Noise Thermometer Research Articles

Precise Calorimetry of Small Metal Samples Using Noise Thermometry

We describe a compact calorimeter that opens ultra-low-temperature heat capacity studies of small metal crystals in moderate magnetic fields. The performance is demonstrated on the canonical heavy fermion metal YbRh2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{2}$$\\end{document}Si2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{2}$$\\end{document}. Thermometry is provided by a fast current sensing noise thermometer. This single thermometer enables us to cover a wide temperature range of interest from 175 µK to 90 mK with temperature-independent relative precision. Temperatures are tied to the international temperature scale with a single-point calibration. A superconducting solenoid surrounding the cell provides the sample field for tuning its properties and operates a superconducting heat switch. Both adiabatic and relaxation calorimetry techniques, as well as magnetic field sweeps, are employed. The design of the calorimeter results in an addendum heat capacity which is negligible for the study reported. The keys to sample and thermometer thermalisation are the lack of dissipation in the temperature measurement and the steps taken to reduce the parasitic heat leak into the cell to the tens of fW level.

SQUID noise thermometers with lithographically defined metal sensing elements

We present SQUID noise thermometers for sub-kelvin thermometry that employ lithographically defined metal thin-film resistors as the temperature sensors. The resistors with values of about 1 milliohm are lithographically fabricated using Au, PdAu and superconducting Nb wiring. In order to ensure constant resistance values in the whole temperature range of operation, the resistive structures are designed to avoid superconducting proximity effects. The thin-film resistor circuits can be easily combined with different types of multi-purpose dc SQUID current sensors to adapt noise temperatures, uncertainties and measurement speeds as well as robustness against magnetic fields in different measurement setups.

Sound-card-based Johnson noise thermometer

This article presents a Johnson noise thermometer with a signal acquisition system based on a sound card. The thermometer uses a simple analogue circuit to measure the Johnson noise on a resistor. No external hardware or power supply is necessary, except for a reference multimeter. Data processing is performed in real time on a personal computer using LabView software. The results show that the developed thermometer has an expanded uncertainty (k = 2) of 0.8 ℃ over a temperature range from − 196 ℃ to 300 ℃, with a measurement time of 5 min.

Progress towards in-situ traceability and digitalization of temperature measurements

Autonomous control systems rely on input from sensors, so it is crucial that the sensor input is validated to ensure that it is ‘right’ and that the measurements are traceable to the International System of Units. The measurement and control of temperature is widespread, and its reliable measurement is key to maximising product quality, optimising efficiency, reducing waste and minimizing emissions such as CO2 and other harmful pollutants. Degradation of temperature sensors in harsh environments such as high temperature, contamination, vibration and ionising radiation causes a progressive loss of accuracy that is not apparent. Here we describe some new developments to overcome the problem of ‘calibration drift’, including self-validating thermocouples and embedded phase-change cells which self-calibrate in situ by means of a built-in temperature reference and practical primary thermometers such as the Johnson noise thermometer which measure temperature directly and do not suffer from calibration drift. All these developments will provide measurement assurance which is an essential part of digitalisation to ensure that sensor output is always ‘right’, as well as providing essential ‘points of truth’ in a sensor network. Some progress in digitalisation of calibrations to make them available to end-users via a website and/or an Application Programming Interface is also described.

Magnetic Cooling and Vibration Isolation of a Sub-kHz Mechanical Resonator

We report recent progress toward the realization of a sub-mK, low-vibration environment at the bottom stage of a dry dilution refrigerator for use in mechanical tests of quantum mechanics. Using adiabatic nuclear demagnetization, we have cooled a silicon cantilever force sensor to Tapprox 1 mK. The temperature of the tip holder of the cantilever chip was determined via a primary magnetic flux noise thermometer. The quality factor of the cantilever continues to increase with decreasing temperature, reaching Qapprox 4cdot 10^4 at 2 mK. To demonstrate that the vibration isolation is not compromised, we report the detection of the thermal motion of the cantilever down to T approx 20 mK, only limited by the coupling to the SQUID readout circuit. We discuss feasible improvements that will allow us to probe unexplored regions of the parameter space of continuous spontaneous localization models.

Set-up for observation thermal voltage noise and determination of absolute temperature and Boltzmann constant

We describe a set-up for measurement of the absolute zero by Johnson–Nyquist thermal noise which can be performed within a week in every high-school or university. Necessary electronic components and technical guidelines for the construction of this noise thermometer are given. The operating temperature used is in the tea cup range from ice to boiling water and in this sense the set-up can be given in the hands of every high school and university physics student. The measurement requires a standard multi-meter with thermocouple and voltage probe and gives excellent for education purposes percent accuracy. The explanation is oriented to university level but due to the simplicity of the explanation motivated high-school students can follow the explanation derivation of the used formulas for determination of the absolute zero and the Boltzmann constant. As a by-product our set-up gives a new method for the determination of the spectral density of the voltage e N and current noise i N of operational amplifiers.

Electronic thermal transport measurement in low-dimensional materials with graphene non-local noise thermometry.

In low-dimensional systems, the combination of reduced dimensionality, strong interactions and topology has led to a growing number of many-body quantum phenomena. Thermal transport, which is sensitive to all energy-carrying degrees of freedom, provides a discriminating probe of emergent excitations in quantum materials and devices. However, thermal transport measurements in low dimensions are dominated by the phonon contribution of the lattice, requiring an experimental approach to isolate the electronic thermal conductance. Here we measured non-local voltage fluctuations in a multi-terminal device to reveal the electronic heat transported across a mesoscopic bridge made of low-dimensional materials. Using two-dimensional graphene as a noise thermometer, we measured the quantitative electronic thermal conductance of graphene and carbon nanotubes up to 70 K, achieving a precision of ~1% of the thermal conductance quantum at 5 K. Employing linear and nonlinear thermal transport, we observed signatures of energy transport mediated by long-range interactions in one-dimensional electron systems, in agreement with a theoretical model.

Ultrasensitive Calorimetric Measurements of the Electronic Heat Capacity of Graphene.

Heat capacity is an invaluable quantity in condensed matter physics and yet has been completely inaccessible in two-dimensional (2D) van der Waals (vdW) materials, owing to their ultrafast thermal relaxation times and the lack of suitable nanoscale thermometers. Here, we demonstrate a novel thermal relaxation calorimetry scheme that allows the first measurements of the electronic heat capacity of graphene. It is enabled by combining a radio frequency Johnson noise thermometer, which can measure the electronic temperature with a sensitivity of ∼20 mK/Hz1/2, and a photomixed optical heater that modulates Te with a frequency of up to Ω = 0.2 THz. This allows record sensitive measurements of the electronic heat capacity Ce < 10 -19 J/K and the fastest measurement of electronic thermal relaxation time τe < 10 -12 s yet achieved by a calorimeter. These features advance heat capacity metrology into the realm of nanoscale and low-dimensional systems and provide an avenue for the investigation of their thermodynamic quantities.

Linearity measurements of critical Johnson noise thermometer components with low-distortion multitones from a Josephson arbitrary waveform synthesizer

Quantum-based and low-distortion multitone signals from a Josephson arbitrary waveform synthesizer are used to calibrate critical noise thermometer components between 8 and 240 kHz at increased input noise levels. The example signal path includes a 24-bit ΣΔ analog-to-digital converter (ADC) and a prototype amplifier for Physikalisch-Technische Bundesanstalt’s new noise thermometer. The signals consist of odd harmonics of the pattern repetition frequency with growing tone spacing, minimizing the influence of intermodulation distortion during calibration. After a detailed description of the calibration procedure, we compare the multitone spectra with growing tone spacing to ones with equally spaced tones. For the example signal path, gain nonlinearities better than ±2 µV V−1 at input rms noise levels between 9.7 and 465 µV are experimentally demonstrated. Furthermore, we investigate the effect of dither and applied offset voltage on the non-linearity of the ADC.

Fabrication and Characterization of a Quantum Voltage Noise Source Chip for a Johnson Noise Thermometer

A Johnson noise thermometer (JNT) determines the thermodynamic temperature through cross-correlation measurement of the Johnson noise in a sense resistor at an unknown temperature. In the quantum voltage calibrated JNT system, a superconductive quantum voltage noise source (QVNS) is required to produce artificial pseudo-random noise to calibrate the gain of the cross-correlation electronics. In this paper, we present the design, fabrication, and characterization of the QVNS chip. Compared with our previous design, a new straightforward mirror symmetric layout is implemented. For this layout, the coplanar waveguides (CPWs) have the same lengths and transmission parameters. Equal pulse magnitudes are delivered to each Josephson junction array under the same output settings of the bipolar pattern generator. The modified QVNS chip is thereby enhanced because the quantum locking range is enlarged. A copper foil shielding package is used to eliminate crosstalk in this design. The first spectral comparison of two Josephson junction (JJ) arrays of with and without shielding is presented in this paper. The comparative results demonstrate that the shielding is effective. The abovementioned improvements enable us to synthesize both single and multitone waveforms with good spectral results, such that the chip satisfies the requirement of a QVNS-based JNT system for temperature measurements.

Research on the Controllability of the Sound Wave of Automobile Whistle Combining Computer Technology and Sound Dispersion Mechanism

At present, the popularity of cars has brought great convenience to our life, but at the same time it has brought about many bad effects, such as noise pollution caused by the sound of car horns. Therefore, it is very important for us to study the controllability of car horn, and the mature development of computer technology provides us with the research conditions and convenience. In this paper, the controllability of sound wave of car horn in two-dimensional space is studied by combining computer technology with sound diffusion mechanism, and a kind of noise thermometer invented by American scientists is taken as an example.

(Invited) Electroluminescent Hyperbolic Cooling of Graphene Field Effect Transistors

Heat management is critical for the performance of most modern electronic devices. It was recently proposed that radiative heat transfer - which is usually negligible in the solid state - could be increased in hyperbolic metamaterials, i.e., materials having a hyperbolic electromagnetic dispersion relation. [1] However, artificial metamaterials can be difficult to fabricate and integrate.Fortunately, most of Van der Waals materials are natural hyperbolic metamaterials. Indeed, due to their anisotropic layered structure, the in-plane and out-of-plane optical phonon energy splitting results in a hyperbolic dispersion of light in the Resstrahlen bands. As a consequence, in these materials, the strong light-matter coupling can give rise to a 102-105 increase in the e.m. local density of states, resulting in a dramatic enhancement of the radiative heat transfer. Moreover, the radiative character of heat exchange results in a propagative heat transport via hyperbolic phonon-polariton (HPhP) modes on micrometric scales.We have studied heat transfer in graphene on hexagonal boron nitride: a natural 2D hyperbolic material. In our devices, graphene is used as a versatile heat source in the near field of a hyperbolic material, and as a sensitive noise thermometer. [2] Using mono-, bi- and trilayer graphene, we demonstrate a strong increase of the electron gas cooling resulting in a large temperature drop when the emission of HPhP sets in. This process shares many analogies with electroluminescence, except that it involves near-field modes. We experimentally evidence that the case of graphene is unique, with cooling powers reaching few milliwatts per micron square [3], i.e., nine orders of magnitude larger than previously reported in the literature. Bibliography [1] S. Biehs, et al "Hyperbolic metamaterials as an analog of a blackbody in the near field." Phys. Rev. Lett. 109, 104301 (2012)[2] W. Yang, et al "A Graphene Zener–Klein Transistor Cooled by a Hyperbolic Substrate." Nat. Nanotech. 13, 47 (2018)[3] E. Baudin, et al "Hyperbolic Phonon Polariton Electroluminescence as an Electronic Cooling Pathway", Adv. Funct. Mat.1904783 (2019) Figure 1

Developments towards an industrial Johnson noise thermometer

In this paper we present new developments in our practical, drift-free Johnson noise thermometer as it moves from a proof-of-principle prototype towards a practical implementation to become a viable primary thermometer for industrial applications. We will discuss bandwidth optimisation to obtain the lowest possible uncertainty of temperature measurements. The concept of weighting the cross-correlation frequency bins to improve the uncertainty will be introduced and it will be shown that this can decrease the measurement uncertainty in our system by 28%. Weighting fundamentally changes the optimum bandwidth calculation such that information from higher parts of the measured spectrum can always contribute to a reduction in total measurement noise. We will present the design approach used to provide extreme immunity to electromagnetic interference, a problem that has severely degraded previous efforts. We describe the results of tests by a third-party test laboratory demonstrating immunity up to field strengths of 10 Vm−1, as required in standards for equipment operating in heavy industrial environments. We have also looked at interference at frequencies that could directly interfere with our thermometer that are not covered in the standards. The latest test results will be presented showing a five-fold improvement in accuracy on an extrapolation to absolute zero compared with the original proof-of-principle prototype with similar measurement parameters. Developments in techniques for providing traceability of the thermometer’s calibration to electrical rather than temperature national standards will be presented.

Development of a driftless Johnson noise thermometer for nuclear applications

Existing temperature sensors such as thermocouples and platinum resistance thermometers suffer from calibration drift, especially in harsh environments, due to mechanical and chemical changes (and transmutation in the case of nuclear applications). A solution to the drift problem is to use temperature sensors based on fundamental thermometry (primary thermometers) where the measured property is related to absolute temperature by a fundamental physical law. A Johnson noise thermometer is such a sensor and uses the measurement of the extremely small thermal voltage noise signals generated by any resistive element to determine temperature using the Johnson-Nyquist equation. A Johnson noise thermometer never needs calibration and is insensitive to the condition of the sensor material, which makes it ideally suited to long-term temperature measurement in harsh environments. These can include reactor coolant circuits, in-pile measurements, nuclear waste management and storage, and severe accident monitoring. There have been a number of previous attempts to develop a Johnson noise thermometer for the nuclear industry, but none have achieved commercialization because of technical difficulties. We describe the results of a collaboration between the National Physical Laboratory and Metrosol Limited, which has led to a new technique for measuring Johnson noise that overcomes the previous problems that have prevented commercialization. The results from a proof-of-principle prototype that demonstrates performance commensurate with the needs of nuclear applications is presented, together with details of progress towards the commercialization of the technology. The development partners have effected a step change in the application of primary thermometry to industrial applications and seek partners for field trials and further exploitation.

Measurement of the Melting Point of Gallium Using a Johnson Noise Thermometer

We measured the thermodynamic temperature of the melting point of gallium $T_{\mathrm {Ga}}$ using a Johnson noise thermometer (JNT) with an integrated quantum voltage noise source (IQVNS) as a reference. $T_{\mathrm {Ga}}$ was calculated using the fundamental constants recommended by the Committee on Data for Science and Technology (CODATA) for the revision of the International System of Units (SI). The measured $T_{\mathrm {Ga}}$ is consistent with the value defined in the International Temperature Scale of 1990.

The Boltzmann Constant: Evaluation of Measurement Relative Uncertainty Using the Information Approach

The purpose of this work is to prove that only by applying a theoretically sound information approach to developing a model for measuring the Boltzmann constant, one can justify and calculate the value of the required relative uncertainty. A dimensionless parameter (comparative uncertainty) was proposed as a universal metric for comparing experimental measurements of Boltzmann constant and simulated data. Examples are given of applying the proposed original method for calculating the relative uncertainty in measuring the Boltzmann constant using an acoustic gas thermometer, dielectric constant gas thermometer, Johnson noise thermometer, Doppler broadening thermometer. The proposed approach is theoretically justified and devoid of the shortcomings inherent in the CODATA concept: a statistically significant trend, a cumulative value of consensus or a statistical control. We tried to show how a mathematical-expert formalism can be replaced by a simple, theoretically grounded postulate on the use of information theory in measurements.

Probing a Spin Transfer Controlled Magnetic Nanowire with a Single Nitrogen-Vacancy Spin in Bulk Diamond.

The point-like nature and exquisite magnetic field sensitivity of the nitrogen vacancy (NV) center in diamond can provide information about the inner workings of magnetic nanocircuits in complement with traditional transport techniques. Here, we use a single NV in bulk diamond to probe the stray field of a ferromagnetic nanowire controlled by spin transfer (ST) torques. We first report an unambiguous measurement of ST tuned, parametrically driven, large-amplitude magnetic oscillations. At the same time, we demonstrate that such magnetic oscillations alone can directly drive NV spin transitions, providing a potential new means of control. Finally, we use the NV as a local noise thermometer, observing strong ST damping of the stray field noise, consistent with magnetic cooling from room temperature to ∼150 K.

Cross-correlation limit of a SQUID-based noise thermometer of the pMFFT type

The primary magnetic field fluctuation thermometer (pMFFT) is a SQUID-based noise thermometer for temperatures below 1 K, which complies with metrological requirements. It combines two signal channels in order to apply the cross-correlation technique, but it requires statistically independent noise signals for proper operation. In order to check the limit of the cross-correlation readout, we have performed zero measurements in the millikelvin range in a setup that is identical to the pMFFT, except for the removed temperature sensor. We examined the influence of different parameters such as SQUID working point or flux-lock loop parameters on the minimum cross-correlation signal down to 24 mK and below 100 kHz. Depending on the configuration, typical minimum SQUID-referred cross-power spectral densities of 1.5 × 10−15 /Hz or even smaller values were observed. For the pMFFT, considering its thermal noise spectrum, these flux densities correspond to a device noise temperature of ≤2.5 µK, thereby ensuring a negligible uncertainty contribution at the lower end of the PLTS-2000 (0.9 mK).

Development of quantum voltage noise source chip for precision measurement of Boltzmann constant

The Johnson noise thermometer is used to precisely measure Boltzmann constant by comparing the thermal noise caused by charge movement and the quantized voltage reference noise synthesized by the quantum voltage noise source (QVNS). The QVNS signal is synthesized based on quantized voltage pulses produced by two channels of superconducting Josephson junction arrays, which are designed for cross-correlation electronics. The Nb/NbxSi1-x/Nb Josephson junction is used as a core device of QVNS chip in this work for its non-hysteretic current-voltage (I-V) characteristics and conveniently adjustable barrier parameters.In this paper, we present the design consideration, fabrication process, and measurement results of the QVNS chip. The QVNS chip contains two Josephson junction arrays, each consists of four 6 μm×12 μm junctions and is embedded in a 50 Ω coplanar waveguide transmission line. The random noise in signals from the two driven channels is eliminated by cross-correlation, and then an accurate quantum noise is obtained. Test chips with different areas of Josephson junctions are also designed on the same mask, aiming at estimating the variation range of Ic. The typical fabrication process for voltage standard chips in our laboratory is used for preparing the QVNS chip.The sample is measured at 4.2 K. The DC I-V curve shows that the critical current Ic is 6.1 mA. The I-V characteristics of the junctions under 5 GHz microwave radiation are measured. For a series array of four junctions, a 41.44 μV one-stage Shapiro step is observed. Calculation shows that the error between the measurement and theoretical value of 41.36 μV is about 1.9‰, which means that the QVNS chip performs well under microwave radiation and can be used for synthesizing the AC quantum voltage reference noise.A single-frequency 100 kHz sinusoidal waveform is synthesized by the QVNS chip under pulse driven signal. A spectrum of the synthesized sinusoidal waveform shows a single peak, which means that the digital pulse signal is perfectly filtered by Josephson junction arrays and the synthesized signals possess quantum accuracy. The results indicate that our chip has good dynamic response and works well in synthesizing a single-frequency AC quantum voltage signal. This work can provide core devices for the noise thermometry system and support the precise measurement of Boltzmann constant as well as redefinition of Kelvin in future. As a next step, the design and package will be further improved, and the probe module will be optimized to reduce the measurement uncertainty.

Magnetic cooling for microkelvin nanoelectronics on a cryofree platform.

We present a parallel network of 16 demagnetization refrigerators mounted on a cryofree dilution refrigerator aimed to cool nanoelectronic devices to sub-millikelvin temperatures. To measure the refrigerator temperature, the thermal motion of electrons in a Ag wire-thermalized by a spot-weld to one of the Cu nuclear refrigerators-is inductively picked-up by a superconducting gradiometer and amplified by a SQUID mounted at 4 K. The noise thermometer as well as other thermometers are used to characterize the performance of the system, finding magnetic field independent heat-leaks of a few nW/mol, cold times of several days below 1 mK, and a lowest temperature of 150 μK of one of the nuclear stages in a final field of 80 mT, close to the intrinsic SQUID noise of about 100 μK. A simple thermal model of the system capturing the nuclear refrigerator, heat leaks, and thermal and Korringa links describes the main features very well, including rather high refrigerator efficiencies typically above 80%.