No Arabic abstract
Nanomechanical resonators are widely operated as force and mass sensors with sensitivities in the zepto-Newton and yocto-gram regime, respectively. Their accuracy, however, is usually undermined by high uncertainties in the effective mass of the system, whose estimation is a non-trivial task. This critical issue can be addressed in levitodynamics, where the nanoresonator typically consists of a single silica nanoparticle of well-defined mass. Yet, current methods assess the mass of the levitated nanoparticles with uncertainties up to a few tens of percent, therefore preventing to achieve unprecedented sensing performances. Here, we present a novel measurement protocol that uses the electrical field from a surrounding plate capacitor to directly drive a charged optically levitated particle in moderate vacuum. The developed technique estimates the mass within a statistical error below 1% and a systematic error of 2%, and paves the way toward more reliable sensing and metrology applications of levitodynamics systems.
Oscillators based on levitated particles are promising for the development of ultrasensitive force detectors. The theoretical performance of levitated nanomechanical sensors is usually characterized by the so-called thermal noise limit force detection sensitivity, which does not exhibit spectral specificity in practical measurements. To characterize the actual detection performance, we propose a method for the force detection sensitivity calibration of a levitated nanomechanical sensor based on the harmonic Coulomb force. Utilizing the measured transfer function, we obtained the force detection sensitivity spectrum from the position spectrum. Although the thermal noise limit force detection sensitivity of the system reached $rmleft( {4.39 pm 0.62} right) times {10^{ - 20}} N/H{z^{1/2}}$ at $rm{2.4times10^{-6} mbar}$ with feedback cooling, the measured sensitivity away from the resonance was of the order of $rm10^{-17} N/Hz^{1/2}$ based on the existing detection noise level. The calibration method established in our study is applicable to the performance evaluation of any optical levitation system for high-sensitivity force measurements.
We report on the injection locking of an optically levitated nanomechanical oscillator (a silica nanosphere) to resonant intensity modulations of an external optical signal. We explore the characteristic features of injection locking in this system, e.g. the phase pull-in effect and the injection-induced reduction of the oscillation linewidth. Our measurements are in good agreement with theoretical predictions and deepen the analogy of injection locking in levitated optomechanical systems to that in optical systems (lasers). By measuring the force noise of our feedback cooled free-running oscillator, we attain a force sensitivity of $sim23~rm{zN}/sqrt{rm{Hz}}$. This can readily allow, in fairly short integration times, for tests of violations of Newtonian gravity and searching for new small-scale forces. As a proof of concept, we show that the injection locking can be exploited to measure the forces optically induced on levitated nanoparticles, with potential applications in explorations of optical binding and entanglement between optically coupled nanomechanical oscillators.
We introduce a micromachined force scale for laser power measurement by means of radiation pressure sensing. With this technique, the measured laser light is not absorbed and can be utilized while being measured. We employ silicon micromachining technology to construct a miniature force scale, opening the potential to its use for fast in-line laser process monitoring. Here we describe the mechanical sensing principle and conversion to an electrical signal. We further outline an electrostatic force substitution process for nulling of the radiation pressure force on the sensor mirror. Finally, we look at the performance of a proof-of-concept device in open-loop operation (without the nulling electrostatic force) subjected to a modulated laser at 250 W and find its response time is less than 20 ms with noise floor dominated by electronics at 2.5 W/root(Hz).
We describe the measurement of the secular motion of a levitated nanoparticle in a Paul trap with a CMOS camera. This simple method enables us to reach signal-to-noise ratios as good as 10$^{6}$ with a displacement sensitivity better than 10$^{-16},m^{2}$/Hz. This method can be used to extract trap parameters as well as the properties of the levitated particles. We demonstrate continuous monitoring of the particle dynamics on timescales of the order of weeks. We show that by using the improvement given by super-resolution imaging, a significant reduction in the noise floor can be attained, with an increase in the bandwidth of the force sensitivity. This approach represents a competitive alternative to standard optical detection for a range of low frequency oscillators where low optical powers are required
We use an optimal control protocol to cool one mode of the center of mass motion of an optically levitated nanoparticle. The feedback technique relies on exerting a Coulomb force on a charged particle with a pair of electrodes and follows the control law of a linear quadratic regulator, whose gains are optimized by a machine learning algorithm in under 5 s. With a simpler and more robust setup than optical feedback schemes, we achieve a minimum center of mass temperature of 5 mK at $3times 10^{-7}$ mbar and transients 10 to 600 times faster than cold damping. This cooling technique can be easily extended to 3D cooling and is particularly relevant for studies demanding high repetition rates and force sensing experiments with levitated objects.