Thermal Noise Limit Research Articles

1∕fαnoise in reaction times: A proposed model based on Piéron’s law and information processing

Piéron's law relates human reaction times to the intensity of a sensory stimulus by a power function. The neural processes responsible for this nonlinear behavior are not understood. A simple neural model based on the Brownian motion of spikes and information theory is presented. The model shows that Piéron's law is a transformation function in time. The shape of Piéron's law is invariant and scales into the intensity-response function of single neurons in a fractal-like process. The model also shows that Piéron's law gives rise to 1/falpha noise together with a high-frequency thermal noise limit. It is proposed that the biophysical origin of reaction time variability is related to a form of noise-induced synchronization in weakly coupled neurons. The implications in visual-motor transduction are discussed.

Potential of interferometric cantilever detection and its application for SFM/AFM inliquids

We have developed an optical cantilever deflection detector with a spot size<3 µm andfm Hz−1/2 sensitivityover a>10 MHz bandwidth. In this work, we demonstrate its potential for detecting small-amplitudeoscillations of various flexural and torsional oscillation modes of cantilevers. The highdeflection sensitivity of the interferometer is particularly useful for detecting cantileveroscillations in aqueous solutions, enabling us to reach the thermal noise limit in scanning oratomic force microscopy experiments with stiff cantilevers. This has resulted inatomic-resolution images of solid–liquid interfaces and submolecular-resolution images ofnative membranes.

Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities

We achieved a 0.5 Hz optical beat note linewidth with $\ensuremath{\sim}0.1\text{ }\text{Hz}/\text{s}$ frequency drift at 972 nm between two external cavity diode lasers independently stabilized to two vertically mounted Fabry-P\'erot (FP) reference cavities with a finesse of 400 000. Vertical FP reference cavities are suspended in midplane such that the influence of vertical vibrations to the mirror separation is significantly suppressed. This makes the setup virtually immune for vertical vibrations that are more difficult to isolate than horizontal vibrations. To compensate for thermal drifts the FP spacers are made from ultralow-expansion (ULE) glass which possesses a zero linear expansion coefficient. A design using Peltier elements in vacuum allows operation at an optimal temperature where the quadratic temperature expansion of ULE could be eliminated as well. The measured linear drift of such ULE FP cavity of 63 mHz/s was due to material aging and the residual frequency fluctuations were less than $\ifmmode\pm\else\textpm\fi{}20\text{ }\text{Hz}$ during 16 h of measurement. Some part of the temperature-caused drift is attributed to the thermal expansion of the mirror coatings. Thermally induced fluctuations that cause vibrations of the mirror surfaces limit the stability of our cavity. By comparing two similar laser systems we obtain an Allan instability of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ between 0.1 and 10 s averaging time, which is close to the theoretical thermal noise limit.

Statistical analysis of neuronal growth: edge dynamics and the effect of a focused laser on growth cone motility

The neuronal growth cone is a small dynamic structure at the tip of neuronal extensions that guides each neurite extension to its correct partner cell. To reach the designated target, the growth cone integrates chemical signals with high accuracy and reliability. This signal detection operates close to the thermal noise limit and is, therefore of high interest not only to understand neuronal growth, but also to investigate the biological mechanisms of signalling and information processing under the influence of noise. To further investigate neuronal growth, a focused laser positioned at the leading edge of the growth cone is used to bias growth direction, however, the mechanisms of this influence are still unclear. We present a detailed measurement and analysis of the leading edge dynamics of laser treated and control growth cones. Based on the edge motility measurements, we can consistently describe neuronal growth with a stochastic model that allows a bistable potential and the noise intensity of the stochastic process to be extracted. The investigation of control growth cones that were not influenced by the laser reveals a nonlinear dependence of the noise on the overall activity of the growth cones. The presented analysis further quantifies the edge dynamics in growth cones that are manipulated by a laser. Growth cones that actively follow the laser show a tilt of the bistable potential in the direction of the laser to favour protrusions, but no significant changes in the leading edge growth velocity. This is in contrast to the potential changes observed in stationary growth cones that were influenced by the laser. Here, the laser does not tilt the potential shape, but increases the edge velocities, probably by an increase in actin polymerization velocity. These measurements provide new quantitative insight into the dynamics underlying growth cone protrusion and movement.

Magnetic resonance force microscopy in fast-relaxing spins using a frequency-modulationmode detection method

We describe a magnetic resonance force microscopy experiment carried out using both afast-relaxing spin system and a frequency-modulation mode detection method, presenting avalidation of the measured signal and sensitivity. The detection method applied along witha self-excited cantilever oscillation worked stably without any serious interference due tospurious cantilever excitation despite application of first-harmonic microwave modulation,and thereby successfully created almost the maximum available signal. The signal couldbe measured without distortion while the magnetic field was swept at a rate of1.9 G s−1. The measured sensitivity approached the thermal noise limit of the cantilever with a highquality factor. The experimental results for both signal and noise were in good agreementwith theoretical predictions.

Coated fused silica fibers for enhanced sensitivity torsion pendulum for LISA

In order to investigate the fundamental thermal noise limit of a torsion pendulum using a fused silica fiber, we systematically measured and modeled the mechanical losses of thin fused silica fibers coated by electrically conductive thin metal films. Our results indicate that it is possible to achieve a thermal noise limit for coated silica a factor of 9 lower than obtained with the tungsten fiber used in the recent LISA torsion pendulum study [L. Carbone, et al., Phys. Rev. Lett. 91 (2003) 151101]. This will allow a corresponding increase in sensitivity of torsion pendula used for small force measurements.

The Effect of Protein Complexation on the Mechanical Stability of Im9

Force mode microscopy can be used to examine the effect of mechanical manipulation on the noncovalent interactions that stabilize proteins and their complexes. Here we describe the effect of complexation by the high affinity protein ligand E9 on the mechanical resistance of the simple four-helical protein, Im9. When concatenated into a construct of alternating I27 domains, Im9 unfolded below the thermal noise limit of the instrument (∼20 pN). Complexation of E9 had little effect on the mechanical resistance of Im9 (unfolding force ∼30 pN) despite the high avidity of this complex ( K d ∼10 fM).

Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1×10^−15

We demonstrate phase and frequency stabilization of a diode laser at the thermal noise limit of a passive optical cavity. The system is compact and exploits a cavity design that reduces vibration sensitivity. The sub-Hz laser is characterized by comparison to a second independent system with similar fractional frequency stability (1 x 10-15 at 1 s). The laser is further characterized by resolving a 2 Hz wide, ultranarrow optical clock transition in ultracold strontium.

Highly sensitive silicon crystal torque sensor operating at the thermal noise limit

We describe a sensitive torque detector, based on a silicon single-crystal double-paddle oscillator (DPO). The high Q-factor (approximately 10(5) at room temperature and in vacuum) makes DPOs well suited for the detection of weak forces. The limiting sensitivity of a sensor is given by Brownian (thermal) noise if all external disturbances are eliminated. In this case, the minimum detectable force can be decreased by measuring over a time significantly longer than the oscillator's relaxation time. We demonstrate operation in this regime, with integration times of up to 14 h. A resulting torque sensitivity of 2 x 10(-18) N m is reached. Tests are performed to show that the sensor is only affected by thermal noise. The present sensor is well suited for measurements of extremely weak forces, e.g., of gravitational attraction between laboratory masses.

Thermal noise and bit error rate limits in nanoscale memories

Analysis of the effects of thermal noise in nanoscale memories is presented. A theoretical analysis of thermal noise is used to predict the number of bit errors per year caused by thermal noise.

VLBI observations of weak sources using fast frequency switching

We have developed a new phase referencing technique for high frequency VLBI observations. In conventional phase referencing, one interleaves short scans on a nearby phase calibrator between the target source observations. In fast frequency switching described here, one observes the target source continuously while switching rapidly between the target frequency and a lower reference frequency. We demonstrate that the technique allows phase calibration almost reaching the thermal noise limit and present the first detection of the AGN in the FR I radio galaxy NGC 4261 at 86 GHz. Although point-like, this is the weakest source ever detected with VLBI at this frequency.

Thermal noise limitations to force measurements with torsion pendulums: Applications to the measurement of the Casimir force and its thermal correction

A general analysis of thermal noise in torsion pendulums is presented. The specific case where the torsion angle is kept fixed by electronic feedback is analyzed. This analysis is applied to a recent experiment that employed a torsion pendulum to measure the Casimir force. The ultimate limit to the distance at which the Casimir force can be measured to high accuracy is discussed, and in particular we elaborate on the prospects for measuring the thermal correction.

Shot noise of large charge quanta in superconductor/semiconductor/superconductor junctions

We have found experimentally that the noise of ballistic electron transport in a superconductor/semiconductor/superconductor junction is enhanced relative to the value given by the general relation, S_V=2eIR^2coth(eV/2kT), for two voltage regions in which this expression reduces to its thermal and shot noise limits. The noise enhancement is explained by the presence of large charge quanta, with effective charge q*=(1+2Delta/eV)e, that generate a noise spectrum S_V=2q*IR^2, as predicted in Phys. Rev. Lett. 76, 3814 (1996). These charge quanta result from multiple Andreev reflections at each junction interface, which are also responsible for the subharmonic gap structure observed in the voltage dependence of the junction's conductance.

Thermal-Noise Limit in the Frequency Stabilization of Lasers with Rigid Cavities

We evaluate thermal noise (Brownian motion) in a rigid reference cavity used for frequency stabilization of lasers, based on the mechanical loss of cavity materials and the numerical analysis of the mirror-spacer mechanics with the direct application of the fluctuation dissipation theorem. This noise sets a fundamental limit for the frequency stability achieved with a rigid frequency-reference cavity of order 1 Hz/ square root Hz (0.01 Hz/ square root Hz) at 10 mHz (100 Hz) at room temperature. This level coincides with the world-highest level stabilization results.

On the thermal noise limit of cellular membranes

Comparison of thermal noise limits and the effects of low frequency electromagnetic fields (LFEMF) on the cellular membrane have important implications for the study of bioelectro-magnetism in this regime. Over a decade ago, Weaver and Astumian developed a model to show that thermal noise can limit the efficacy of LFEMF. A recent report by Kaune [Kaune (2002) Bioelectromagnetics 23:622-628], however, contradicted their findings. Kaune assumes that the conductance noise current of cell membrane can be decomposed into two components, where one of them is identical regarding all segments (coherent), while the other is different (incoherent). Besides, this decomposition is not unequivocal and contradicts to the statistical independence of the segment noise currents, and therefore to the second law of thermodynamics as well. We suggest the procedure based on the method of symmetrical components, by the means of which we can re-interpret the result of Kaune in a correct way.

Improving the sensitivity of frequency modulation spectroscopy using nanomechanical cantilevers

It is suggested that nanomechanical cantilevers can be employed as high-Q filters to circumvent laser noise limitations on the sensitivity of frequency modulation spectroscopy. In this approach, a cantilever is actuated by the radiation pressure of the amplitude modulated light that emerges from an absorber. Numerical estimates indicate that laser intensity noise will not prevent a cantilever from operating in the thermal noise limit, where the high Q’s of cantilevers are most advantageous.

Excitation Frequency Effect of Differential CapacitanceTransducer for Equivalence Principle Test

We discuss effects of the excitation frequency in an ac bridgedifferential capacitance transducer for the equivalence-principle teston the frequency-dependent characteristics of a practical operationalamplifier, the thermal noise limitation, and stray-immune. Basicrequirements of choosing the excitation frequency of the ac bridgecapacitance transducer are given based on the three effects, which aresignificant for designing a capacitance transducer and choosing properelectric elements.

Reply to Dr. Adair's comment on “Thermal noise limit on the sensitivity of cellular membranes to power frequency electric and magnetic fields”

BioelectromagneticsVolume 24, Issue 6 p. 446-447 Reply Reply to Dr. Adair's comment on “Thermal noise limit on the sensitivity of cellular membranes to power frequency electric and magnetic fields” W.T. Kaune, Corresponding Author W.T. Kaune wtkaune@ieee.org Richland, Washington111 Piper Ct, Richland, WA 99352.Search for more papers by this author W.T. Kaune, Corresponding Author W.T. Kaune wtkaune@ieee.org Richland, Washington111 Piper Ct, Richland, WA 99352.Search for more papers by this author First published: 13 August 2003 https://doi.org/10.1002/bem.10159AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume24, Issue6September 2003Pages 446-447 RelatedInformation

"Real time" noise measurements with sensitivity exceeding the standard thermal noise limit

A possibility of "real-time" noise measurements with spectral resolution better than a standard thermal noise limit has been experimentally demonstrated at microwave frequencies. The enhancement in the sensitivity of spectral measurements was achieved due to more efficient use of the signal power via the power recycling technique. By utilizing such a technique, the noise floor of a 9 GHz "real time" measurement system was reduced by 3 dB below the standard thermal noise limit. This makes possible the characterization of intrinsic fluctuations in individual low-noise microwave components, such as ferrite circulators, without the need for cascading them or using the cross-correlation signal processing.

A Broadband Ocean-Bottom Seismometer System Based on a 1-Hz Natural Period Geophone

Recent work with broadband sensors has demonstrated that useful data can be obtained from seismic sensors deployed on the deep seafloor for periods as long as 300 sec, but ocean-bottom seismometer (OBS) systems using conventional broadband sensors have proven fragile and expensive to build and operate. The intrinsic thermal (Brownian motion) noise limit for large 1-Hz geophone sensors such as the Mark Products L-4 is far below typical noise levels at seafloor sites. In response to the need for large numbers of OBS systems for experiments studying the oceanic upper mantle and crust, we have developed a very low-noise amplifier that can be used with short-period sensors. The new amplifiers push noise levels at the 100 sec period some 40 dB below standard short-period OBS noise levels. Useful data can then be obtained from these short-period sensors in the broad-frequency range from 0.005 to 50 Hz. Noise levels rise from 5 × 10 –16 ( m /sec 2 ) 2 /Hz at a 20-sec period to 5 × 10 –14 ( m /sec 2 ) 2 /Hz at a 200-sec period. Power requirements are less than 35 mW for three channels. These amplifiers have been installed in the first 24 instruments of the new NSF-sponsored LDEO OBS Instrument Center. We believe this system is an excellent compromise between cost, reliability, and noise level. The new amplifiers may also prove useful for work on land, extending the useful range of short-period sensors to a much longer period.