Nanotube mechanical resonators with quality factors of up to 5 million

Abstract

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 [1][2][3][4]. However, their small dimensions result in fragile vibrational states that are difficult to measure. Here we observe quality factors Q as high as 5×10 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 [5, 6], 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 In recent years, endeavours to boost quality factors in nano and micromechanical resonators have been stimulated by the need to develop innovative approaches to sensing [7], signal processing [8] and quantum physics [9]. Strategies to enhance quality factors have proceeded along three main routes. Firstly, the quality of the host material has been improved. To this end, new materials have been employed, such as high tensile stress silicon nitride membranes [5, 10] and single crystal diamond films [11]. In addition, surface friction has been lowered by optimizing fabrication processes and reducing contamination [12].Secondly, schemes to isolate the resonator from its surrounding environment have been developed, based on new resonator layouts [13,14], and on optical trapping of thin membranes and levitated particles [15,16]. Thirdly, and most straightforwardly, Q-factors have been improved by operating resonators at cryogenic temperatures [17].Schemes to enhance Q-factors in nanotube resonators have focused on reducing contamination by growing ultra-clean nanotubes, and cooling resonators down to millikelvin temperatures [2]. Even though Q-factors, measured from the linewidth of driven resonances, have been improved up to ∼ 1.5 × 10 5 , they are still much lower than values routinely obtained with larger resonators fabricated from bulk materials using top-down techniques [6]. This result is somewhat disappointing, since the high crystallinity of nanotubes and their lack of dangling bonds at the surface are expected to minimize surface friction that limits the Q-factor in some nanomechanical systems [18].Here we find that the actual values of the Q-factors can be significantly higher than hitherto appreciated, but that revealing these values requires to perfect the measurement technique. Namely, the dynamics of the nanotube has to be captured in a regime of vanishingly small displacement in order to minimize nonline...

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