B. D. Hauer

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.

Quantitative Magneto-Mechanical Detection and Control of the Barkhausen Effect

Controlling Magnetic Noise Ferromagnetic materials contain a number of magnetic domains, with individual domains switching stochastically as the field strength is increased. As magnetic memory elements shrink in size, it is important to understand, and ultimately control, this magnetic noise. Using a magnetic vortex core integrated with a nanomechanical torsion balance, Burgess et al. (p. 1051, published online 17 January) created a two-dimensional map of the magnetic potential within the sample with nanoscale resolution. Moreover, introducing geometric defects (dimples) in the sample allowed the magnetization to be stabilized. A magnetic vortex core is used to probe nanoscale changes in magnetization. Quantitative characterization of intrinsic and artificial defects in ferromagnetic structures is critical to future magnetic storage based on vortices or domain walls moving through nanostructured devices. Using torsional magnetometry, we observe finite size modifications to the Barkhausen effect in the limiting case of a single vortex core interacting with individual pointlike pinning sites in a magnetic thin film. The Barkhausen effect in this limit becomes a quantitative two-dimensional nanoscale probe of local energetics in the film. Tailoring the pinning potential using single-point focused ion beam implantation demonstrates control of the effect and points the way to integrated magneto-mechanical devices incorporating quantum pinning effects.

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

High-Q Gold and Silicon Nitride Bilayer Nanostrings

Low-mass, high-Q, silicon nitride nanostrings are at the cutting edge of nanomechanical devices for sensing applications. Here we show that the addition of a chemically functionalizable gold overlayer does not adversely affect the Q of the fundamental out-of-plane mode. Instead the device retains its mechanical responsiveness while gaining sensitivity to molecular bonding. Furthermore, differences in thermal expansion within the bilayer give rise to internal stresses that can be electrically controlled. In particular, an alternating current (AC) excites resonant motion of the nanostring. This AC thermoelastic actuation is simple, robust, and provides an integrated approach to sensor actuation.

Dissipation mechanisms in thermomechanically driven silicon nitride nanostrings

High-stress silicon nitride nanostrings are a promising system for sensing applications because of their ultra-high mechanical quality factors (Qs). By performing thermomechanical calibration across multiple vibrational modes, we are able to assess the roles of the various dissipation mechanisms in these devices. Specifically, we possess a set of nanostrings in which all measured modes fall upon a single curve of peak displacement versus frequency. This allows us to rule out bulk bending and intrinsic loss mechanisms as dominant sources of dissipation and to conclude that the most significant contribution to dissipation in high-stress nanostrings occurs at the anchor points.

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.

Optomechanics and thermometry of cryogenic silica microresonators

We present measurements of silica optomechanical resonators, known as bottle resonators, passively cooled in a cryogenic environment. These devices possess a suite of properties that make them advantageous for preparation and measurement in the mechanical ground state, including high mechanical frequency, high optical and mechanical quality factors, and optomechanical sideband resolution. Performing thermometry of the mechanical motion, we find that the optical and mechanical modes demonstrate quantitatively similar laser-induced heating, limiting the lowest average phonon occupation observed to just ~1500. Thermalization to the 9 mK thermal bath would facilitate quantum measurements on these promising nanogram-scale mechanical resonators.