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Register a new userNanotube mechanical resonators with quality factors of up to 5 million
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Carbon nanotube mechanical resonators have attracted considerable interest because of their small mass, the high quality of their surface, and the pristine electronic states they host. However, their small dimensions result in fragile vibrational states that are difficult to measure. Here we observe quality factors $Q$ as high as $5times10^6$ in ultra-clean nanotube resonators at a cryostat temperature of 30 mK, where we define $Q$ as the ratio of the resonant frequency over the linewidth. Measuring such high quality factors requires both employing an ultra-low noise method to detect minuscule vibrations rapidly, and carefully reducing the noise of the electrostatic environment. We observe that the measured quality factors fluctuate because of fluctuations of the resonant frequency. The quality factors we measure are record high; they are comparable to the highest $Q$ reported in mechanical resonators of much larger size, a remarkable result considering that reducing the size of resonators is usually concomitant with decreasing quality factors. The combination of ultra-low size and very large $Q$ offers new opportunities for ultra-sensitive detection schemes and quantum optomechanical experiments.
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We describe the fabrication and measurement of microwave coplanar waveguide resonators with internal quality factors above 10 million at high microwave powers and over 1 million at low powers, with the best low power results approaching 2 million, corresponding to ~1 photon in the resonator. These quality factors are achieved by controllably producing very smooth and clean interfaces between the resonators aluminum metallization and the underlying single crystal sapphire substrate. Additionally, we describe a method for analyzing the resonator microwave response, with which we can directly determine the internal quality factor and frequency of a resonator embedded in an imperfect measurement circuit.
We present nanofabrication and mechanical measurements of single-crystal diamond cantilevers with thickness down to 85 nm, thickness uniformity better than 20 nm, and lateral dimensions up to 240 um. Quality factors exceeding one million are found at room temperature, surpassing those of state-of-the-art single-crystal silicon cantilevers of similar dimensions by roughly an order of magnitude. Force sensitivities of a few hundred zeptonewtons result for the best cantilevers at millikelvin temperatures. Single-crystal diamond could thus directly improve existing force and mass sensors by a simple substitution of resonator material, and lead to quantum nanomechanical devices with exceptionally low energy dissipation.
We have observed the transversal vibration mode of suspended carbon nanotubes at millikelvin temperatures by measuring the single-electron tunneling current. The suspended nanotubes are actuated contact-free by the radio frequency electric field of a nearby antenna; the mechanical resonance is detected in the time-averaged current through the nanotube. Sharp, gate-tuneable resonances due to the bending mode of the nanotube are observed, combining resonance frequencies of up to u_0 = 350 MHz with quality factors above Q = 10^5, much higher than previously reported results on suspended carbon nanotube resonators. The measured magnitude and temperature dependence of the Q-factor shows a remarkable agreement with the intrinsic damping predicted for a suspended carbon nanotube. By adjusting the RF power on the antenna, we find that the nanotube resonator can easily be driven into the non-linear regime.
Graphene and carbon nanotubes represent the ultimate size limit of one and two-dimensional nanoelectromechanical resonators. Because of their reduced dimensionality, graphene and carbon nanotubes display unusual mechanical behavior; in particular, their dynamics is highly nonlinear. Here, we review several types of nonlinear behavior in resonators made from nanotubes and graphene. We first discuss an unprecedented scenario where damping is described by a nonlinear force. This scenario is supported by several experimental facts: (i) the quality factor varies with the amplitude of the motion as a power law whose exponent coincides with the value predicted by the nonlinear damping model, (ii) hysteretic behavior (of the motional amplitude as a function of driving frequency) is absent in some of our resonators even for large driving forces, as expected when nonlinear damping forces are large, and (iii) when we quantify the linear damping force (by performing parametric excitation measurements) we find that it is significantly smaller than the nonlinear damping force. We then review parametric excitation measurements, an alternative actuation method which is based on nonlinear dynamics. Finally, we discuss experiments where the mechanical motion is coupled to electron transport through a nanotube. The coupling can be made so strong that the associated force acting on the nanotube becomes highly nonlinear with displacement and velocity. Overall, graphene and nanotube resonators hold promise for future studies on classical and quantum nonlinear dynamics.
Graphene is an attractive material for nanomechanical devices because it allows for exceptional properties, such as high frequencies and quality factors, and low mass. An outstanding challenge, however, has been to obtain large coupling between the motion and external systems for efficient readout and manipulation. Here, we report on a novel approach, in which we capacitively couple a high-Q graphene mechanical resonator ($Q sim 10^5$) to a superconducting microwave cavity. The initial devices exhibit a large single-photon coupling of $sim 10$ Hz. Remarkably, we can electrostatically change the graphene equilibrium position and thereby tune the single photon coupling, the mechanical resonance frequency and the sign and magnitude of the observed Duffing nonlinearity. The strong tunability opens up new possibilities, such as the tuning of the optomechanical coupling strength on a time scale faster than the inverse of the cavity linewidth. With realistic improvements, it should be possible to enter the regime of quantum optomechanics.
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