A. K. Naik

Towards single-molecule nanomechanical mass spectrometry

Mass spectrometry (MS) provides rapid and quantitative identification of protein species with relatively low sample consumption. Yet with the trend toward biological analysis at increasingly smaller scales, ultimately down to the volume of an individual cell, MS with few-to-single molecule sensitivity will be required. Nanoelectromechanical systems (NEMS) provide unparalleled mass sensitivity, which is now sufficient for the detection of individual molecular species in real time. Here we report the first demonstration of MS based on single-biological-molecule detection with NEMS. In our NEMS-MS system, nanoparticles and protein species are introduced by electrospray injection from fluid phase in ambient conditions into vacuum and subsequently delivered to the NEMS detector by hexapole ion optics. Precipitous frequency shifts, proportional to the mass, are recorded in real time as analytes adsorb, one-by-one, onto a phase-locked, ultrahigh frequency NEMS resonator. These first NEMS-MS spectra, obtained with modest mass sensitivity from only several hundred mass adsorption events, presage the future capabilities of this approach. We also outline the substantial improvements that are feasible in the near term, some of which are unique to NEMS-MS.

Single-protein nanomechanical mass spectrometry in real time

Nanoelectromechanical systems (NEMS) resonators can detect mass with exceptional sensitivity. Previously, mass spectra from several hundred adsorption events were assembled in NEMS-based mass spectrometry using statistical analysis. Here, we report the first realization of single-molecule NEMS-based mass spectrometry in real time. As each molecule in the sample adsorbs upon the NEMS resonator, its mass and the position-of-adsorption are determined by continuously tracking two driven vibrational modes of the device. We demonstrate the potential of multimode NEMS-based mass spectrometry by analyzing IgM antibody complexes in real-time. NEMS-MS is a unique and promising new form of mass spectrometry: it can resolve neutral species, provides resolving power that increases markedly for very large masses, and allows acquisition of spectra, molecule-by-molecule, in real-time.

Cooling a nanomechanical resonator with quantum back-action

Quantum mechanics demands that the act of measurement must affect the measured object. When a linear amplifier is used to continuously monitor the position of an object, the Heisenberg uncertainty relationship requires that the object be driven by force impulses, called back-action. Here we measure the back-action of a superconducting single-electron transistor (SSET) on a radio-frequency nanomechanical resonator. The conductance of the SSET, which is capacitively coupled to the resonator, provides a sensitive probe of the latters position; back-action effects manifest themselves as an effective thermal bath, the properties of which depend sensitively on SSET bias conditions. Surprisingly, when the SSET is biased near a transport resonance, we observe cooling of the nanomechanical mode from 550 mK to 300 mK—an effect that is analogous to laser cooling in atomic physics. Our measurements have implications for nanomechanical readout of quantum information devices and the limits of ultrasensitive force microscopy (such as single-nuclear-spin magnetic resonance force microscopy). Furthermore, we anticipate the use of these back-action effects to prepare ultracold and quantum states of mechanical structures, which would not be accessible with existing technology.

Frequency fluctuations in silicon nanoresonators

Frequency stability is key to performance of nanoresonators. This stability is thought to reach a limit with the resonator’s ability to resolve thermally-induced vibrations. Although measurements and predictions of resonator stability usually disregard fluctuations in the mechanical frequency response, these fluctuations have recently attracted considerable theoretical interest. However, their existence is very difficult to demonstrate experimentally. Here, through a literature review, we show that all studies of frequency stability report values several orders of magnitude larger than the limit imposed by thermomechanical noise. We studied a monocrystalline silicon nanoresonator at room temperature, and found a similar discrepancy. We propose a new method to show this was due to the presence of frequency fluctuations, of unexpected level. The fluctuations were not due to the instrumentation system, or to any other of the known sources investigated. These results challenge our current understanding of frequency fluctuations and call for a change in practices.

Nonlinear mode coupling and internal resonances in MoS2 nanoelectromechanical system

Atomically thin two dimensional (2D) layered materials have emerged as a new class of material for nanoelectromechanical systems (NEMS) due to their extraordinary mechanical properties and ultralow mass density. Among them, graphene has been the material of choice for nanomechanical resonator. However, recent interest in 2D chalcogenide compounds has also spurred research in using materials such as MoS2 for the NEMS applications. As the dimensions of devices fabricated using these materials shrink down to atomically thin membrane, strain and nonlinear effects have become important. A clear understanding of the nonlinear effects and the ability to manipulate them is essential for next generation sensors. Here, we report on all electrical actuation and detection of few-layer MoS2 resonator. The ability to electrically detect multiple modes and actuate the modes deep into the nonlinear regime enables us to probe the nonlinear coupling between various vibrational modes. The modal coupling in our device is strong enough to detect three distinct internal resonances

Dynamic range tuning of graphene nanoresonators

From sensing perspective, smaller electromechanical devices, in general, are expected to be more responsive to the stimuli. This enhanced performance, however, is contingent upon the noise sources remaining unchanged and the onset of nonlinear behavior not being precipitated by miniaturization. In this paper, we study the effect of strain on the nonlinearities and dynamic range in graphene nanoresonators. The dynamic response and the onset of nonlinearity in these devices are sensitive both to the electrostatic field used to actuate the device and the strain. By tuning the strain of the device by two orders of magnitude, we observe an enhancement of 25 dB in the dynamic range leading to a mass resolution of 100 yoctogram. The increase in dynamic range in our devices is modeled as a combined effect of strain and partial cancellation of elastic and electrostatic nonlinearities.

Single-particle mass spectrometry with arrays of frequency-addressed nanomechanical resonators

One of the main challenges to overcome to perform nanomechanical mass spectrometry analysis in a practical time frame stems from the size mismatch between the analyte beam and the small nanomechanical detector area. We report here the demonstration of mass spectrometry with arrays of 20 multiplexed nanomechanical resonators; each resonator is designed with a distinct resonance frequency which becomes its individual address. Mass spectra of metallic aggregates in the MDa range are acquired with more than one order of magnitude improvement in analysis time compared to individual resonators. A 20 NEMS array is probed in 150 ms with the same mass limit of detection as a single resonator. Spectra acquired with a conventional time-of-flight mass spectrometer in the same system show excellent agreement. We also demonstrate how mass spectrometry imaging at the single-particle level becomes possible by mapping a 4-cm-particle beam in the MDa range and above.Nano-electro-mechanical system-based mass spectrometry holds promise for detecting supramolecular assemblies at large molecular weights, but its efficiency is too poor to be practical. Sage et al. overcome this problem using a nanomechanical resonator array, which significantly decreases detection time.

On-chip optical transduction scheme for graphene nano-electro-mechanical systems in silicon-photonic platform

We present a scheme for on-chip optical transduction of strain and displacement of graphene-based nano-electro-mechanical systems (NEMS). A detailed numerical study on the feasibility of three silicon-photonic integrated circuit configurations is presented: the Mach-Zehnder interferometer (MZI), the micro-ring resonator, and the ring-loaded MZI. An index sensing based technique using an MZI loaded with a ring resonator with a moderate Q-factor of 2400 can yield a sensitivity of 28  fm/Hz and 6.5×10-6%/Hz for displacement and strain, respectively. Though any phase-sensitive integrated-photonic device could be used for optical transduction, here we show that optimal sensitivity is achievable by combining resonance with phase sensitivity.

Silicon photonics based on-chip vibrometer

In this paper, we demonstrate a compact silicon photonics based vibrometer using an on-chip photonic grating (OPG) based sensor. OPG works on the principle of interference where the motion of the cantilever is captured at the output as an intensity variation. The advantage of OPG based sensor over conventional Laser Doppler vibrometer is increased tolerance to alignment errors as both the grating and the cantilever can be integrated on a single chip. The grating parameters were optimized using 2D-FDTD to achieved maximum sensitivity to the displacement of a cantilever. OPG with on-chip germanium photodetector is studied, which indicates a sensitivity of 54 μW/nm. We experimentally demonstrate the feasibility of the proposed sensor that can achieve a displacement sensitivity of 5.3 μW/nm.

Tuning of geometric nonlinearity in ultrathin nanoelectromechanical systems

Nonlinearities in nanoelectromechanical systems (NEMS) play a vital role in dynamics of the device. Clear understanding of nonlinearities and ability to tune and manipulate them to enhance the performance are crucial for applications with these devices. Here, we utilize an electrostatic mechanism to tune the geometric nonlinearity of an atomically thin NEMS. The exquisite tuning enables us to demonstrate hardening, softening, and mixed nonlinear responses in the device. The electrostatic tuning over the nonlinearity is utilized to effectively nullify Duffing nonlinearity in a specific regime. The observed mixed nonlinear response is the result of cross coupling between strong quadratic and quartic nonlinearities, an aspect explained by method of multiple scale analysis.Nonlinearities in nanoelectromechanical systems (NEMS) play a vital role in dynamics of the device. Clear understanding of nonlinearities and ability to tune and manipulate them to enhance the performance are crucial for applications with these devices. Here, we utilize an electrostatic mechanism to tune the geometric nonlinearity of an atomically thin NEMS. The exquisite tuning enables us to demonstrate hardening, softening, and mixed nonlinear responses in the device. The electrostatic tuning over the nonlinearity is utilized to effectively nullify Duffing nonlinearity in a specific regime. The observed mixed nonlinear response is the result of cross coupling between strong quadratic and quartic nonlinearities, an aspect explained by method of multiple scale analysis.