Showing papers on "Noise (electronics) published in 2015"

The Dark Energy Camera

Abstract: The Dark Energy Camera is a new imager with a 2.2-degree diameter field of view mounted at the prime focus of the Victor M. Blanco 4-meter telescope on Cerro Tololo near La Serena, Chile. The camera was designed and constructed by the Dark Energy Survey Collaboration, and meets or exceeds the stringent requirements designed for the wide-field and supernova surveys for which the collaboration uses it. The camera consists of a five element optical corrector, seven filters, a shutter with a 60 cm aperture, and a CCD focal plane of 250 micron thick fully-depleted CCDs cooled inside a vacuum Dewar. The 570 Mpixel focal plane comprises 62 2kx4k CCDs for imaging and 12 2kx2k CCDs for guiding and focus. The CCDs have 15 microns x15 microns pixels with a plate scale of 0.263 arc sec per pixel. A hexapod system provides state-of-the-art focus and alignment capability. The camera is read out in 20 seconds with 6-9 electrons readout noise. This paper provides a technical description of the camera's engineering, construction, installation, and current status.

Ultralow noise miniature external cavity semiconductor laser

Abstract: Advanced applications in optical metrology demand improved lasers with high spectral purity, in form factors that are small and insensitive to environmental perturbations. While laboratory-scale lasers with extraordinarily high stability and low noise have been reported, all-integrated chip-scale devices with sub-100 Hz linewidth have not been previously demonstrated. Lasers integrated with optical microresonators as external cavities have the potential for substantial reduction of noise. However, stability and spectral purity improvements of these lasers have only been validated with rack-mounted support equipment, assembled with fibre lasers to marginally improve their noise performance. In this work we report on a realization of a heterogeneously integrated, chip-scale semiconductor laser featuring 30-Hz integral linewidth as well as sub-Hz instantaneous linewidth. Optical metrology applications require lasers with high spectral purity but on-chip devices with sub-100 Hz linewidth are yet to be realized. Here, Liang et al.present a heterogeneously integrated, chip-scale semiconductor laser with 30 Hz integral linewidth and sub-Hz instantaneous linewidth.

Spectrum of controlling and observing complex networks

Abstract: Recent studies have made important advances in identifying sensor or driver nodes, through which we can observe or control a complex system. But the observational uncertainty induced by measurement noise and the energy required for control continue to be significant challenges in practical applications. Here we show that the variability of control energy and observational uncertainty for different directions of the state space depend strongly on the number of driver nodes. In particular, we find that if all nodes are directly driven, control is energetically feasible, as the maximum energy increases sublinearly with the system size. If, however, we aim to control a system through a single node, control in some directions is energetically prohibitive, increasing exponentially with the system size. For the cases in between, the maximum energy decays exponentially when the number of driver nodes increases. We validate our findings in several model and real networks, arriving at a series of fundamental laws to describe the control energy that together deepen our understanding of complex systems. The complex interactions inherent in real-world networks grant us precise system control via manipulation of a subset of nodes. It turns out that the extent to which we can exercise this control depends sensitively on the number of nodes perturbed.

Quantitative differential phase contrast imaging in an LED array microscope.

Abstract: Illumination-based differential phase contrast (DPC) is a phase imaging method that uses a pair of images with asymmetric illumination patterns. Distinct from coherent techniques, DPC relies on spatially partially coherent light, providing 2× better lateral resolution, better optical sectioning and immunity to speckle noise. In this paper, we derive the 2D weak object transfer function (WOTF) and develop a quantitative phase reconstruction method that is robust to noise. The effect of spatial coherence is studied experimentally, and multiple-angle DPC is shown to provide improved frequency coverage for more stable phase recovery. Our method uses an LED array microscope to achieve real-time (10 Hz) quantitative phase imaging with in vitro live cell samples.

Isotopically enhanced triple-quantum-dot qubit.

Abstract: Like modern microprocessors today, future processors of quantum information may be implemented using all-electrical control of silicon-based devices. A semiconductor spin qubit may be controlled without the use of magnetic fields by using three electrons in three tunnel-coupled quantum dots. Triple dots have previously been implemented in GaAs, but this material suffers from intrinsic nuclear magnetic noise. Reduction of this noise is possible by fabricating devices using isotopically purified silicon. We demonstrate universal coherent control of a triple-quantum-dot qubit implemented in an isotopically enhanced Si/SiGe heterostructure. Composite pulses are used to implement spin-echo type sequences, and differential charge sensing enables single-shot state readout. These experiments demonstrate sufficient control with sufficiently low noise to enable the long pulse sequences required for exchange-only two-qubit logic and randomized benchmarking.

Entanglement-enhanced sensing in a lossy and noisy environment.

Abstract: Nonclassical states are essential for optics-based quantum information processing, but their fragility limits their utility for practical scenarios in which loss and noise inevitably degrade, if not destroy, nonclassicality. Exploiting nonclassical states in quantum metrology yields sensitivity advantages over all classical schemes delivering the same energy per measurement interval to the sample being probed. These enhancements, almost without exception, are severely diminished by quantum decoherence. Here, we experimentally demonstrate an entanglement-enhanced sensing system that is resilient to quantum decoherence. We employ entanglement to realize a 20% signal-to-noise ratio improvement over the optimum classical scheme in an entanglement-breaking environment plagued by 14 dB of loss and a noise background 75 dB stronger than the returned probe light. Our result suggests that advantageous quantum-sensing technology could be developed for practical situations.

21CMMC: an MCMC analysis tool enabling astrophysical parameter studies of the cosmic 21 cm signal

Abstract: We introduce 21CMMC: a parallelized, Monte Carlo Markov Chain analysis tool, incorporating the epoch of reionization (EoR) seminumerical simulation 21CMFAST. 21CMMC estimates astrophysical parameter constraints from 21 cm EoR experiments, accommodating a variety of EoR models, as well as priors on model parameters and the reionization history. To illustrate its utility, we consider two different EoR scenarios, one with a single population of galaxies (with a mass-independent ionizing efficiency) and a second, more general model with two different, feedback-regulated populations (each with mass-dependent ionizing efficiencies). As an example, combining three observations (z=8, 9 and 10) of the 21 cm power spectrum with a conservative noise estimate and uniform model priors, we find that interferometers with specifications like the Low Frequency Array/Hydrogen Epoch of Reionization Array (HERA)/Square Kilometre Array 1 (SKA1) can constrain common reionization parameters: the ionizing efficiency (or similarly the escape fraction), the mean free path of ionizing photons and the log of the minimum virial temperature of star-forming haloes to within 45.3/22.0/16.7, 33.5/18.4/17.8 and 6.3/3.3/2.4 per cent, ~$1\sigma$ fractional uncertainty, respectively. Instead, if we optimistically assume that we can perfectly characterize the EoR modelling uncertainties, we can improve on these constraints by up to a factor of ~few. Similarly, the fractional uncertainty on the average neutral fraction can be constrained to within $\lesssim10$ per cent for HERA and SKA1. By studying the resulting impact on astrophysical constraints, 21CMMC can be used to optimize (i) interferometer designs; (ii) foreground cleaning algorithms; (iii) observing strategies; (iv) alternative statistics characterizing the 21 cm signal; and (v) synergies with other observational programs.

Achieving Undetectable Communication

Abstract: In this paper we consider the problem of achieving a positive error-free communications rate without being detected by an eavesdropper—we coin this the privacy rate. Specifically, we analyze the privacy rate over additive white Gaussian Noise (AWGN) channels with finite and infinite number of samples and Rayleigh single input-single (SISO) and multiple input-multiple output (MIMO) channels with infinite samples when an eavesdropper employs a radiometer detector and has uncertainty about his noise variance. Leveraging recent results on the phenomenon of a signal-to-noise ratio (SNR) wall when there is eavesdropper noise power measurement uncertainty, we show that a nonzero privacy rate is possible. We also show that in this scenario, the detector should not necessarily take as many samples as possible.

Internal Resonance Energy Harvesting

Abstract: Internal resonance is explored as a possible mechanism to enhance vibration-based energy harvesting. An electromagnetic device with snap-through nonlinearity is proposed as an archetype of an internal resonance energy harvester. Based on the equations governing the vibration measured from a stable equilibrium position, the method of multiple scales is applied to derive the amplitude–frequency response relationships of the displacement and the power in the first primary resonances with the two-to-one internal resonance. The amplitude–frequency response curves have two peaks bending to the left and the right, respectively. The numerical simulations support the analytical results. Then the averaged power is calculated under the Gaussian white noise, the narrow-band noise, the colored noise defined by a second-order filter, and the exponentially correlated noise. The results demonstrate numerically that the internal resonance design produces more power than other designs under the Gaussian white noise and the exponentially correlated noise. Besides, the internal resonance energy harvester can outperform the linear energy harvesters with the same natural frequencies and in the same size under Gaussian white noise.

GLEAM: The GaLactic and Extragalactic All-sky MWA survey

Abstract: GLEAM, the GaLactic and Extragalactic All-sky MWA survey, is a survey of the entire radio sky south of declination +25 deg at frequencies between 72 and 231 MHz, made with the Murchison Widefield Array (MWA) using a drift scan method that makes efficient use of the MWA's very large field-of-view. We present the observation details, imaging strategies and theoretical sensitivity for GLEAM. The survey ran for two years, the first year using 40 kHz frequency resolution and 0.5 s time resolution; the second year using 10 kHz frequency resolution and 2 s time resolution. The resulting image resolution and sensitivity depends on observing frequency, sky pointing and image weighting scheme. At 154 MHz the image resolution is approximately 2.5 x 2.2/cos(DEC+26.7) arcmin with sensitivity to structures up to ~10 deg in angular size. We provide tables to calculate the expected thermal noise for GLEAM mosaics depending on pointing and frequency and discuss limitations to achieving theoretical noise in Stokes I images. We discuss challenges, and their solutions, that arise for GLEAM including ionospheric effects on source positions and linearly polarised emission, and the instrumental polarisation effects inherent to the MWA's primary beam.

On the Optimality of Treating Interference as Noise

Abstract: It is shown that in the $K$ -user interference channel, if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in decibel scale), then the simple scheme of using point-to-point Gaussian codebooks with appropriate power levels at each transmitter and treating interference as noise (TIN) at every receiver (in short, TIN scheme) achieves all points in the capacity region to within a constant gap. The generalized degrees of freedom (GDoF) region under this condition is a polyhedron, which is shown to be fully achieved by the same scheme, without the need for time-sharing. The results are proved by first deriving a polyhedral relaxation of the GDoF region achieved by TIN, and then providing a dual characterization of this polyhedral region via the use of potential functions, and finally proving the optimality of this region in the desired regime.

Inter-Channel Nonlinear Interference Noise in WDM Systems: Modeling and Mitigation

Abstract: We review the modeling of inter-channel nonlinear interference noise (NLIN) in fiber-optic communication systems, focusing on the accurate extraction of the NLIN variance, the dependence on modulation format, the role of nonlinear phase-noise, and the existence of temporal correlations. We show ways in which temporal correlations can be exploited for reducing the impact of NLIN, and discuss the prospects of this procedure in future systems.

Coexistence of continuous variable QKD with intense DWDM classical channels

Abstract: We demonstrate experimentally the feasibility of continuous variable quantum key distribution (CV-QKD) in dense-wavelength-division multiplexing networks (DWDM), where QKD will typically have to coexist with several co-propagating (forward or backward) C-band classical channels whose launch power is around 0 dBm. We have conducted experimental tests of the coexistence of CV-QKD multiplexed with an intense classical channel, for different input powers and different DWDM wavelengths. Over a 25 km fiber, a CV-QKD operated over the 1530.12 nm channel can tolerate the noise arising from up to 11.5 dBm classical channel at 1550.12 nm in the forward direction (9.7 dBm in backward). A positive key rate (0.49 kbits s−1) can be obtained at 75 km with classical channel power of respectively −3 and −9 dBm in forward and backward. Based on these measurements, we have also simulated the excess noise and optimized channel allocation for the integration of CV-QKD in some access networks. We have, for example, shown that CV-QKD could coexist with five pairs of channels (with nominal input powers: 2 dBm forward and 1 dBm backward) over a 25 km WDM-PON network. The obtained results demonstrate the outstanding capacity of CV-QKD to coexist with classical signals of realistic intensity in optical networks.

Composite-light-pulse technique for high-precision atom interferometry.

Abstract: By keeping its atomic components in the same state, a team was able to reduce one typical source of noise in a rotation-measuring device.

$1/f$ Noise and Defects in Microelectronic Materials and Devices

Abstract: This paper reviews and compares predictions of the Dutta-Horn model of low-frequency excess ( ${\bf 1}/\mbi{f}$ ) noise with experimental results for thin metal films, MOS transistors, and GaN/AlGaN high-electron mobility transistors (HEMTs). For metal films, mobility fluctuations associated with carrier-defect scattering lead to ${\bf 1}/\mbi{f}$ noise. In contrast, for most semiconductor devices, the noise usually results from fluctuations in the number of carriers due to charge exchange between the channel and defects, usually at or near a critical semiconductor/insulator interface. The Dutta-Horn model describes the noise with high precision in most cases. Insight into the physical mechanisms that lead to noise in microelectronic materials and devices has been obtained via total-ionizing-dose irradiation and/or thermal annealing, as illustrated with several examples. With the assistance of the Dutta-Horn model, measurements of the noise magnitude and temperature and/or voltage dependence of the noise enable estimates of the energy distributions of defects that lead to ${\bf 1}/\mbi{f}$ noise. The microstructure of several defects and/or impurities that cause noise in MOS devices (primarily O vacancies) and GaN/AlGaN HEMTs (e.g., hydrogenated impurity centers, N vacancies, and/or Fe centers) have been identified via experiments and density functional theory calculations.

1/f noise in graphene nanopores

Abstract: Graphene nanopores are receiving great attention due to their atomically thin membranes and intrinsic electrical properties that appear greatly beneficial for biosensing and DNA sequencing. Here, we present an extensive study of the low-frequency 1/f noise in the ionic current through graphene nanopores and compare it to noise levels in silicon nitride pore currents. We find that the 1/f noise magnitude is very high for graphene nanopores: typically two orders of magnitude higher than for silicon nitride pores. This is a drawback as it significantly lowers the signal-to-noise ratio in DNA translocation experiments. We evaluate possible explanations for these exceptionally high noise levels in graphene pores. From examining the noise for pores of different diameters and at various salt concentrations, we find that in contrast to silicon nitride pores, the 1/f noise in graphene pores does not follow Hooge's relation. In addition, from studying the dependence on the buffer pH, we show that the increased noise cannot be explained by charge fluctuations of chemical groups on the pore rim. Finally, we compare single and bilayer graphene to few-layer and multi-layer graphene and boron nitride (h-BN), and we find that the noise reduces with layer thickness for both materials, which suggests that mechanical fluctuations may be the underlying cause of the high 1/f noise levels in monolayer graphene nanopore devices.

Sum-Rate and Power Scaling of Massive MIMO Systems With Channel Aging

Abstract: This paper investigates the achievable sum-rate of massive multiple-input multiple-output (MIMO) systems in the presence of channel aging. For the uplink, by assuming that the base station (BS) deploys maximum ratio combining (MRC) or zero-forcing (ZF) receivers, we present tight closed-form lower bounds on the achievable sum-rate for both receivers with aged channel state information (CSI). In addition, the benefit of implementing channel prediction methods on the sum-rate is examined, and closed-form sum-rate lower bounds are derived. Moreover, the impact of channel aging and channel prediction on the power scaling law is characterized. Extension to the downlink scenario and multicell scenario is also considered. It is found that, for a system with/without channel prediction, the transmit power of each user can be scaled down at most by $1/\sqrt{M}$ (where $M$ is the number of BS antennas), which indicates that aged CSI does not degrade the power scaling law, and channel prediction does not enhance the power scaling law; instead, these phenomena affect the achievable sum-rate by degrading or enhancing the effective signal to interference and noise ratio, respectively.

A 3.7 mW Low-Noise Wide-Bandwidth 4.5 GHz Digital Fractional-N PLL Using Time Amplifier-Based TDC

Abstract: A digital fractional-N PLL that employs a high resolution TDC and a truly $\Delta \Sigma$ fractional divider to achieve low in-band noise with a wide bandwidth is presented. The fractional divider employs a digital-to-time converter (DTC) to cancel out $\Delta \Sigma$ quantization noise in time domain, thus alleviating TDC dynamic range requirements. The proposed digital architecture adopts a narrow range low-power time-amplifier based TDC (TA-TDC) to achieve sub 1 ps resolution. By using TA-TDC in place of a BBPD, the limit cycle behavior that plagues BB-PLLs is greatly suppressed by the TA-TDC, thus permitting wide PLL bandwidth. The proposed architecture is also less susceptible to DTC nonlinearity and has faster settling and tracking behavior compared to a BB-PLL. Fabricated in 65 nm CMOS process, the prototype PLL achieves better than ${-}$ 106 dBc/Hz in-band noise and 3 MHz PLL bandwidth at 4.5 GHz output frequency using 50 MHz reference. The PLL consumes 3.7 mW and achieves better than 490 fs $ _{{\rm rms}}$ integrated jitter. This translates to a FoM $ _{{\rm J}}$ of ${-}$ 240.5 dB, which is the best among the reported fractional-N PLLs.

Ultralow-Noise SiN Trampoline Resonators for Sensing and Optomechanics

Abstract: In force sensing, optomechanics, and quantum motion experiments, it is typically advantageous to create lightweight, compliant mechanical elements with the lowest possible force noise. Here we report wafer-scale batch fabrication and characterization of high-aspect-ratio, nanogram-scale Si$_3$N$_4$ "trampolines" having quality factors above $4 \times 10^7$ and ringdown times exceeding five minutes (1 mHz linewidth). We measure a thermally limited force noise sensitivity of 16.2$\pm$0.8 aN/Hz$^{1/2}$ at room temperature, with a spring constant ($\sim$1 N/m) 2-5 orders of magnitude larger than those of competing technologies. We also characterize the suitability of these devices for high-finesse cavity readout and optomechanics applications, finding no evidence of surface or bulk optical losses from the processed nitride in a cavity achieving finesse 40,000. These parameters provide access to a single-photon cooperativity $C_0 \sim 8$ in the resolved-sideband limit, wherein a variety of outstanding optomechanics goals become feasible.

True Random Number Generation by Variability of Resistive Switching in Oxide-Based Devices

Abstract: Scalable, low-power random number generator (RNG) blocks are essential for encryption in today's communication systems. To allow for true RNG, a system must display an inherently-random physical phenomenon, such as the timing of individual fluctuations in random telegraph noise or the random trapping/detrapping phenomena in dielectrics. In this work, a true RNG based on set variability in a resistive switching memory (RRAM) is demonstrated. The RNG relies on a single RRAM device, which is repeatedly programmed at a constant voltage close to the nominal set voltage. Due to the statistical variability of the set voltage, set transition takes place only in 50% of the applied pulses, thus resulting in a bimodal distribution of resistance. The bimodal distribution of analog resistance is finally converted into a 0/1 distribution of output voltage values through digital regeneration with a CMOS inverter.

Maximizing Iodine Contrast-to-Noise Ratios in Abdominal CT Imaging through Use of Energy Domain Noise Reduction and Virtual Monoenergetic Dual-Energy CT

Abstract: The optimal iodine contrast-to-noise ratio (CNR) of virtual monoenergetic images with energy domain noise reduction was similar to or better than the CNR of single-energy CT images obtained with optimal tube potential.

Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics

Abstract: We provide a complete and rigorous description of phase transitions for kinetic models of self-propelled particles interacting through alignment. These models exhibit a competition between alignment and noise. Both the alignment frequency and noise intensity depend on a measure of the local alignment. We show that, in the spatially homogeneous case, the phase transition features (number and nature of equilibria, stability, convergence rate, phase diagram, hysteresis) are totally encoded in how the ratio between the alignment and noise intensities depend on the local alignment. In the spatially inhomogeneous case, we derive the macroscopic models associated to the stable equilibria and classify their hyperbolicity according to the same function.

Full counting statistics of vibrationally assisted electronic conduction: Transport and fluctuations of thermoelectric efficiency

Abstract: We study the statistical properties of charge and energy transport in electron conducting junctions with electron-phonon interactions, specifically, the thermoelectric efficiency and its fluctuations. The system comprises donor and acceptor electronic states, representing a two-site molecule or a double-quantum-dot system. Electron transfer between metals through the two molecular sites is coupled to a particular vibrational mode which is taken to be either harmonic or anharmonic, a truncated (two-state) spectrum. Considering these models we derive the cumulant generating function in steady state for charge and energy transfer, correct to second order in the electron-phonon interaction, but exact to all orders in the metal-molecule coupling strength. This is achieved by using the nonequilibrium Green's function approach (harmonic mode) and a kinetic quantum master-equation method (anharmonic mode). From the cumulant generating function we calculate the charge current and its noise and the large-deviation function for the thermoelectric efficiency. We demonstrate that at large bias the charge current, differential conductance, and the current noise can identify energetic and structural properties of the junction. We further examine the operation of the junction as a thermoelectric engine and show that while the macroscopic thermoelectric efficiency is indifferent to the nature of the mode (harmonic or anharmonic), efficiency fluctuations do reflect this property.

Ultrastable low-noise current amplifier: A novel device for measuring small electric currents with high accuracy

Abstract: An ultrastable low-noise current amplifier (ULCA) is presented. The ULCA is a non-cryogenic instrument based on specially designed operational amplifiers and resistor networks. It involves two stages, the first providing a 1000-fold current gain and the second performing a current-to-voltage conversion via an internal 1 MΩ reference resistor or, optionally, an external standard resistor. The ULCA’s transfer coefficient is highly stable versus time, temperature, and current amplitude within the full dynamic range of ±5 nA. The low noise level of 2.4 fA/√Hz helps to keep averaging times short at small input currents. A cryogenic current comparator is used to calibrate both input current gain and output transresistance, providing traceability to the quantum Hall effect. Within one week after calibration, the uncertainty contribution from short-term fluctuations and drift of the transresistance is about 0.1 parts per million (ppm). The long-term drift is typically 5 ppm/yr. A high-accuracy variant is available that shows improved stability of the input gain at the expense of a higher noise level of 7.5 fA/√Hz. The ULCA also allows the traceable generation of small electric currents or the calibration of high-ohmic resistors.

Suppression of 1/f noise in near-ballistic h-BN-graphene-h-BN heterostructure field-effect transistors

Abstract: We have investigated low-frequency 1/f noise in the boron nitride–graphene–boron nitride heterostructure field-effect transistors on Si/SiO2 substrates (f is a frequency). The device channel was implemented with a single layer graphene encased between two layers of hexagonal boron nitride. The transistors had the charge carrier mobility in the range from ∼30 000 to ∼36 000 cm2/Vs at room temperature. It was established that the noise spectral density normalized to the channel area in such devices can be suppressed to ∼5 × 10−9 μm2 Hz−1, which is a factor of ×5 – ×10 lower than that in non-encapsulated graphene devices on Si/SiO2. The physical mechanism of noise suppression was attributed to screening of the charge carriers in the channel from traps in SiO2 gate dielectric and surface defects. The obtained results are important for the electronic and optoelectronic applications of graphene.

Cavity-Enhanced Raman Spectroscopy of Natural Gas with Optical Feedback cw-Diode Lasers

Abstract: We report on improvements made on our previously introduced technique of cavity-enhanced Raman spectroscopy (CERS) with optical feedback cw-diode lasers in the gas phase, including a new mode-matching procedure which keeps the laser in resonance with the optical cavity without inducing long-term frequency shifts of the laser, and using a new CCD camera with improved noise performance. With 10 mW of 636.2 nm diode laser excitation and 30 s integration time, cavity enhancement achieves noise-equivalent detection limits below 1 mbar at 1 bar total pressure, depending on Raman cross sections. Detection limits can be easily improved using higher power diodes. We further demonstrate a relevant analytical application of CERS, the multicomponent analysis of natural gas samples. Several spectroscopic features have been identified and characterized. CERS with low power diode lasers is suitable for online monitoring of natural gas mixtures with sensitivity and spectroscopic selectivity, including monitoring H2, H2S, N2, CO2, and alkanes.

Eddy-covariance data with low signal-to-noise ratio: time-lag determination, uncertainties and limit of detection

Abstract: . All eddy-covariance flux measurements are associated with random uncertainties which are a combination of sampling error due to natural variability in turbulence and sensor noise. The former is the principal error for systems where the signal-to-noise ratio of the analyser is high, as is usually the case when measuring fluxes of heat, CO2 or H2O. Where signal is limited, which is often the case for measurements of other trace gases and aerosols, instrument uncertainties dominate. Here, we are applying a consistent approach based on auto- and cross-covariance functions to quantify the total random flux error and the random error due to instrument noise separately. As with previous approaches, the random error quantification assumes that the time lag between wind and concentration measurement is known. However, if combined with commonly used automated methods that identify the individual time lag by looking for the maximum in the cross-covariance function of the two entities, analyser noise additionally leads to a systematic bias in the fluxes. Combining data sets from several analysers and using simulations, we show that the method of time-lag determination becomes increasingly important as the magnitude of the instrument error approaches that of the sampling error. The flux bias can be particularly significant for disjunct data, whereas using a prescribed time lag eliminates these effects (provided the time lag does not fluctuate unduly over time). We also demonstrate that when sampling at higher elevations, where low frequency turbulence dominates and covariance peaks are broader, both the probability and magnitude of bias are magnified. We show that the statistical significance of noisy flux data can be increased (limit of detection can be decreased) by appropriate averaging of individual fluxes, but only if systematic biases are avoided by using a prescribed time lag. Finally, we make recommendations for the analysis and reporting of data with low signal-to-noise and their associated errors.

Optimal State Estimation for Cavity Optomechanical Systems

Abstract: We demonstrate optimal state estimation for a cavity optomechanical system through Kalman filtering. By taking into account nontrivial experimental noise sources, such as colored laser noise and spurious mechanical modes, we implement a realistic state-space model. This allows us to obtain the conditional system state, i.e., conditioned on previous measurements, with a minimal least-squares estimation error. We apply this method to estimate the mechanical state, as well as optomechanical correlations both in the weak and strong coupling regime. The application of the Kalman filter is an important next step for achieving real-time optimal (classical and quantum) control of cavity optomechanical systems.

A force sensor based on three weakly coupled resonators with ultrahigh sensitivity

Abstract: A proof-of-concept force sensor based on three degree-of-freedom (DoF) weakly coupled resonators was fabricated using a silicon-on-insulator (SOI) process and electrically tested in 20 μTorr vacuum. Compared to the conventional single resonator force sensor with frequency shift as output, by measuring the amplitude ratio of two of the three resonators, the measured force sensitivity of the 3DoF sensor was 4.9 × 106/N, which was improved by two orders magnitude. A bias stiffness perturbation was applied to avoid mode aliasing effect and improve the linearity of the sensor. The noise floor of the amplitude ratio output of the sensor was theoretically analyzed for the first time, using the transfer function model of the 3DoF weakly coupled resonator system. It was shown based on measurement results that the output noise was mainly due to the thermal–electrical noise of the interface electronics. The output noise spectral density was measured, and agreed well with theoretical estimations. The noise floor of the force sensor output was estimated to be approximately 1.39nN for an assumed 10 Hz bandwidth of the output signal, resulting in a dynamic range of 74.8 dB.