Accurate Mass Measurement of a Levitated Nanomechanical Resonator for Precision Force-Sensing

Nano-Optomechanical Resonators Based on Suspended Graphene for Thermal Stress Sensing

Nanomechanical resonators made from suspended graphene combine the properties of ultracompactness and ultrahigh detection sensitivity, making them interesting devices for sensing applications. However, nanomechanical systems can be affected by membrane stress. The present work developed an optomechanical resonator for thermal stress sensing. The proposed resonator consists of a section of hollow core fiber (HCF) and a trampoline graphene-Au membrane. An all-optical system that integrated optical excitation and optical detection was applied. Then, the resonance frequency of the resonator was obtained through this all-optical system. In addition, this system and the resonator were used to detect the membrane's built-in stress, which depended on the ambient temperature, by monitoring the resonance frequency shift. The results verified that the temperature-induced thermal effect had a significant impact on membrane stress. Temperature sensitivities of 2.2646 kHz/°C and 2.3212 kHz/°C were obtained when the temperature rose and fell, respectively. As such, we believe that this device will be beneficial for the quality monitoring of graphene mechanical resonators.

Nano-optomechanical Resonators for Sensitive Pressure Sensing

Nanomechanical sensors made from suspended graphene are sensitive to pressure changes. However, these devices typically function by obtaining an electrical signal based on the static displacement of a suspended graphene membrane and so, in practice, have limited sensitivity and operational range. The present work demonstrates an optomechanical Au/graphene membrane-based gas pressure sensor with ultrahigh sensitivity. This sensor comprises a suspended Au/graphene membrane appended to a section of hollow-core fiber to form a sealed Fabry-Pérot cavity. In contrast to conventional nanomechanical pressure sensors, pressure changes are monitored via resonant sensing with an optical readout. A miniature pressure sensor based on this principle was able to detect an ultrasmall pressure difference of 1 × 10-7 mbar in the ultrahigh-vacuum region with a pressure range of 4.1 × 10-5 to 8.3 × 10-6 mbar. Furthermore, this pressure sensor can work over an extended pressure range of 7 × 10-6 mbar to 1000 mbar at room temperature, outperforming commercial pressure sensors. Similar results were obtained using both the fundamental and higher-order resonant frequencies but with the latter providing improved sensitivity. This sensor has a wide range of potential applications, including indoor navigation, altitude monitoring, and motion detection.

A Chemical Nanoreactor Based on a Levitated Nanoparticle in Vacuum

A single levitated nanoparticle is used as a nanoreactor for studying surface chemistry at the nanoscale. Optical levitation under controlled pressure, surrounding gas composition, and humidity provides extreme control over the nanoparticle, including dynamics, charge, and surface chemistry. Using a single nanoparticle avoids ensemble averages and allows studying how the presence of silanol groups at its surface affects the adsorption and desorption of water from the background gas with excellent spatial and temporal resolution. Herein, we demonstrate the potential of this versatile platform by studying the Zhuravlev model in silica particles. In contrast to standard methods, our system allowed the observation of an abrupt and irreversible change in scattering cross section, mass, and mechanical eigenfrequency during the dehydroxylation process, indicating changes in density, refractive index, and volume.

Analysis and Suppression of Laser Intensity Fluctuation in a Dual-Beam Optical Levitation System

Levitated micro-resonators in vacuums have attracted widespread attention due to their application potential in precision force sensing, acceleration sensing, mass measurement and gravitational wave sensing. The optically levitated microsphere in a counter-propagating dual-beam optical trap has been of particular interest because of its large measurement range and flexible manipulation. In this system, laser intensity fluctuation directly influences the trap stability and measurement sensitivity, which makes it a crucial factor in improving trapping performance. In this paper, a time-varying optical force (TVOF) model is established to characterize the influence of laser intensity fluctuation in a dual-beam optical trap. The model describes the relationship between the laser intensity fluctuation, optical force and the dynamic motion of the micro-sized sphere. In addition, an external laser intensity control method is proposed, which achieved a 16.9 dB laser power stability control at the relaxation oscillation frequency. The long-term laser intensity fluctuation was suppressed from 3% to 0.4% in a one-hour period. Experiments showed that the particle's position detection sensitivity and the stability of the relaxation oscillation could be improved by laser intensity fluctuation suppression.

Precision Calibration of the Duffing Oscillator with Phase Control

The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to an external excitation. When changing the amplitude or frequency of the external excitation, a sudden jump in the response function reveals the nonlinear dynamics prominently. However, this bistability leaves part of the full response function unobserved, which limits the precise measurement of the system parameters. Here, we exploit the often unknown fact that the response of a Duffing oscillator with nonlinear damping is a unique function of its phase. By actively stabilizing the oscillator's phase we map out the full response function. This phase control allows us to precisely determine the system parameters. Our results are particularly important for characterizing nanoscale resonators, where nonlinear effects are observed readily and which hold great promise for next generation of ultrasensitive force and mass measurements. We demonstrate our approach experimentally with an optically levitated particle in high vacuum.

Levitodynamics: Levitation and control of microscopic objects in vacuum

[Figure: see text].

Fast size estimation of single-levitated nanoparticles in a vacuum optomechanical system

Optical trapping of single nanoparticles in vacuum has various applications in both precise measurements and fundamental physics. However, to date, the number and size of randomly loaded nanoparticles in an optical trap is difficult to determine unless in vacuum. In this Letter, an efficient method for nanoparticle size estimation in an optical tweezer system before the evacuation of air was proposed and demonstrated experimentally, using scattering light from levitated particles. The particle radii deduced from the scattering light power in our proposal and from the kinetic theory of particles in gas match well (with the differences of less than 10%). For sample particles with radii ranging within 50-100 nm, we also provide a preselection rule based on this method, where over half of the trapped particles are verified as single particles. Such a particle analysis method is applicable also for the size estimation of levitated diamond particles, gold particles, and other plasmonic particles and can be applied to discovering novel scattering effects.

Review on Carbon Nanomaterials-Based Nano-Mass and Nano-Force Sensors by Theoretical Analysis of Vibration Behavior

Carbon nanomaterials, such as carbon nanotubes (CNTs), graphene sheets (GSs), and carbyne, are an important new class of technological materials, and have been proposed as nano-mechanical sensors because of their extremely superior mechanical, thermal, and electrical performance. The present work reviews the recent studies of carbon nanomaterials-based nano-force and nano-mass sensors using mechanical analysis of vibration behavior. The mechanism of the two kinds of frequency-based nano sensors is firstly introduced with mathematical models and expressions. Afterward, the modeling perspective of carbon nanomaterials using continuum mechanical approaches as well as the determination of their material properties matching with their continuum models are concluded. Moreover, we summarize the representative works of CNTs/GSs/carbyne-based nano-mass and nano-force sensors and overview the technology for future challenges. It is hoped that the present review can provide an insight into the application of carbon nanomaterials-based nano-mechanical sensors. Showing remarkable results, carbon nanomaterials-based nano-mass and nano-force sensors perform with a much higher sensitivity than using other traditional materials as resonators, such as silicon and ZnO. Thus, more intensive investigations of carbon nanomaterials-based nano sensors are preferred and expected.

Extending Vacuum Trapping to Absorbing Objects with Hybrid Paul-Optical Traps

The levitation of condensed matter in vacuum allows the study of its physical properties under extreme isolation from the environment. It also offers a venue to investigate quantum mechanics with large systems, at the transition between the quantum and classical worlds. In this work, we study a novel hybrid levitation platform that combines a Paul trap with a weak but highly focused laser beam, a configuration that integrates a deep potential with excellent confinement and motion detection. We combine simulations and experiments to demonstrate the potential of this approach to extend vacuum trapping and interrogation to a broader range of nanomaterials, such as absorbing particles. We study the stability and dynamics of different specimens, such as fluorescent dielectric crystals and gold nanorods, and demonstrate stable trapping down to pressures of 1 mbar.

Robust Optical-Levitation-Based Metrology of Nanoparticle's Position and Mass

Light has shown an incredible capability in precision measurement based on optomechanic interaction in high vacuum by isolating environment noises. However, there are still obstructions, such as displacement and mass estimation error, highly hampering the improvement of absolute accuracy at the nanoscale. Here, we present a nonlinearity based metrology to precisely measure the position and mass of a nanoparticle with optical levitation under 10^{-5}  mbar. By precisely controlling the oscillation amplitude of the levitated nanoparticle at the nonlinear regime for high accuracy calibration, we realized a feasible sub-picometer-level position measurement with an uncertainty of 1.0% without the prior information of mass, which can be further applied to weigh the femtogram-level mass with an uncertainty of 2.2%. It will also pave the way to construct a fine-calibrated optomechanic platform in high vacuum for high sensitivity and accuracy measurement in force and acceleration at the nanoscale and the study in quantum superposition at the mesoscopic scale.

Ultrasensitive torque detection with an optically levitated nanorotor

Torque sensors such as the torsion balance enabled the first determination of the gravitational constant by Henri Cavendish¹ and the discovery of Coulomb's law. Torque sensors are also widely used in studying small-scale magnetism^2,3, the Casimir effect⁴ and other applications⁵. Great effort has been made to improve the torque detection sensitivity by nanofabrication and cryogenic cooling. Until now, the most sensitive torque sensor has achieved a remarkable sensitivity of 2.9 × 10^-24 N m Hz^-1/2 at millikelvin temperatures in a dilution refrigerator⁶. Here, we show a torque sensor reaching sensitivity of (4.2 ± 1.2) × 10^-27 N m Hz^-1/2 at room temperature. It is created by an optically levitated nanoparticle in vacuum. Our system does not require complex nanofabrication. Moreover, we drive a nanoparticle to rotate at a record high speed beyond 5 GHz (300 billion r.p.m.). Our calculations show that this system will be able to detect the long sought after vacuum friction^7-10 near a surface under realistic conditions. The optically levitated nanorotor will also have applications in studying nanoscale magnetism^2,3 and the quantum geometric phase¹¹.