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Circuit-based quantum devices rely on keeping electrons at millikelvin temperatures. Improved coherence and sensitivity as well as discovering new physical phenomena motivate pursuing ever lower electron temperatures, accessible using on-chip cooling techniques. Here we show that a two-dimensional electron gas (2DEG), manipulated using gate voltages, works as an on-chip heat sink only limited by a fundamental phonon heat-leak. A single-shot 2DEG cooler can reduce the electron temperature by a factor of two with a hold time up to a second. Integrating an array of such coolers to obtain continuous cooldown in will allow reaching down to microkelvin device temperatures., Comment: 7 pages, 3 figures, 1 table

Replacing the bulky cryo-liquid based cooling stages of cryo-enabled instruments by chip scale refrigeration is envisioned to disruptively reduce the system size similarly as microprocessors did for computers. Electronic refrigerators based on superconducting tunnel junctions have been envisioned to provide a solution, but reaching the necessary above 1 kelvin operation temperature range has remained a goal out of reach for several decades. We show efficient electronic refrigeration by Al-AlOx-Nb superconducting tunnel junctions starting from bath temperatures above 2 K. The junctions can deliver electronic cooling power up to $\sim$mW/mm$^2$, which enables us to demonstrate tunnel current driven electron temperature reduction from 2.4 K to below 1.6 K (34% relative cooling) against the phonon bath. Our work shows that the key material of integrated superconducting circuits - niobium - enables powerful cryogenic refrigerator technology. This result is a prerequisite for practical cryogenic chip scale refrigerators and, at the same time, it introduces a new electro-thermal tool for quantum heat transport experiments.

Scalable quantum information processing with superconducting circuits is expected to advance from individual processors located in single dilution refrigerators to more powerful distributed quantum computing systems. The realization of hardware platforms for quantum local area networks (QLANs) compatible with superconducting technology is of high importance in order to achieve a practical quantum advantage. Here, we present a fundamental prototype platform for a microwave QLAN based on a cryogenic link connecting two separate dilution cryostats over a distance of $6.6$ m with a base temperature of $52$ mK in the center. Superconducting microwave coaxial cables are employed to form a quantum communication channel between the distributed network nodes. We demonstrate the continuous-variable entanglement distribution between the remote dilution refrigerators in the form of two-mode squeezed microwave states, reaching squeezing of $2.10 \pm 0.02$ dB and negativity of $0.501 \pm 0.011$. Furthermore, we show that quantum entanglement is preserved at channel center temperatures up to $1$ K, paving the way towards microwave quantum communication at elevated temperatures. Consequently, such a QLAN system can form the backbone for future distributed quantum computing with superconducting circuits.

On-chip demagnetization refrigeration has recently emerged as a powerful tool for reaching microkelvin electron temperatures in nanoscale structures. The relative importance of cooling on-chip and off-chip components and the thermal subsystem dynamics are yet to be analyzed. We study a Coulomb blockade thermometer with on-chip copper refrigerant both experimentally and numerically, showing that dynamics in this device are captured by a first-principles model. Our work shows how to simulate thermal dynamics in devices down to microkelvin temperatures, and outlines a recipe for a low-investment platform for quantum technologies and fundamental nanoscience in this novel temperature range., Comment: 11 pages, 10 figures

Refrigeration is an important enabler for quantum technology. The very low energy of the fundamental excitations typically utilized in quantum technology devices and systems requires temperature well below 1 K. Expensive cryostats are utilized in reaching sub-1 K regime and solid-state cooling solutions would revolutionize the field. New electronic micro-coolers based on phonon-blocked semiconductor-superconductor junctions could provide a viable route to such miniaturization. Here, we investigate the performance limits of these junction refrigerators., Comment: 5 pages, 3 figures, published in 2020 International Electron Devices Meeting (IEDM)

We fabricate and characterize superconducting through-silicon vias and electrodes suitable for superconducting quantum processors. We measure internal quality factors of a million for test resonators excited at single-photon levels, on chips with superconducting vias used to stitch ground planes on the front and back sides of the chips. This resonator performance is on par with the state of the art for silicon-based planar solutions, despite the presence of vias. Via stitching of ground planes is an important enabling technology for increasing the physical size of quantum processor chips, and is a first step toward more complex quantum devices with three-dimensional integration., Comment: Accepted version. 11 pages, 7 figures, 2 tables with appendices included

The Coulomb Blockade Thermometer (CBT) is a primary thermometer for cryogenic temperatures, with demonstrated operation from below 1 mK up to 60 K. Its performance as a primary thermometer has been verified at temperatures from 20 mK to 200 mK at uncertainty level below 1 % (k = 2). In a new project, our aim is to extend the metrologically verified temperature range of the primary CBT up to 25 K. We also demonstrate close-to-ideal operation of a CBT with only two tunnel junctions when the device is embedded in a low-impedance environment., Comment: 2 pages, 3 figures, 2020 Conference on Precision Electromagnetic Measurements (CPEM), Denver (Aurora), CO, USA, 2020

We demonstrate highly transparent silicon-vanadium and silicon-aluminum tunnel junctions with relatively low sub-gap leakage current and discuss how a trade-off typically encountered between transparency and leakage affects their refrigeration performance. We theoretically investigate cascaded superconducting tunnel junction refrigerators with two or more refrigeration stages. In particular, we develop an approximate method that takes into account self-heating effects but still allows us to optimize the cascade a single stage at a time. We design a cascade consisting of energy-efficient refrigeration stages, which makes cooling of, e.g., quantum devices from above 1 K to below 100 mK a realistic experimental target., Comment: 5 pages, 4 figures

Since the introduction of bolometers more than a century ago, they have been applied in a broad spectrum of contexts ranging from security and the construction industry to particle physics and astronomy. However, emerging technologies and missions call for faster bolometers with lower noise. Here, we demonstrate a nanobolometer that exhibits roughly an order of magnitude lower noise equivalent power, $20\textrm{ zW}/\sqrt{\textrm{Hz}}$, than previously reported for any bolometer. Importantly, it is more than an order of magnitude faster than other low-noise bolometers, with a time constant of 30 $\mu$s at $60\textrm{ zW}/\sqrt{\textrm{Hz}}$. These results suggest a calorimetric energy resolution of $0.3\textrm{ zJ}=h\times 0.4$ THz with a time constant of 30 $\mu$s. Thus the introduced nanobolometer is a promising candidate for future applications requiring extreme precision and speed such as those in astronomy and terahertz photon counting.

We have fabricated disordered superconducting nanowires of molybdenium silicide. A molybdenium nanowire is first deposited on top of silicon, and the alloy is formed by rapid thermal annealing. The method allows tuning of the crystal growth to optimise, e.g., the resistivity of the alloy for potential applications in quantum phase slip devices and superconducting nanowire single-photon detectors. The wires have effective diameters from 42 to 79 nm, enabling the observation of crossover from conventional superconductivity to regimes affected by thermal and quantum fluctuations. In the smallest diameter wire and at temperatures well below the superconducting critical temperature, we observe residual resistance and negative magnetoresistance, which can be considered as fingerprints of quantum phase slips.

We demonstrate significant cooling of electrons in a nanostructure below 10 mK by demagnetisation of thin-film copper on a silicon chip. Our approach overcomes the typical bottleneck of weak electron-phonon scattering by coupling the electrons directly to a bath of refrigerated nuclei, rather than cooling via phonons in the host lattice. Consequently, weak electron-phonon scattering becomes an advantage. It allows the electrons to be cooled for an experimentally useful period of time to temperatures colder than the dilution refrigerator platform, the incoming electrical connections, and the host lattice. There are efforts worldwide to reach sub-millikelvin electron temperatures in nanostructures to study coherent electronic phenomena and improve the operation of nanoelectronic devices. On-chip magnetic cooling is a promising approach to meet this challenge. The method can be used to reach low, local electron temperatures in other nanostructures, obviating the need to adapt traditional, large demagnetisation stages. We demonstrate the technique by applying it to a nanoelectronic primary thermometer that measures its internal electron temperature. Using an optimised demagnetisation process, we demonstrate cooling of the on-chip electrons from 9 mK to below 5 mK for over 1000 seconds., Comment: 9 pages, 5 figures

We describe the optical characterisation of two silicon cold-electron bolometers each consisting of a small ($32 \times 14~\mathrm{\mu m}$) island of degenerately doped silicon with superconducting aluminium contacts. Radiation is coupled into the silicon absorber with a twin-slot antenna designed to couple to 160-GHz radiation through a silicon lens.The first device has a highly doped silicon absorber, the second has a highly doped strained-silicon absorber.Using a novel method of cross-correlating the outputs from two parallel amplifiers, we measure noise-equivalent powers of $3.0 \times 10^{-16}$ and $6.6 \times 10^{-17}~\mathrm{W\,Hz^{-1/2}}$ for the control and strained device, respectively, when observing radiation from a 77-K source. In the case of the strained device, the noise-equivalent power is limited by the photon noise., Comment: Accepted for publication in Journal of Low Tempature Physics

We report the cooling of electrons in nanoelectronic Coulomb blockade thermometers below 4 mK. Above 7 mK the devices are in good thermal contact with the environment, well isolated from electrical noise, and not susceptible to self-heating. This is attributed to an optimised design that incorporates cooling fins with a high electron-phonon coupling and on-chip electronic filters, combined with a low-noise electronic measurement setup. Below 7 mK the electron temperature is seen to diverge from the ambient temperature. By immersing a Coulomb Blockade Thermometer in the 3He/4He refrigerant of a dilution refrigerator, we measure a lowest electron temperature of 3.7 mK., Comment: 11 pages, 4 figures. (Fixed fitted saturation T_e on p9)

We describe optical characterisation of a Strained Silicon Cold Electron Bolometer (CEB), operating on a $350~\mathrm{mK}$ stage, designed for absorption of millimetre-wave radiation. The silicon Cold Electron Bolometer utilises Schottky contacts between a superconductor and an n++ doped silicon island to detect changes in the temperature of the charge carriers in the silicon, due to variations in absorbed radiation. By using strained silicon as the absorber, we decrease the electron-phonon coupling in the device and increase the responsivity to incoming power. The strained silicon absorber is coupled to a planar aluminium twin-slot antenna designed to couple to $160~\mathrm{GHz}$ and that serves as the superconducting contacts. From the measured optical responsivity and spectral response, we calculate a maximum optical efficiency of $50~\%$ for radiation coupled into the device by the planar antenna and an overall noise equivalent power (NEP), referred to absorbed optical power, of $1.1 \times 10^{-16}~\mathrm{\mbox{W Hz}^{-1/2}}$ when the detector is observing a $300~\mathrm{K}$ source through a $4~\mathrm{K}$ throughput limiting aperture. Even though this optical system is not optimised we measure a system noise equivalent temperature difference (NETD) of $6~\mathrm{\mbox{mK Hz}^{-1/2}}$. We measure the noise of the device using a cross-correlation of time stream data measured simultaneously with two junction field-effect transistor (JFET) amplifiers, with a base correlated noise level of $300~\mathrm{\mbox{pV Hz}^{-1/2}}$ and find that the total noise is consistent with a combination of photon noise, current shot noise and electron-phonon thermal noise., Comment: Published in Applied Physics Letters, 105, pp. 043509

We demonstrate electron cooling in silicon using platinum silicide as a superconductor contact to selectively remove the highest energy electrons. The superconducting critical temperature of bulk PtSi is reduced from around 1 K to 0.79 K using a thin film (10 nm) of PtSi, which enhances cooling performance at lower temperatures and enables electron cooling to be demonstrated from 100 mK to 50 mK., Comment: 4 pages, 4 figures

We study the relaxation of coherent acoustic phonon modes with frequencies up to 500 GHz in ultra-thin free-standing silicon membranes. Using an ultrafast pump-probe technique of asynchronous optical sampling, we observe that the decay time of the first-order dilatational mode decreases significantly from \sim 4.7 ns to 5 ps with decreasing membrane thickness from \sim 194 to 8 nm. The experimental results are compared with theories considering both intrinsic phonon-phonon interactions and extrinsic surface roughness scattering including a wavelength-dependent specularity. Our results provide insight to understand some of the limits of nanomechanical resonators and thermal transport in nanostructures.

We investigate Coulomb blockade thermometers (CBT) in an intermediate temperature regime, where measurements with enhanced accuracy are possible due to the increased magnitude of the differential conductance dip. Previous theoretical results show that corrections to the half width and to the depth of the measured conductance dip of a sensor are needed, when leaving the regime of weak Coulomb blockade towards lower temperatures. In the present work, we demonstrate experimentally that the temperature range of a CBT sensor can be extended by employing these corrections without compromising the primary nature or the accuracy of the thermometer., Comment: 8 pages, 4 figures

Enhanced electron cooling is demonstrated in a strained-silicon/superconductor tunnel junction refrigerator of volume 40 um^3. The electron temperature is reduced from 300 mK to 174 mK, with the enhancement over an unstrained silicon control (300 mK to 258 mK) being attributed to the smaller electron-phonon coupling in the strained case. Modeling and the resulting predictions of silicon-based cooler performance are presented. Further reductions in the minimum temperature are expected if the junction sub-gap leakage and tunnel resistance can be reduced. However, if only tunnel resistance is reduced, Joule heating is predicted to dominate., Comment: 3 pages, 5 figures

We demonstrate significant modification of the electron-phonon energy loss rate in a many-valley semiconductor system due to lattice mismatch induced strain. We show that the thermal conductance from the electron system to the phonon bath in strained n + Si, at phonon temperatures between 200 mK and 450 mK, is more than an order of magnitude lower than that for a similar unstrained sample.

We investigate a wafer scale tunnel junction fabrication method, where a plasma etched via through a dielectric layer covering bottom Al electrode defines the tunnel junction area. The ex-situ tunnel barrier is formed by oxidation of the bottom electrode in the junction area. Room temperature resistance mapping over a 150 mm wafer give local deviation values of the tunnel junction resistance that fall below 7.5 % with an average of 1.3 %. The deviation is further investigated by sub-1 K measurements of a device, which has one tunnel junction connected to four arrays consisting of N junctions (N = 41, junction diameter 700 nm). The differential conductance is measured in single-junction and array Coulomb blockade thermometer operation modes. By fitting the experimental data to the theoretical models we found an upper limit for the local tunnel junction resistance deviation of ~5 % for the array of 2N+1 junctions. This value is of the same order as the minimum detectable deviation defined by the accuracy of our experimental setup.

We investigate carrier transport in a single 22 nm-thick double-gated Si quantum well device, which has independent contacts to electrons and holes. Conductance, Hall density and Hall mobility are mapped in a broad double-gate voltage window. When the gate voltage asymmetry is not too large only either electrons or holes occupy the Si well and the Hall mobility shows the fingerprints of volume inversion/accumulation. At strongly asymmetric double-gate voltage an electric field induced electron-hole (EH) bi-layer is formed inside the well. The EH drag resistance R_{he} is explored at balanced carrier densities: R_{he} decreases monotonically from 860 to 37 Ohms when the electron and hole density is varied between ~0.4-1.7x10^{16} m^{-2}.

The gate bias dependency of conductivity is examined in two Si quantum wells with well thickness tw = 7 nm and tw = 14 nm. The conductivity of the thinner device behaves smoothly whereas the thicker device shows strong non-monotonic features as a function of gate voltages. We show that a strong minimum in conductivity occurs close to the threshold of second sub-band. Another minimum is seen at high electron density at symmetric well potential. This feature is addressed to sub-band wave function delocalization in the quantization direction., Comment: To appear in the Proceedings of ICPS28th (Vienna, Austria, July 24-28, 2006)

The temperature dependent energy transfer rate between charge carriers and lattice has been experimentally investigated in ferromagnetic semiconductors. Studied 100 nm thick low-temperature MBE grown Mn_{x}Ga_{1-x}As samples had manganese concentrations x=3.7 % and 4.0 %. Curie temperatures estimated from temperatures of peak resistivities were 60 K and 62 K, respectively., Comment: To appear in the Proceedings of ICPS28th (Vienna, Austria, July 24-28, 2006)

We report on detailed room temperature and low temperature transport properties of double-gate Si MOSFETs with the Si well thickness in the range 7-17 nm. The devices were fabricated on silicon-on-insulator wafers utilizing wafer bonding, which enabled us to use heavily doped metallic back gate. We observe mobility enhancement effects at symmetric gate bias at room temperature, which is the finger print of the volume inversion/accumulation effect. An asymmetry in the mobility is detected at 300 K and at 1.6 K between the top and back interfaces of the Si well, which is interpreted to arise from different surface roughnesses of the interfaces. Low temperature peak mobilities of the reported devices scale monotonically with Si well thickness and the maximum low temperature mobility was 1.9 m2/Vs, which was measured from a 16.5 nm thick device. In the magneto transport data we observe single and two sub-band Landau level filling factor behavior depending on the well thickness and gate biasing.

We report on the effect of elastic intervalley scattering on the energy transport between electrons and phonons in many-valley semiconductors. We derive a general expression for the electron-phonon energy flow rate at the limit where elastic intervalley scattering dominates over diffusion. Electron heating experiments on heavily doped n-type Si samples with electron concentration in the range $3.5-16.0\times 10^{25}$ m$^{-3}$ are performed at sub-1 K temperatures. We find a good agreement between the theory and the experiment., Comment: v2: Notations changed: $\Delta_i$ --> $\delta v_i$, $\tau_{eff}$ removed. Eq. (1) changed, Eq. (2) added and complete derivation of Eq. (3) included. Some further discussion about single vs. many valley added [3rd paragraph after Eq. (7)]. End notes removed and new reference added [Kragler and Thomas]. Typos in references corrected