Strong and tunable mode coupling in carbon nanotube resonators

Abstract

The nonlinear interaction between two mechanical resonances of the same freely suspended carbon nanotube resonator is studied. We find that, in the Coulomb-blockade regime, the nonlinear modal interaction is dominated by single-electron-tunneling processes and that the mode-coupling parameter can be tuned with the gate voltage, allowing both mode-softening and mode-stiffening behaviors. This is in striking contrast to tension-induced mode coupling in strings where the coupling parameter is positive and gives rise to a stiffening of the mode. The strength of the mode coupling in carbon nanotubes in the Coulomb-blockade regime is observed to be 6 orders of magnitude larger than the mechanical-mode coupling in micromechanical resonators. Carbon nanotubes present remarkable properties for applications in nanoelectromechanical systems (NEMS), such as low mass density, high Young's modulus, and high crystallinity.1,2 This fact has motivated the use of carbon nanotubes to fabricate high-quality factor (Q) mechanical resonators 3 that can be operated at ultrahigh frequencies 4,5 and can be used as ultrasensitive mass sensors.6-8 Additionally, both the mechanical tension and the electrical properties of carbon nanotubes can be tuned to a large extent by an external electric field, 9 making nanotubes a very versatile component in NEMS devices.Due to the small diameter of carbon nanotubes, they can be easily excited in the nonlinear oscillation regime. 10 Moreover, it has been demonstrated that the nonlinear dynamics of carbon nanotubes can be tuned over a large range 11,12 making nanotube NEMS excellent candidates for the implementation of sensing schemes based on nonlinearity and for the study of fundamental problems on nonlinear dynamics. The nonlinear interaction between mechanical resonance modes is interesting both from a fundamental and from an applied perspective. Nonlinear modal interactions have been studied recently in micro-and nanoresonators. [13][14][15][16][17][18] These studies concentrated on mechanical coupling between the modes via the geometric nonlinearity or via the displacement-induced tension, the same mechanism responsible for the Duffing nonlinearity in doubly clamped resonators. By employing a different mode of the same resonator as a phonon cavity, the mechanical mode can be controlled in situ, and its damping characteristics can be modified to a great extent, leading to cooling of the mode and parametric mode splitting. 13,16 The nonlinear coupling can also be used to detect resonance modes that would otherwise be inaccessible by the experiment 18 to increase the dynamic range of resonators by tuning the nonlinearity constant 18 and for mechanical frequency conversion.17 Additionally, nonlinear coupling has been proposed as a quantum nondemolition scheme to probe mechanical resonators in their quantum ground state 19 and as a way of generating entanglement between different mechanical modes. 20 Furthermore, a recent theoretical paper suggests that the interaction between mechanical resonances c...

Observation of decoherence in a carbon nanotube mechanical resonator

“…In comparison to conventional nanoelectromechanical system, carbon nanotube (CNT) resonators are very sensitive to their environment. Owing to a low mass and spring constant, nanotube mechanical resonators show a strong dispersion with the gate voltage 13 , are sensitive to the force of a single-electron charge 14,15 , exhibit strong mode coupling 16,17 and strong nonlinearities 18 . These strong coupling effects may give rise to dephasing, making them an interesting candidate for exploring mechanical decoherence.…”

Submicrosecond-timescale readout of carbon nanotube mechanical motion

“…A possible origin of such observed quality factors is spectral broadening from thermal motion of other mechanical modes, 18 an effect that is strong in carbon nanotubes due to their strong mode coupling. 6,7 A signature of such spectral broadening would be a difference between the mechanical quality factor Q s measured from the spectral linewidth of the resonance and the quality factor Q r measured from a ring-down experiment.…”

Coupling between flexural modes in free vibration of single-walled carbon nanotubes

“…[15][16][17][18] It is well known that nonlinearity may play an important role in the thermal and electrical transport of nanotubes, nanoribbons and nanowires. [19][20][21][22][23] For nonlinear vibration of CNTs actuated by a direct current (DC) or alternating current (AC) load, it has been found that the type vibration may suddenly transition from a planar motion to a whirling, "jump rope" like motion. 24,25 The effect of initial curvature of CNTs has also been investigated using a two dimensional nonlinear curved beam model, and it shows the transfer of energy among the vibration modes involved in the veering phenomenon.…”