 20 microm were patterned using this technique and their resonant motion was actuated and detected optically. Resonance frequencies of the order of tens of megahertz were measured for most devices, indicating that the resonators are much stiffer than expected for beams under no tension. Raman spectroscopy suggests that the graphene is not chemically modified during the release of the devices, demonstrating that the technique is a robust means of fabricating large-area suspended graphene structures.

High-stress silicon nitride microresonators exhibit a remarkable room temperature Q factor that even exceeds that of single crystal silicon. A study of the temperature dependent variation of the Q of a 255 micromx255 micromx30 nm thick high-stress Si3N4 membrane reveals that the dissipation Q-1 decreases with lower temperatures and is approximately 3 orders of magnitude smaller than the universal behavior. Stress-relieved cantilevers fabricated from the same material show a Q that is more consistent with typical disordered materials. e-beam and x-ray studies of the nitride film's structure reveal characteristics consistent with a disordered state. Thus, it is shown that stress alters the Q-1, violating the universality of dissipation in disordered materials in a self-supporting structure.

We demonstrate that a monolayer graphene membrane is impermeable to standard gases including helium. By applying a pressure difference across the membrane, we measure both the elastic constants and the mass of a single layer of graphene. This pressurized graphene membrane is the world's thinnest balloon and provides a unique separation barrier between 2 distinct regions that is only one atom thick.

We have made reliable measurements of the sound velocity delta v/v(0) and internal friction Q(-1) in vitreous silica at 1.03, 3.74, and 14.0 kHz between 1 mK and 0.5 K. In contrast with earlier studies that did not span as wide a temperature and frequency range, our measurements of Q(-1) reveal a crossover (as T decreases) only near 10 mK from the T(3) dependence predicted by the standard tunneling model to a T dependence predicted if interactions are accounted for. We find good fits at all frequencies using a single interaction parameter, the prefactor of the interaction-driven relaxation rate, in contrast to earlier claims of a frequency dependent power law. We also show that the discrepancy in the slopes d(delta v/v(0))/d(log(10)T) below and above the sound velocity maximum (1: -1 observed, 1: -2 predicted) can be resolved by assuming a modified distribution of tunneling states.

We have employed a chip-bending method to exert continuous and reversible control over the tensile stress in doubly clamped nanomechanical beam resonators. Tensile stress is shown to increase the quality factor of both silicon nitride and single-crystal silicon resonators, implying that added tension can be used as a general, material-independent route to increased quality factor. With this direct stretching technique, we demonstrate beam resonators with unprecedented tunability of both frequency and quality factor. Devices can be tuned back and forth between a high and low stress state, with frequency tunability as large as several hundred percent demonstrated. Over this wide range of frequency, quality factor is also tuned by as much as several hundred percent, providing insights into the loss mechanisms in these materials and this class of nanoresonator. Devices with frequencies in the 1-100 MHz range are studied, with quality factor as high as 390,000 achieved at room temperature, for a silicon nitride device with cross-sectional dimensions below 1 microm, operating in a high stress state. This direct stretching technique may prove useful for the identification of loss mechanisms that contribute to the energy balance in nanomechanical resonators, allowing for the development of new designs that would display higher quality factors. Such devices would have the ability to resolve smaller addendum masses and thus allow more sensitive detection and offer the potential for providing access to previously inaccessible dissipation regimes at low temperatures. This technique provides the ability to dramatically tune both frequency and quality factor, enabling future mechanical resonators to be used as variable frequency references as well as variable band-pass filters in signal-processing applications.

Nanoelectromechanical systems were fabricated from single- and multilayer graphene sheets by mechanically exfoliating thin sheets from graphite over trenches in silicon oxide. Vibrations with fundamental resonant frequencies in the megahertz range are actuated either optically or electrically and detected optically by interferometry. We demonstrate room-temperature charge sensitivities down to 8 x 10(-4) electrons per root hertz. The thinnest resonator consists of a single suspended layer of atoms and represents the ultimate limit of two-dimensional nanoelectromechanical systems.

We demonstrate the operation of radio frequency nanoscale flexural resonators in air and liquid. Doubly clamped string, as well as singly clamped cantilever resonators, with nanoscale cross-sectional dimensions and resonant frequencies as high as 145 MHz are driven in air as well as liquid with an amplitude modulated laser. We show that this laser drive technique can impart sufficient energy to a nanoscale resonator to overcome the strong viscous damping present in these media, resulting in a mechanical resonance that can be measured by optical interference techniques. Resonance in air, isopropyl alcohol, acetone, water, and phosphate-buffered saline is demonstrated for devices having cross-sectional dimensions close to 100 nm. For operation in air, quality factors as high as 400 at 145 MHz are demonstrated. In liquid, quality factors ranging from 3 to 10 and frequencies ranging from 20 to 100 MHz are observed. These devices, and an all-optical actuation and detection system, may provide insight into the physics of the interaction of nanoscale mechanical structures with their environments, greatly extending the viscosity range over which such small flexural resonant devices can be operated.

We report on the mechanical behavior of an a-SiO2 84 kHz torsional oscillator operated between 100> or =T> or =1.0 mK. Below 10 mK we observed well-differentiated transient responses which we attribute to the interaction with low-level background radiation (gamma quanta and cosmic ray micro) and which can be modeled in terms of a change in the spring constant.

We have investigated the dissipation (Q-1) using the torsion pendulum technique for pure 3He and 3He-4He mixtures in silica aerogel near the 3He superfluid transition (T(c)) in aerogel. With pure 3He the Q-1 decreases at the onset of superfluidity. When phase separated 3He-4He mixtures are introduced into the aerogel, the Q-1 does not decrease as rapidly and eventually increases for the highest 4He content. We provide a model for the related attenuation of transverse sound alpha that takes into account elastic and inelastic scattering processes and exhibits a decrease in alpha at T(c).

We report the first observation of longitudinal sound propagation in three dimensionally distributed Bose and Fermi superfluids in an acoustic investigation of phase separated 3He-4He mixtures confined to aerogel. At mK temperatures, this inhomogeneous system exhibits simultaneous 3He and 4He superfluidity leading to two "slow modes" along with the conventional sound mode. We also infer the superfluidity of isolated bubbles of pure 3He in a large 4He concentration sample.

The heat capacity of pure 3He in low density aerogel is measured at 22.5 bars. The superfluid response is simultaneously monitored with a torsional oscillator. A slightly rounded heat capacity peak, 65 microK in width, is observed at the 3He-aerogel superfluid transition, T(ca). Subtracting the bulk 3He contribution, the heat capacity shows a Fermi-liquid form above T(ca). We can fit the heat capacity attributed to superfluid within the aerogel with a rounded BCS form accounting for 0.30 of the nonbulk fluid in the aerogel, or by assuming a substantial reduction in the superfluid order parameter. Both approaches are consistent with earlier superfluid density measurements.

Internal friction and speed of sound were measured on a-SiO2 above 6 mK using a torsional oscillator at 90 kHz, controlling for thermal decoupling, vibrational heating, background losses, and nonlinear effects. Strain amplitudes epsilon(A) = 10(-8) mark the transition between the linear and nonlinear regimes. In the former, agreement with the tunneling model was observed for both internal friction and speed of sound above 25 mK. The observed deviations in the speed of sound below 25 mK can be described with a cutoff energy of Delta(0, min)/k(B) = 6+/-0.5 mK. In the nonlinear regime, above 10 mK the behavior was typical for nonlinear harmonic oscillators, while below 10 mK different behavior was found.

We have investigated the superfluid transition of 3He in different samples of silica aerogel. By comparing new measurements on a 99.5% sample with previous observations on the behavior of 3He in 98% porous aerogel, we have found evidence for a scaling of the transition temperature and superfluid density of 3He to the correlation length of the aerogel.