We present a microfluidic 'megapixel' digital PCR device that uses surface tension-based sample partitioning and dehydration control to enable high-fidelity single DNA molecule amplification in 1,000,000 reactors of picoliter volume with densities up to 440,000 reactors cm(-2). This device achieves a dynamic range of 10(7), single-nucleotide-variant detection below one copy per 100,000 wild-type sequences and the discrimination of a 1% difference in chromosome copy number.

We provide a detailed description of a general procedure by which a nano/micro-mechanical resonator can be calibrated using its thermal 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. The effective masses for a number of different resonator geometries are determined using both finite element method (FEM) modeling and analytical calculations.

Here we present an integrated microfluidic device for the high-throughput digital polymerase chain reaction (dPCR) analysis of single cells. This device allows for the parallel processing of single cells and executes all steps of analysis, including cell capture, washing, lysis, reverse transcription, and dPCR analysis. The cDNA from each single cell is distributed into a dedicated dPCR array consisting of 1020 chambers, each having a volume of 25 pL, using surface-tension-based sample partitioning. The high density of this dPCR format (118,900 chambers/cm(2)) allows the analysis of 200 single cells per run, for a total of 204,000 PCR reactions using a device footprint of 10 cm(2). Experiments using RNA dilutions show this device achieves shot-noise-limited performance in quantifying single molecules, with a dynamic range of 10(4). We performed over 1200 single-cell measurements, demonstrating the use of this platform in the absolute quantification of both high- and low-abundance mRNA transcripts, as well as micro-RNAs that are not easily measured using alternative hybridization methods. We further apply the specificity and sensitivity of single-cell dPCR to performing measurements of RNA editing events in single cells. High-throughput dPCR provides a new tool in the arsenal of single-cell analysis methods, with a unique combination of speed, precision, sensitivity, and specificity. We anticipate this approach will enable new studies where high-performance single-cell measurements are essential, including the analysis of transcriptional noise, allelic imbalance, and RNA processing.

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 resonator's 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.Cavity optomechanics has resulted in new levels of extremely precise displacement transduction [1, 2] of ultrahigh frequency resonators [3]. This has created much interest in pursuing quantum measurements [4] of nanomechancial devices [5][6][7], as well as dynamical back action cooling [8][9][10][11].One of the most fundamental, and as of yet unattained, quantum measurements that could be performed is that of the quantized energy eigenstates of a nanomechanical resonator (as has been demonstrated with an electron in a cyclotron orbit [12]). To achieve this, one cannot measure the displacement of the resonator [13], but instead must measure the energy directly -preferably without destroying the quantum state, a so-called quantum non-demolition (QND) measurement. Whereas the accuracy in continuously measuring two conjugate quantities is limited by the Heisenberg uncertainty principle to the standard quantum limit (SQL) [13], QND measurements allow for continuous measurements of an observable to be taken to arbitrary precision [14][15][16][17]. Here our interest lies in a QND measurement of the energy, and thereby the number of phonons [18]. In an optomechanical system, this is expected to be possible by having strong second order optomechanical coupling [19][20][21][22]. This has been demonstrated in membrane-in-the-middle Fabry-Pérot cavities [23,24], however it has been pointed out there remains first order coupling between the two optical modes, possibly obscuring QND measurements [25].Signal from second order optomechanical coupling, hence measurement of x 2 , will display mechanical peaks at twice the fundamental frequency. However, we would also expect that nonlinear transduction of the displacement, x, of a mechanical resonator from a nonlinear optical transfer function would also appear at harmonics of the mechanical resonance frequency, as has been observed [26][27][28].In this Letter we report observation of peaks in the mechanical power spectra at exactly twice the fundamental mechanical frequency, as shown in Fig. 1. We derive a model for the origin of the harmonic signal, as well as the optical spring effect, from bo...

Non-linear mixing in coupled photonic crystal nanobeam cavities due to cross-coupling opto-mechanical mechanisms Appl.

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.

Nanomechanical resonators have demonstrated great potential for use as versatile tools in a number of emerging quantum technologies. For such applications, the performance of these systems is restricted by the decoherence of their fragile quantum states, necessitating a thorough understanding of their dissipative coupling to the surrounding environment. In bulk amorphous solids, these dissipation channels are dominated at low temperatures by parasitic coupling to intrinsic two-level system (TLS) defects, however, there remains a disconnect between theory and experiment on how this damping manifests in dimensionally-reduced nanomechanical resonators. Here, we present an optomechanically-mediated thermal ringdown technique, which we use to perform simultaneous measurements of the dissipation in four mechanical modes of a cryogenically-cooled silicon nanoresonator, with resonant frequencies ranging from 3 -19 MHz. Analyzing the device's mechanical damping rate at fridge temperatures between 10 mK -10 K, we demonstrate quantitative agreement with the standard tunneling model for TLS ensembles confined to one dimension. From these fits, we extract the defect density of states (P 0 ∼ 1 -4 × 10 44 J −1 m −3 ) and deformation potentials (γ ∼ 1 -2 eV), showing that each mechanical mode couples on average to less than a single thermally-active defect at 10 mK.

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, highfrequency nanomechanical cantilevers (up to 20 MHz) that surpass these limits, anticipating their use for single-molecule force measurements. These cantilevers achieve 2 fm/ √ Hz displacement noise floors, and force sensitivity down to 132 aN/ √ Hz. Furthermore, the ability to resolve both in-plane and out-of-plane motion of our cantilevers opens the door for ultrasensitive multidimensional force spectroscopy, and optomechanical interactions, such as tuning of the cantilever frequency in situ, provide new opportunities in high-speed, high-resolution experiments.