Arbitrary distribution and nonlinear modal interaction in coupled nanomechanical resonators

We propose a general one-dimensional {\em continuous} formulation to analyze the vibrational modes of antenna-like nanomechanical resonators consisting of two symmetric arrays of cantilevers affixed to a central nano-beam. The cantilever arrays can have arbitrary density and length profile along the beam. We obtain the secular equation that allows for the determination of their frequency spectrum and illustrate the results on the particular examples of structures with constant or alternating cantilever length profiles. We show that our analytical results capture the vibration spectrum of such resonators and elucidate key relationships that could prove advantageous for experimental device performance. Furthermore, using a perturbative approach to treat the nonlinear and dissipative dynamics of driven structures, we analyze the anharmonic coupling between two specific widely spaced modes of the coupled-element device, with direct application to experiments.Comment: 8 pages, 5 figures, additional info can be found at http://nano.bu.ed

Evidence for Quantized Displacement in Macroscopic Nanomechanical Oscillators

We report the observation of discrete displacement of nanomechanical oscillators with gigahertz-range resonance frequencies at millikelvin temperatures. The oscillators are nanomachined single-crystal structures of silicon, designed to provide two distinct sets of coupled elements with very low and very high frequencies. With this novel design, femtometer-level displacement of the frequency-determining element is amplified into collective motion of the entire micron-sized structure. The observed discrete response possibly results from energy quantization at the onset of the quantum regime in these macroscopic nanomechanical oscillators.Comment: 4 pages, two-column format. Related papers available at http://nano.bu.edu

Quantum Friction in Nanomechanical Oscillators at Millikelvin Temperatures

We report low-temperature measurements of dissipation in megahertz-range, suspended, single-crystal nanomechanical oscillators. At millikelvin temperatures, both dissipation (inverse quality factor) and shift in the resonance frequency display reproducible features, similar to those observed in sound attenuation experiments in disordered glasses and consistent with measurements in larger micromechanical oscillators fabricated from single-crystal silicon. Dissipation in our single-crystal nanomechanical structures is dominated by internal quantum friction due to an estimated number of roughly 50 two-level systems, which represent both dangling bonds on the surface and bulk defects.Comment: 5 pages, two-column format. Related papers available at http://nano.bu.ed

Coherent Signal Amplification in Bistable Nanomechanical Oscillators by Stochastic Resonance

Stochastic resonance is a counter-intuitive concept[1,2], ; the addition of noise to a noisy system induces coherent amplification of its response. First suggested as a mechanism for the cyclic recurrence of ice ages, stochastic resonance has been seen in a wide variety of macroscopic physical systems: bistable ring lasers[3], SQUIDs[4,5], magnetoelastic ribbons[6], and neurophysiological systems such as the receptors in crickets[7] and crayfish[8]. Although it is fundamentally important as a mechanism of coherent signal amplification, stochastic resonance is yet to be observed in nanoscale systems. Here we report the observation of stochastic resonance in bistable nanomechanical silicon oscillators, which can play an important role in the realization of controllable high-speed nanomechanical memory cells. Our nanomechanical systems were excited into a dynamic bistable state and modulated in order to induce controllable switching; the addition of white noise showed a marked amplification of the signal strength. Stochastic resonance in nanomechanical systems paves the way for exploring macroscopic quantum coherence and tunneling, and controlling nanoscale quantum systems for their eventual use as robust quantum logic devices.Comment: 18 pages, 4 figure

Nonlinear response of a driven vibrating nanobeam in the quantum regime

We analytically investigate the nonlinear response of a damped doubly clamped nanomechanical beam under static longitudinal compression which is excited to transverse vibrations. Starting from a continuous elasticity model for the beam, we consider the dynamics of the beam close to the Euler buckling instability. There, the fundamental transverse mode dominates and a quantum mechanical time-dependent effective single particle Hamiltonian for its amplitude can be derived. In addition, we include the influence of a dissipative Ohmic or super-Ohmic environment. In the rotating frame, a Markovian master equation is derived which includes also the effect of the time-dependent driving in a non-trivial way. The quasienergies of the pure system show multiple avoided level crossings corresponding to multiphonon transitions in the resonator. Around the resonances, the master equation is solved analytically using Van Vleck perturbation theory. Their lineshapes are calculated resulting in simple expressions. We find the general solution for the multiple multiphonon resonances and, most interestingly, a bath-induced transition from a resonant to an antiresonant behavior of the nonlinear response.Comment: 25 pages, 5 figures, submitted to NJ

Nanomechanical Detection of Itinerant Electron Spin Flip

Spin is an intrinsically quantum property, characterized by angular momentum. A change in the spin state is equivalent to a change in the angular momentum or mechanical torque. This spin-induced torque has been invoked as the intrinsic mechanism in experiments ranging from the measurements of angular momentum of photons g-factor of metals and magnetic resonance to the magnetization reversal in magnetic multi-layers A spin-polarized current introduced into a nonmagnetic nanowire produces a torque associated with the itinerant electron spin flip. Here, we report direct measurement of this mechanical torque and itinerant electron spin polarization in an integrated nanoscale torsion oscillator, which could yield new information on the itinerancy of the d-band electrons. The unprecedented torque sensitivity of 10^{-22} N m/ \sqrt{Hz} may enable applications for spintronics, precision measurements of CP-violating forces, untwisting of DNA and torque generating molecules.Comment: 14 pages, 4 figures. visit http://nano.bu.edu/ for related paper

Response Spectrum of Coupled Nanomechanical Resonators

International audienceWe develop a simple continuum model to analyze the vibrational modes of a nanomechanical multielement structure. In this model, arrays of submicron cantilevers located symmetrically on both sides of the central clamped-clamped nanobeam are replaced by a continuum. In this approach, the equations of motion of the structure become exactly solvable. Our analytical results capture the main features of the vibrational modes observed both numerically and experimentally and can be applied to a general class of scale-independent elasticaly coupled resonator structures

СИНТЕЗ ФТОРОВМІСНИХ АНАЛОГІВ НОВОКАЇНАМІДУ

Methods for the synthesis of (2-N,N-diethylaminoethyl)amides of meta- and parapentafluoroethoxybenzoic acids starting with respective ethyl pentafluoroethoxybenzoates have been developed. Firstly, ethyl m- and p-pentafluoroethoxybenzoates were treated with sodium hydroxide in aqueous-alcoholic solution. The mixture obtained was acidified with concentrated hydrochloric acid giving respective meta- or para-pentafluoroethoxybenzoic acids. The acids obtained were dried and treated with excess of thionyl chloride giving respective acid chlorides that further reacted with N,N-diethylethylene-1,2-diamine. N,N-diethylethylenediamine was obtained by treating N,N-diethyl-2-chloro-ethylamine hydrochloride with aqueous ammonia solution (25%). The resulting product contained secondary and tertiary amines that could not be separated by distillation. In order to purify N,N-diethylethylene-1,2-diamine the mixture was treated with phthalic anhydride, the desired product was separated in the form of respective phthalimide and then phthalimide protecting group was removed by hydrazinolysis. After such purification N,N-diethylethylene-1,2-diamine contained no secondary or tertiary amines. The condensation of meta- and parapentafluoroethoxybenzoic acid chlorides with N,N-diethylethylenediamine was conducted in 1,2-dichloroethane solution with a little molar excess of triethylamine that was used as HCl scavenger. The reaction mixture was heated for two hours, cooled to room temperature, the residue was filtered off and volatile compounds were removed under reduced pressure. It should be noted that triethylamine is necessary, because otherwise the reaction mixture gets dark brown color and the desired product can’t be isolated. Procainamide analogues, obtained in the present paper, were tested for local anesthetic activity in capsaicin test. Both (2-N,N-diethyl-aminoethyl)amides of meta- and para-pentafluoroethoxybenzoic acids showed better local anesthetic activity, compared to anesthesine.Розроблено методи синтезу (N,N-діетил-2-аміноетил)амідів м- та п-пентафторетоксибензойних кислот, які є фторовмісними аналогами новокаїнаміду. Показано, що синтезовані аналоги мають більш високу місцевоанестезуючу активність, ніж анестезин