Coupled mechanical oscillations were first observed in paired pendulum clocks in the mid-seventeenth century and were extensively studied for their novel sympathetic oscillation dynamics [1, 2]. In this era of nanotechnologies, coupled oscillations have again emerged as subjects of interest when realized in nanomechanical resonators for both practical applications and fundamental studies [3][4][5][6][7][8][9][10][11]. However, a key obstacle to the further development of this architecture is the ability to coherently manipulate the coupled oscillations. This limitation arises as a consequence of the usually weak coupling between the constituent nanomechanical elements. Here, we report parametrically coupled mechanical resonators in which the coupling strength can be dynamically adjusted by modulating (pumping) the stress in the mechanical elements via a piezoelectric transducer. The parametric control enables the coupling rate between the two resonators to be made so strong that it exceeds their intrinsic energy dissipation rate by more than a factor of four. This ultra-strong coupling can be exploited to coherently transfer phonon populations, namely phonon Rabi oscillations [12,13], between the mechanical resonators via two coupled vibration modes, realizing superposition states of the two modes and their time-domain control. More unexpectedly, the nature of the parametric coupling can also be tuned from a linear first-order interaction to a non-linear higher-order process in which more than one pump phonon mediates the coherent oscillations. This demonstration of multipump phonon mixing echoes multi-wave photon mixing [14] and suggests that concepts from nonlinear optics can also be applied to mechanical systems. Ultimately, the parametric pumping is not only useful for controlling classical oscillations [15] but can also be extended to the quantum regime [12,13,[16][17][18], opening up the prospect of entangling two distinct macroscopic mechanical objects [19,20].The dynamic parametric coupling is developed in GaAs-based paired mechanical beams shown in Fig. 1a, in which the piezoelectric effect is exploited to mediate all-electrical displacement transduction [21]. The frequency response of beam 1 measured by harmonically driving it while the parametric pump is deactivated displays two coupled vibration modes (Fig. 1b), where mode 1 (ω 1 = 2π × 293.93 kHz) is dominated by the vibration of beam 1 while mode 2 (ω 2 = 2π × 294.37 kHz) is dominated by the vibration of beam 2. The amplitude of mode 2 is much smaller than that of mode 1 reflecting the energy exchange due to the structural coupling via the overhang is inefficient because of the eigenfrequency difference between the two beams. This difference can be compensated by activating the parametric pump, which is induced by piezoelectrically modulating the spring constant of beam 1 with the pump frequency ω p at around the frequency difference between the two modes, ∆ω ≡ ω 2 − ω 1 (Fig. 1c).The dynamics of this system can then be expressed by the following e...

Low-energy electron microscopy (LEEM) was used to measure the reflectivity of low-energy electrons from graphitized SiC(0001). The reflectivity shows distinct quantized oscillations as a function of the electron energy and graphite thickness. Conduction bands in thin graphite films form discrete energy levels whose wave vectors are normal to the surface. Resonance of the incident electrons with these quantized conduction band states enhances electrons to transmit through the film into the SiC substrate, resulting in dips in the reflectivity. The dip positions are well explained using tight-binding and first-principles calculations. The graphite thickness distribution can be determined microscopically from LEEM reflectivity measurements.Recently, thin graphite films, especially single graphite sheets called graphene, have attracted much attention. This is because they exhibit interesting electronic transport properties, such as field effects and quantum hall effects. 1-3 So far, thin graphite films have been formed in two ways. One is based on processing bulk graphite using oxygen plasma etching, 1,4 but this method cannot provide thin graphite layers with a large area. The other is to anneal SiC surfaces at high temperatures in an ultrahigh vacuum (UHV). Selective sublimation of Si from the substrate results in the graphite films on the surface. 5-10 The graphite films can be processed to fabricate device structures using standard lithographic techniques, and the magnetotransport measurements of the structures have revealed signatures of quantum confinement. 9 This method may provide wide graphite films, which would make it more suitable for device application. However, to use the thin graphite on the SiC substrate for device fabrication, we need a reproducible way of forming graphite films with an intended thickness. For this purpose, it is essential to determine the graphite thickness during various stages of the formation processes. Auger spectroscopy has been used to estimate thickness of graphite formed on SiC. 7 More recently, it has been shown that the number of graphene layers in the graphite film can be determined from the band structure measured using angle-resolved photoemission spectroscopy, 10 but this method also provides only spatially-averaged information. Local thickness distributions are more desirable.Confinement of electrons in thin films creates quantum well (QW) bound states. QW resonant states can form as well at energies above the confinement potential barrier, because the potential discontinuity scatters electrons quantum-mechanically.To date, photoemission spectroscopy has provided the most direct observation of the QW states, both bound and resonance states, below the Fermi level. 11 Photoemission spectroscopy measurements have revealed that the QW states can cause dramatic quantum size effects on the film properties, such as film stability, 12 magnetic interlayer coupling, 13 and superconductivity. 14 The QW states at discrete energy levels produce peaks in the photoemission energy spe...

The Parametron was first proposed as a logic-processing system almost 50 years ago. In this approach the two stable phases of an excited harmonic oscillator provide the basis for logic operations. Computer architectures based on LC oscillators were developed for this approach, but high power consumption and difficulties with integration meant that the Parametron was rendered obsolete by the transistor. Here we propose an approach to mechanical logic based on nanoelectromechanical systems that is a variation on the Parametron architecture and, as a first step towards a possible nanomechanical computer, we demonstrate both bit storage and bit flip operations.

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