Macroscopic quantum effects in nanomechanical systems

– We investigate quantum effects in the mechanical properties of elastic beams on the nanoscale. Transverse quantum and thermal fluctuations and the nonlinear excitation energies are calculated for beams compressed in longitudinal direction. Near the Euler instability, the system is described by a one dimensional Ginzburg-Landau model where the order parameter is the amplitude of the buckling mode. We show that in single wall carbon nanotubes with lengths of order or smaller than 100 nm zero point fluctuations are accessible and discuss the possibility of observing macroscopic quantum coherence in nanobeams near the critical strain. Introduction. – The progress in miniaturization of electromechanical devices towards the nanometer scale (NEMS) is beginning to reach the limit, where quantum effects play an important role [1, 2, 3]. For example, in nanoscale beams phonons may propagate ballistically, leading to a quantized thermal conductance [4]. Moreover a sizeable contribution to the forces between plates and beams which are separated by less than one micron is the Casimir force between neutral objects due to the modification of the electromagnetic vacuum [5, 6]. The combination of electrical and mechanical properties may be studied via quantized transverse deflection due to charge quantization of charged, suspended beams in an electric field [7]. Similarly the standard Coulomb-blockade in small metallic islands or in semiconducting quantum dots may be used to mechanically transfer single electrons with a nanomechanical oscillator [8, 9]. Regarding possible applications of nanomechanical sensors, Si-based resonators in the radio-frequency regime were recently fabricated and manipulated [10]. In the present work we focus on quantum effects in mechanical resonators on the nanometer scale, in particular in single wall carbon nanotubes (SWNT). Due to their small masses and remarkable elastic properties down to nanometer scale, carbon nanotubes are ideally suited to study effects like phonon quantization [11], the generation of non-classical states of mechanical motion [12] or macroscopic quantum tunnelling out of a metastable configuration [13]. On the classical level, both the thermal Brownian motion of single nanotubes clamped on one side [14] and the discrete eigenmodes of charged multiwall nanotubes excited by an ac-voltage [15] have been detected experimentally. More recently, the thermal vibrations of doubly clamped SWNT’s