Fundamental Noise Processes Research Articles

The Allan variance in the presence of a compound Poisson process modelling clock frequency jumps

Atomic clocks can be affected by frequency jumps occurring at random times and with a random amplitude. The frequency jumps degrade the clock stability and this is captured by the Allan variance. In this work we assume that the random jumps can be modelled by a compound Poisson process, independent of the other stochastic and deterministic processes affecting the clock stability. Then, we derive the analytical expression of the Allan variance of a jumping clock. We find that the analytical Allan variance does not depend on the actual shape of the jumps amplitude distribution, but only on its first and second moments, and its final form is the same as for a clock with a random walk of frequency and a frequency drift. We conclude that the Allan variance cannot distinguish between a compound Poisson process and a Wiener process, hence it may not be sufficient to correctly identify the fundamental noise processes affecting a clock. The result is general and applicable to any oscillator, whose frequency is affected by a jump process with the described statistics.

Overwhelming Thermomechanical Motion with Microwave Radiation Pressure Shot Noise.

We measure the fundamental noise processes associated with a continuous linear position measurement of a micromechanical membrane incorporated in a microwave cavity optomechanical circuit. We observe the trade-off between the two fundamental sources of noise that enforce the standard quantum limit: the measurement imprecision and radiation pressure backaction from photon shot noise. We demonstrate that the quantum backaction of the measurement can overwhelm the intrinsic thermal motion by 24dB, entering a new regime for cavity optomechanical systems.

Phase errors in diffraction-limited imaging: contrast limits for sparse aperture masking

Bispectrum phase, closure phase and their generalisation to kernel-phase are all independent of pupil-plane phase errors to first-order. This property, when used with Sparse Aperture Masking (SAM) behind adaptive optics, has been used recently in high-contrast observations at or inside the formal diffraction limit of large telescopes. Finding the limitations to these techniques requires an understanding of spatial and temporal third-order phase effects, as well as effects such as time-variable dispersion when coupled with the non-zero bandwidths in real observations. In this paper, formulae describing many of these errors are developed, so that a comparison can be made to fundamental noise processes of photon- and background-noise. I show that the current generation of aperture-masking observations of young solar-type stars, taken carefully in excellent observing conditions, are consistent with being limited by temporal phase noise and photon noise. This has relevance for plans to combine pupil-remapping with spatial filtering. Finally, I describe calibration strategies for kernel-phase, including the optimised calibrator weighting as used for LkCa 15, and the restricted kernel-phase POISE technique that avoids explicit dependence on calibrators.

Nanomechanical Torsional Resonators for Frequency-Shift Infrared Thermal Sensing

We investigate use of nanomechanical torsional resonators for frequency-shift-based infrared (IR) thermal sensing. Nanoscale torsion rods, ~1 μm long and 50-100 nm in diameter, provide both extraordinary thermal isolation and excellent angular displacement and torque sensitivities, of order ~10(-7) rad·Hz(-1/2) and ~10(-22) (N·m) Hz(-1/2), respectively. Furthermore, these nanorods act as linear torsional springs, yielding a maximum angular displacement of 3.6° and a dynamic range of over 100 dB; this exceeds the performance of flexural modes by as much as 5 orders of magnitude. These attributes lead to superior noise performance for torsional-mode sensing. We demonstrate the operational principles of torsional-mode IR detection, attaining an uncooled noise equivalent temperature difference (NETD) of 390 mK. By modeling the fundamental noise processes, we project that further reduction of device size can significantly improve thermal responsivity; a room-temperature NETD below 10 mK appears feasible.

Fundamental Noise Processes in TES Devices

Microcalorimeters and bolometers are noise-limited devices, therefore, a proper understanding of all noise sources is essential to predict and interpret their performance. In this paper, I review the fundamental noise processes contributing to Transition Edge Sensor (TES) microcalorimeters and bolometers and their effect on device performance. In particular, I will start with a simple, monolithic device model, moving to a more complex one involving discrete components, to finally move to today's more realistic, comprehensive model. In addition to the basic noise contribution (equilibrium Johnson noise and phonon noise), TES are significantly affected by extra noise, which is commonly referred to as “excess noise”. Different fundamental processes have been proposed and investigated to explain the origin of this excess noise, in particular near equilibrium non-linear Johnson noise, flux-flow noise, and internal thermal fluctuation noise. Experimental evidence shows that all three processes are real and contribute, at different levels, to the TES noise, although different processes become important at different regimes. It is therefore time to discard the term “excess noise” and consider these terms part of the “fundamental noise processes” instead.

Measurement uncertainty in the presence of low-frequency noise

We discuss the measurement uncertainty in the presence of different types of fundamental noise processes, especially 1/f noise. The treatment is based on the Allan variance of an n-sample average with two deadtime parameters relevant in metrology. Some results applicable to situations that are common in metrology, e.g., international comparisons, are derived. Experimentally, the output of Zener voltage standards in the frequency range from 10/sup -6/ Hz to 10/sup 3/ Hz is studied and behavior closely resembling that of 1/f noise is found at all time scales of practical interest. The noise floor of a 10 V Zener standard was found to be 60 nV and the 1/f corner frequency 3.5 Hz. Environmental variations cause the long-term (>100 s) deviations of the Zener voltage to slightly increase from the limiting 1/f noise level.

Noise in self-electrooptic effect device logic gates

We study the fundamental noise processes of SEED-based logic gates. The noise is calculated for symmetric SEEDs (S-SEEDs), asymmetric Fabry-Perot S-SEEDs (ASFP S-SEEDs), and SEEDs combined with transistor driving circuits (FET-SEEDs). The source of noise which determines the minimum power required to switch the SEEDs in a given time increment is quantum noise associated with photon absorption and subsequent carrier or exciton recombination. The results show that FET-SEED logic gates have the lowest noise power as compared with S-SEEDs and ASFP S-SEEDs. >

Low heat capacity He 3-cooled bolometers of differentiated structure

The performance of far-infrared bolometers is analyzed in terms of two fundamental noise processes: radiation noise from thermal emission of the background, and detector noise from Johnson and temperature fluctuation thermodynamic contributions. In terms of the former process, generally imposed by the conditions of the experiment itself, an optimization scheme assuring quasi-BLIP performance is suggested. The importance of operation at low temperatures and low heat capacity is discussed and a summary of the heat capacities per unit volume of materials entering into the construction of bolometers is given. Techniques for the construction of an ultra-low heat capacity bolometer for operation at He 3 temperatures are discussed.