C. Doolin

Nanoscale torsional optomechanics

Optomechanical transduction is demonstrated for nanoscale torsional resonators evanescently coupled to optical microdisk whispering gallery mode resonators. The on-chip, integrated devices are measured using a fully fiber-based system, including a tapered and dimpled optical fiber probe. With a thermomechanically calibrated optomechanical noise floor down to 7 fm/Hz, these devices open the door for a wide range of physical measurements involving extremely small torques, as little as 4×10−20N·m.

A general procedure for thermomechanical calibration of nano/micro-mechanical resonators

Abstract We describe a general procedure to calibrate the detection of a nano/micro-mechanical resonator’s displacement as it undergoes thermal Brownian motion. A brief introduction to the equations of motion for such a resonator is presented, followed by a detailed derivation of the corresponding power spectral density (PSD) function, which is identical in all situations aside from a system-dependent effective mass value. The effective masses for a number of different resonator geometries are determined using both finite element method (FEM) modeling and analytical calculations.

Nonlinear optomechanics in the stationary regime

We have observed nonlinear transduction of the thermomechanical motion of a nanomechanical resonator when detected as laser transmission through a sideband unresolved optomechanical cavity. Nonlinear detection mechanisms are of considerable interest as special cases allow for quantum nondemolition measurements of the mechanical resonators energy. We investigate the origin of the nonlinearity in the optomechanical detection apparatus and derive a theoretical framework for the nonlinear signal transduction, and the optical spring effect, from both nonlinearities in the optical transfer function and second order optomechanical coupling. By measuring the dependence of the linear and nonlinear signal transduction -- as well as the mechanical frequency shift -- on laser detuning from optical resonance, we provide estimates of the contributions from the linear and quadratic optomechanical couplings.

Multidimensional optomechanical cantilevers for high-frequency force sensing

High-frequency atomic force microscopy has enabled extraordinary new science through large bandwidth, high-speed measurements of atomic and molecular structures. However, traditional optical detection schemes restrict the dimensions, and therefore the frequency, of the cantilever?ultimately setting a limit to the time resolution of experiments. Here we demonstrate optomechanical detection of low-mass, high-frequency nanomechanical cantilevers (up to 20 MHz) and anticipate their use for single-molecule force measurements. These cantilevers achieve 2 fm displacement noise floors, and force sensitivity down to 132 aN . Furthermore, the ability to resolve both in-plane and out-of-plane motion of our cantilevers makes them excellent candidates for ultrasensitive multidimensional force spectroscopy, and optomechanical interactions, such as tuning of the cantilever frequency in situ, provide opportunities in high-speed, high-resolution experiments.

On-chip cavity optomechanical coupling

AbstractBackgroundOn-chip cavity optomechanics, in which strong co-localization of light and mechanical motion is engineered, relies on efficient coupling of light both into and out of the on-chip optical resonator. Here we detail our particular style of tapered and dimpled optical fibers, pioneered by the Painter group at Caltech, which are a versatile and reliable solution to efficient on-chip coupling. A brief overview of tapered, single mode fibers is presented, in which the single mode cutoff diameter is highlighted.MethodsThe apparatus used to create a dimpled tapered fiber is described, followed by a comprehensive account of the procedure by which a dimpled tapered fiber is produced and mounted in our system. The custom-built optical access vacuum chambers in which our on-chip optomechanical measurements are performed are then discussed. Finally, the process by which our optomechanical devices are fabricated and the method by which we explore their optical and mechanical properties is explained.ResultsUsing this method of on-chip optomechanical coupling, angular and displacement noise floors of 4 nrad/ and 2 fm/ have been demonstrated, corresponding to torque and force sensitivities of and 132 aN/ , respectively.ConclusionThe methods and results of our on-chip optomechanical coupling system are summarized. It is our expectation that this manuscript will enable the novice to develop advanced optomechanical experiments.PACS codes07.60.-j; 07.10.Cm; 42.50.Wk

Approaching the standard quantum limit of mechanical torque sensing.

Reducing the moment of inertia improves the sensitivity of a mechanically based torque sensor, the parallel of reducing the mass of a force sensor, yet the correspondingly small displacements can be difficult to measure. To resolve this, we incorporate cavity optomechanics, which involves co-localizing an optical and mechanical resonance. With the resulting enhanced readout, cavity-optomechanical torque sensors are now limited only by thermal noise. Further progress requires thermalizing such sensors to low temperatures, where sensitivity limitations are instead imposed by quantum noise. Here, by cooling a cavity-optomechanical torque sensor to 25 mK, we demonstrate a torque sensitivity of 2.9 yNm/. At just over a factor of ten above its quantum-limited sensitivity, such cryogenic optomechanical torque sensors will enable both static and dynamic measurements of integrated samples at the level of a few hundred spins.

Remote Sensing in Hybridized Arrays of Nanostrings

We study high-Q nanostrings that are joined end-to-end to form coupled linear arrays. Whereas isolated individual resonators exhibit sinusoidal vibrational modes with an almost perfectly harmonic spectrum, the modes of the interacting strings are substantially hybridized. Even far-separated strings can show significantly correlated displacement. This remote coupling property is exploited to quantify the deposition of femtogram-scale masses with string-by-string positional discrimination based on measurements of one string only.

Femtogram-Scale Photothermal Spectroscopy of Explosive Molecules on Nanostrings

We demonstrate detection of femtogram-scale quantities of the explosive molecule 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) via combined nanomechanical photothermal spectroscopy and mass desorption. Photothermal spectroscopy provides a spectroscopic fingerprint of the molecule, which is unavailable using mass adsorption/desorption alone. Our measurement, based on thermomechanical measurement of silicon nitride nanostrings, represents the highest mass resolution ever demonstrated via nanomechanical photothermal spectroscopy. This detection scheme is quick, label-free, and is compatible with parallelized molecular analysis of multicomponent targets.

Time-Resolved Mass Sensing of a Molecular Adsorbate Nonuniformly Distributed Along a Nanomechnical String

We show that the particular distribution of mass deposited on the surface of a nanomechanical resonator can be estimated by tracking the evolution of the devices resonance frequencies during the process of desorption. The technique, which relies on analytical models we have developed for the multimodal response of the system, enables mass sensing at much higher levels of accuracy than is typically achieved with a single frequency-shift measurement and no rigorous knowledge of the mass profile. We report on a series of demonstration experiments, in which the explosive molecule 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) is vapor deposited along the length of a silicon nitride nanostring to create a dense, random covering of RDX crystallites on the surface. In some cases, the deposition is biased to produce distributions with a slight excess or deficit of mass at the string midpoint. The added mass is then allowed to sublimate away under vacuum conditions, with the device returning to its original state over about 4 h (and the resonance frequencies, measured via optical interferometry, relaxing back to their pre-mass-deposition values). Our claim is that the detailed time trace of observed frequency shifts is rich in information---not only about the quantity of RDX initially deposited but also about its spatial arrangement along the nanostring. The data also reveal that sublimation in this case follows a nontrivial rate law, consistent with mass loss occurring at the exposed surface area of the RDX crystallites.

Refractometric sensing of Li salt with visible-light Si3N4 microdisk resonators

We demonstrate aqueous refractive index sensing with 15 to 30 {\mu}m diameter silicon nitride microdisk resonators to detect small concentrations of Li salt. A dimpled-tapered fiber is used to couple 780 nm visible light to the microdisks, in order to perform spectroscopy their optical resonances. The dimpled fiber probe allows testing of multiple devices on a chip in a single experiment. This sensing system is versatile and easy to use, while remaining competitive with other refractometric sensors. For example, from a 20 {\mu}m diameter device we measure a sensitivity of 200