Noise Thermometry Research Articles

Boltzmann Constant Measurements Using QVNS-Based Johnson Noise Thermometry at NMIJ, AIST

Among various methodologies of thermodynamic temperature measurements, Johnson noise thermometry (JNT) has an advantage that the structure and size of the temperature sensing probe are similar to conventional probes for contact thermometry. Another distinguishing feature is that the measurements are all electronic. Furthermore, the application of a quantum voltage noise source (QVNS), first introduced by the National Institute of Standards and Technology (NIST), has improved the accuracy of JNT during the past ten years. These developments have been driven under the rationale to determine the Boltzmann constant $$k$$ , in support of the proposed redefinition of the kelvin, and later to provide practical realization of the kelvin. At NMIJ, AIST, we have been developing a QVNS-based JNT system to first measure the Boltzmann constant and then aim to extend the temperature range to higher temperatures where $$T-T_{90}$$ data are lacking. An impact feature of our system is that most of our key elements have been built independently from NIST and the National Institute of Metrology, China (NIM); in particular that the Josephson junction array has been built in house at NeRI, AIST, and its driving method differs from that of either NIST or NIM. In this paper, the unique elements of the system as well as our initial results on the Boltzmann constant measurements are reported.

Electron-phonon coupling in suspended graphene: supercollisions by ripples.

Using electrical transport experiments and shot noise thermometry, we find strong evidence that "supercollision" scattering processes by flexural modes are the dominant electron-phonon energy transfer mechanism in high-quality, suspended graphene around room temperature. The power law dependence of the electron-phonon coupling changes from cubic to quintic with temperature. The change of the temperature exponent by two is reflected in the quadratic dependence on chemical potential, which is an inherent feature of two-phonon quantum processes.

Universal departure from Johnson-Nyquist relation caused by limited resolution

Exploiting the two-point measurement statistics, we propose a quantum measurement scheme of current with limited resolution of electron counting. Our scheme is equivalent to the full counting statistics in the long-time measurement with the ideal resolution, but is theoretically extended to take into account the resolution limit of actual measurement devices. Applying our scheme to a resonant level model, we show that the limited resolution of current measurement gives rise to a positive excess noise, which leads to a deviation from the Johnson-Nyquist relation. The deviation exhibits universal single-parameter scaling with the scaling variable $Q\ensuremath{\equiv}{S}_{\mathrm{M}}/{S}_{0}$, which represents the degree of the insufficiency of the resolution. Here, ${S}_{0}$ is the intrinsic noise, and ${S}_{\mathrm{M}}$ is the positive quantity that has the same dimension as ${S}_{0}$ and is defined solely by the measurement scheme. For the lack of the ideal resolution, the deviation emerges for $Q<1$ as $2exp[\ensuremath{-}{(2\ensuremath{\pi})}^{2}/Q]$ having an essential singularity at $Q=0$, which followed by the square root dependence $\sqrt{Q/4\ensuremath{\pi}}$ for $Q\ensuremath{\gg}1$. Our findings offer an explanation for the anomalous enhancement of noise temperature observed in Johnson noise thermometry.

Integrated quantum voltage noise source for Johnson noise thermometry

We have been developing a new implementation of quantum voltage noise source (QVNS), an integrated QVNS (IQVNS), for Johnson noise thermometry (JNT) in thermal metrology. We designed an IQVNS chip based on rapid single flux quantum (RSFQ) technology. A general formula for the output power spectrum has been derived by using a Fourier analysis method, which shows that the spectrum is calculable with sufficiently small errors for practical JNT measurements.

A Microkelvin Magnetic Flux Noise Thermometer

Due to its non-driven nature, noise thermometry intrinsically is the method of choice when minimal heat input during the temperature measurement is required. Our noise thermometer, experimentally characterized for temperatures between 42 \({{\upmu }}\)K and 0.8 K, is a magnetic Johnson noise thermometer. The noise source is a cold-worked high purity copper cylinder, 5 mm in diameter and 20 mm long. The magnetic flux fluctuations generated by the electrons’ Brownian motion is measured inductively by two dc-SQUID magnetometers simultaneously. Cross-correlation of the two channels leads to reduction of parasitic noise by more than one order of magnitude which allows for measuring the tiny noise powers at microkelvin temperatures.

Thermometry of Cold Atoms in Optical Lattices via Artificial Gauge Fields

Artificial gauge fields are a unique way of manipulating the motional state of cold atoms. Here we propose the use (practical or conceptual) of artificial gauge fields--obtained, e.g., experimentally via lattice shaking or conceptually via a Galilean transformation--to perform primary noise thermometry of cold atoms in optical lattices, not requiring any form of prior calibration. The proposed thermometric scheme relies on fundamental fluctuation--dissipation relations, connecting the global response to the variation of the applied gauge field and the fluctuation of quantities related to the momentum distribution (such as the average kinetic energy or the average current). We demonstrate gauge-field thermometry for several physical situations, including free fermions and interacting bosons. The proposed approach is extremely robust to quantum fluctuations-even in the vicinity of a quantum phase transition--when it relies on the thermal fluctuations of an emerging classical field, associated with the onset of Bose condensation or chiral order.

Graphene Microbolometers with Superconducting Contacts for Terahertz Photon Detection

We report on noise and thermal conductance measurements taken in order to determine an upper bound on the performance of graphene as a terahertz photon detector. The main mechanism for sensitive terahertz detection in graphene is bolometric heating of the electron system. To study the properties of a device using this mechanism to detect terahertz photons, we perform Johnson noise thermometry measurements on graphene samples. These measurements probe the electron–phonon behavior of graphene on silicon dioxide at low temperatures. Because the electron–phonon coupling is weak in graphene, superconducting contacts with large gap are used to confine the hot electrons and prevent their out-diffusion. We use niobium nitride leads with a $$T_\mathrm {c}\approx 10$$ K to contact the graphene. We find these leads make good ohmic contact with very low contact resistance. Our measurements find an electron–phonon thermal conductance that depends quadratically on temperature above 4 K and is compatible with single terahertz photon detection.

Graphene nanotransistors for RF charge detection

We have studied the static and dynamical properties of a graphene microwave nanotransistor to be used as sensitive fast charge detectors. The channel consists of exfoliated graphene on SiO2 with a 120 nm long, 900–1500 nm wide top-gate deposited on 5 nm AlOx dielectric. The scattering parameters were measured up to 60 GHz from which we deduce the gate capacitance, the drain conductance and the transconductance as a function of gate voltage. The broad measuring band allows us to measure the current gain and to map its full spectrum so as to extract reliable values of the transit frequency fT. From these measurements, we could estimate the carrier mobility, the doping of the access leads, the gate capacitance and the transconductance. The transconductance per unit width and bias voltage is larger than 1 mS µm−1 V−1 which compares with the performance of high electron mobility transistors. High-frequency characterization is achieved using microwave probe stations. Finally, using recent noise thermometry measurements, we estimate the charge resolution of graphene nanotransistors.

Prospective Performance of Graphene HEB for Ultrasensitive Detection of Sub-mm Radiation

Noise equivalent power and time constant of a submillimeter wave hot-electron bolometer (HEB) made from monolayer graphene are analyzed using the lowest electron-phonon thermal conductance data reported to date. Frequency-domain multiplexed Johnson Noise Thermometry (JNT) is used for the detector readout. Planar microantennas or waveguides can provide efficient coupling of the graphene microdevice to radiation. The results show that the graphene HEB detector can be radiation background limited at very low level corresponding to the photon noise on a space telescope with cryogenically cooled mirror. Beside the high sensitivity, absence of a hard power saturation limit, higher operating temperature, and the ability to read 1,000s of elements with a single broadband amplifier will be the advantages of such a detector.

Graphene-based terahertz photodetector by noise thermometry technique

We report the characteristics of graphene-based terahertz (THz) photodetector based on noise thermometry technique by measuring its noise power at frequency from 4 to 6 GHz. Hot electron system in graphene microbridge is generated after THz photon pumping and creates extra noise power. The equivalent noise temperature and electron temperature increase rapidly in low THz pumping regime and saturate gradually in high THz power regime which is attributed to a faster energy relaxation process involved by stronger electron-phonon interaction. Based on this detector, a conversion efficiency around 0.15 from THz power to noise power in 4–6 GHz span has been achieved.

Normal-Metal Hot-Electron Nanobolometer With Johnson Noise Thermometry Readout

The sensitivity of a THz hot-electron nanobolometer (nano-HEB) made from a normal metal is analyzed. Johnson Noise Thermometry (JNT) is employed as a readout technique. In contrast to its superconducting Transition-Edge Sensor (TES) counterpart, the normal-metal nano-HEB can operate at any cryogenic temperature depending on the required radiation background limited Noise Equivalent Power (NEP). It does not require bias lines; 100s of nano-HEBs can be read by a single low-noise <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$X$</tex> </formula> -band amplifier via a filter bank channelizer. The modeling predicts that even with the sensitivity penalty due to the amplifier noise, an <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm NEP}{\sim} 10^{-20}{\hbox{--}}10^{-19}{\hbox{W/Hz}}^{1/2}$</tex> </formula> can be expected at 50–100 mK in 10–20 nm thin titanium (Ti) normal metal HEBs with niobium (Nb) contacts. This NEP is fairly constant over a range of readout frequencies <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\sim$</tex></formula> 10 GHz. Although materials with weaker electron-phonon coupling (bismuth, graphene) do not improve the minimum achievable NEP, they can be considered if a larger than 10 GHz readout bandwidth is required.

A microkelvin cryogen-free experimental platform with integrated noise thermometry

We report experimental demonstration of the feasibility of reaching temperatures below 1 mK using cryogen-free technology. Our prototype system comprises an adiabatic nuclear demagnetization stage, based on hyperfine-enhanced nuclear magnetic cooling, integrated with a commercial cryogen-free dilution refrigerator and 8 T superconducting magnet. Thermometry was provided by a current-sensing noise thermometer. The minimum temperature achieved at the experimental platform was 600 μK. The platform remained below 1 mK for over 24 h, indicating a total residual heat-leak into the experimental stage of 5 nW. We discuss straightforward improvements to the design of the current prototype that are expected to lead to enhanced performance. This opens the way to widening the accessibility of temperatures in the microkelvin regime, of potential importance in the application of strongly correlated electron states in nanodevices to quantum computing.

Hot-spot detection and calibration of a scanning thermal probe with a noise thermometry gold wire sample

Measuring the temperature profile of a nanoscale sample using scanning thermal microscopy is challenging due to a scanning probe's non-uniform heating. In order to address this challenge, we have developed a calibration sample consisting of a 1-μm wide gold wire, which can be heated electrically by a small bias current. The Joule heating in the calibration sample wire is characterized using noise thermometry. A thermal probe was scanned in contact over the gold wire and measured temperature changes as small as 0.4 K, corresponding to 17 ppm changes in probe resistance. The non-uniformity of the probe's temperature profile during a typical scan necessitated the introduction of a temperature conversion factor, η, which is defined as the ratio of the average temperature change of the probe with respect to the temperature change of the substrate. The conversion factor was calculated to be 0.035 ± 0.007. Finite element analysis simulations indicate a strong correlation between thermal probe sensitivity and probe tip curvature, suggesting that the sensitivity of the thermal probe can be improved by increasing the probe tip curvature, though at the expense of the spatial resolution provided by sharper tips. Simulations also indicate that a bow-tie metallization design could yield an additional 5- to 7-fold increase in sensitivity.

Noise thermometry at low temperatures: MFFT measurements between 1.6 K and 1 mK

Reliable and traceable thermometry is a demanding task at low temperatures. Recently, we have developed a dc SQUID-based noise thermometer, the magnetic field fluctuation thermometer (MFFT), for practical thermometry in the low temperature range [1]. Its operational principle is based on the Nyquist theorem ensuring a linear characteristic over a wide range of temperatures. This makes the MFFT capable to replace a variety of secondary thermometers, which are normally used in the low temperature range.For the first time, we report on MFFT measurements over more than 3 decades in temperature from about 1.6 K down to below 1 mK The deviations from a high-accuracy realization of the PLTS-2000 are found to be ≍ 1%.

Supercollision cooling in undoped graphene

Carrier mobility in solids is generally limited by electron-impurity or electron–phonon scattering, depending on the most frequently occurring event. Three-body collisions between carriers and both phonons and impurities are rare; they are denoted supercollisions. Elusive in electronic transport they should emerge in relaxation processes as they allow for larger energy transfers. This is the case in undoped graphene, where the small Fermi surface drastically restricts the allowed phonon energy in ordinary collisions. Using electrical heating and sensitive noise thermometry we report on supercollision cooling in diffusive monolayer graphene. At low carrier density and high phonon temperature the Joule power P obeys a P Te3 law as a function of electronic temperature Te. It overrules the linear law expected for ordinary collisions which has recently been observed in resistivity measurements. The cubic law is characteristic of supercollisions and departs from the Te4 dependence recently reported for doped graphene below the Bloch–Grüneisen temperature. These supercollisions are important for applications of graphene in bolometry and photo-detection. Charge transport is usually limited by collisions between the carriers, impurities and/or phonons. Collisions involving three bodies are generally much rarer. A study now reveals, however, that such supercollisions can play an important role in the properties of graphene.

Non-linearity in Johnson noise thermometry

This paper discusses the effects of non-linearity, some of the mechanisms responsible for non-linearity, and methods for measuring non-linearity in Johnson noise thermometry. Mechanisms considered include quantum tunnelling, bipolar junction transistor and junction field-effect transistor amplifiers, feedback, clipping, output-stage crossover, quantization and dither. It is found that even- and odd-order effects behave differently in correlator-based noise thermometers, with the dominant even-order effects contributing as intermodulation products whereas the dominant odd-order contributions are third-order and at the same frequencies as the parent signals. Possible test methods include the use of discrete tones, changes in spectral shape, and direct measurement using reference noise powers. For correlators operated at constant noise power, direct measurement of non-linearity using reference noise powers enables corrections to be made with negligible additional uncertainty and measurement time.

Hot Electron Cooling by Acoustic Phonons in Graphene

We have investigated the energy loss of hot electrons in metallic graphene by means of GHz noise thermometry at liquid helium temperature. We observe the electronic temperature T ∝ V at low bias in agreement with the heat diffusion to the leads described by the Wiedemann-Franz law. We report on T ∝ √V behavior at high bias, which corresponds to a T(4) dependence of the cooling power. This is the signature of a 2D acoustic phonon cooling mechanism. From a heat equation analysis of the two regimes we extract accurate values of the electron-acoustic phonon coupling constant Σ in monolayer graphene. Our measurements point to an important effect of lattice disorder in the reduction of Σ, not yet considered by theory. Moreover, our study provides a strong and firm support to the rising field of graphene bolometric detectors.

Ultrasensitive and Wide-Bandwidth Thermal Measurements of Graphene at Low Temperatures

Graphene is a material with remarkable electronic properties and exceptional thermal transport properties near room temperature, which have been well examined and understood. However at very low temperatures the thermodynamic and thermal transport properties are much less well explored and somewhat surprisingly, is expected to exhibit extreme thermal isolation. Here we demonstrate an ultra-sensitive, wide-bandwidth measurement scheme to probe the thermal transport and thermodynamic properties of the electron gas of graphene. We employ Johnson noise thermometry at microwave frequency to sensitively measure the temperature of the electron gas with resolution of $4 mK/\sqrt{Hz}$ and a bandwidth of 80 MHz. We have measured the electron-phonon coupling from 2-30 K at a charge density of $2\cdot 10^{11} cm^{-2}$. Utilizing bolometric mixing, we have sensed temperature oscillations with period of 430 ps and have determined the heat capacity of the electron gas to be $2\cdot 10^{-21} J/(K\cdot \mu m^2)$ at 5 K which is consistent with that of a two dimensional, Dirac electron gas. These measurements suggest that graphene-based devices together with wide bandwidth noise thermometry can generate substantial advances in the areas of ultra-sensitive bolometry, calorimetry, microwave and terahertz photo-detection, and bolometric mixing for applications in areas such as observational astronomy and quantum information and measurement.

Noise thermometry in narrow two-dimensional electron gas heat baths connected to a quasi-one-dimensional interferometer

Thermal voltage noise measurements are performed in order to determine the electron temperature in nanopatterned channels of a GaAs/AlGaAs heterostructure at bath temperatures of 4.2 and 1.4 K. Two narrow two-dimensional (2D) heating channels, close to the transition to the one-dimensional (1D) regime, are connected by a quasi-1D quantum interferometer. Under dc current heating of the electrons in one heating channel, we perform cross-correlated noise measurements locally in the directly heated channel and nonlocally in the other channel, which is indirectly heated by hot electron diffusion across the quasi-1D connection. We observe the same functional dependence of the thermal noise on the heating current. The temperature dependence of the electron energy-loss rate is reduced compared to wider 2D systems. In the quantum interferometer, we show the decoherence due to the diffusion of hot electrons from the heating channel into the quasi-1D system, which causes a thermal gradient.

The contrasting method in noise thermometry as a development of the ideas of P. G. Strelkov

The place of the contrasting method among other methods of noise thermometry and its influence on the development of these methods is determined. The results of an investigation of the thermal characteristics of refractory metals and alloys on samples heated by a current with a direct measurement of their thermal noise and its oscillations are presented.