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The accidental discovery of mercury’s zero resistance at temperatures lower than 4.2 K which took place in 1911 by the Dutch physicist Heike Kamerlingh Onnes in his laboratory at the University of Leiden, appeared to be one of the greatest breakthroughs of physics of all time. It has led to the creation of an entirely new field within physics called superconductivity; this attracted many of the finest minds in physics whose work in this area produced no less than six Nobel Prizes to date. Zero resistance, together with the expulsion of magnetic fields which was discovered many years later, are the two unique and intriguing properties of superconductors which puzzled scientists’ brains for a proper theoretical explanation of the observed phenomena. However in 1935, the phe-nomenological theory proposed by Fritz and Heinz London (known as the London theory) was the first success in the field, which was followed in the 1950s by another phenomenological theory put forward by Vitaly Ginzburg and Lev Landau. Despite this, a satisfactory microscopic theory for super-conductivity had to wait until 1957 when John Bardeen, Leon Cooper and John Robert Schrieffer proposed their theory, which was nicknamed the BCS theory in their honour.The more recent discovery of the cuprate high temperature superconductors (HTS) in 1986 gave a new momentum to the field and intensified the search for room temperature superconductors which continues to this day. While this quest is under way, and new theories of superconductivity are being developed, physicists, material scientists and engineers are using superconductors to establish new technologies and build machines, devices and tools with unprecedented properties. Today superconductors are widely used in healthcare, particle accelerators, ultrasensitive instrumentation and microwave engineering and they are being developed for use in many other areas as well. In this review, we will trace the history of superconductors and provide a brief o

We present the simulated performance of a Josephson traveling wave parametric amplifier based on a one-dimensional array of radio-frequency single-junction superconducting quantum interference devices. Using the capabilities allowed by the WRspice simulation platform and previous works on this scheme, we include in our study the effects of fabrication tolerances in the device parameters on the gain of the amplifier. Our simulations show the negative effects of parameter variation and the resulting microwave reflections of signal and pump waves between individual cells. We present a method to understand the inner dynamics of the device using an impedance model that substitutes the need to simultaneously consider phase bias points and wave mixing dynamics. This should allow the application of the results presented here to more complex schemes, which promise higher amplification and fewer drawbacks. We highlight the strict limitations on parameter spread in these devices while also discussing the robustness of the scheme to defects.

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.

The accuracy of single-electron currents produced in hybrid turnstiles at high operation frequencies is, among other errors, limited by electrons tunneling in the wrong direction. Increasing the barrier transparency between the island and the leads, and the source-drain bias helps to suppress these events in a larger frequency range, although they lead to some additional errors. We experimentally demonstrate a driving scheme that suppresses tunneling in the wrong direction hence extending the range of frequencies for generating accurate single-electron currents. The main feature of this approach is an additional AC signal applied to the bias with twice the frequency as the one applied to the gate electrode. This allows additional modulation of the island chemical potential. By using the new approach under certain parameters, we improve the single-electron current accuracy by one order of magnitude. Finally, we show through experimentally-contrasted calculations that our method can improve accuracy even in devices for which the usual gate driving gives errors ∼10^(−3) at high frequencies and can bring them under 5×10^(−4).

We investigate the time traces of currents induced in five segmented electrodes by the motion of electrons on the surface of liquid 4 He at ∼ 0.3 K, that are placed in a perpendicular magnetic field and exposed to microwave radiation. Nonlinear dynamics methods are utilized to explore the characteristic features of the current oscillations in the electrodes for different electron densities and pressing voltages. The wavelet phase coherence and phase shift are calculated to obtain the coherence relationships between the signals in all five electrodes as functions of the pressing voltage. Coupling analysis of the ridge-extracted instantaneous frequencies revealed the directions of motion of electrons inside the cell and provided evidence of strong phase coupling at a pressing voltage of 4.20 V. These classical methods reveal that the motion is oscillatory, with a varying frequency subject to a constant frequency modulation. High harmonics due to nonlinearity arise at higher frequencies where the resonance condition is satisfied at a pressing voltage of 4.20 V for low-electron density. Our approach provides a platform for investigating these phenomena analytically. We show that slow gravity waves on the helium surface modulate the electronic oscillatory behavior and illustrate that the model in fact produces three-dimensional dynamics. Motion of electrons on the surface of liquid helium is shown to be a paradigmatic example of a chronotaxic system, i.e., a system that undergoes continuous perturbation but is nonetheless capable of maintaining its stability.

Parametric amplifiers based on non-linear superconducting transmission lines have seen rapid progress in the last few years, although many fabricated samples still behave well below the optimal performance that is theorised. A part of this discrepancy is due to the attenuation of travelling waves that occurs in realised schemes due to dielectric losses or resistance losses on the superconductor surface. As interests turn towards designs utilising more complex non-linear elements such as SNAILs or materials near the superconductor–insulator transition, we address the question of dissipative losses in heretofore common schemes with a methodology that can be extended to other superconducting metamaterial devices.

Nanomechanical resonators made from van der Waals materials (vdW NMRs) provide a new tool for sensing absorbed laser power. The photothermal response of vdW NMRs, quantified from the resonant frequency shifts induced by optical absorption, is enhanced when incorporated in a Fabry-Pérot (FP) interferometer. Along with the enhancement comes the dependence of the photothermal response on NMR displacement, which lacks investigation. Here, we address the knowledge gap by studying electromotively driven niobium diselenide drumheads fabricated on highly reflective substrates. We use a FP-mediated absorptive heating model to explain the measured variations of the photothermal response. The model predicts a higher magnitude and tuning range of photothermal responses on few-layer and monolayer NbSe drumheads, which outperform other clamped vdW drum-type NMRs at a laser wavelength of 532 nm. Further analysis of the model shows that both the magnitude and tuning range of NbSe drumheads scale with thickness, establishing a displacement-based framework for building bolometers using FP-mediated vdW NMRs.

Studies involving nanomechanical motion have evolved from the detection and understanding of its fundamental aspects to its promising practical utility as an integral component of hybrid systems. The nanomechanical resonators’ indispensable role as transducers between optical and microwave fields in hybrid systems, such as quantum communications interfaces, have elevated their importance in recent years. It is therefore crucial to determine which among the family of nanomechanical resonators is more suitable for this role. Most of the studies revolve around nanomechanical resonators of ultrathin structures because of their inherently large mechanical amplitude due to their very low mass. Here, we argue that the underutilized nanomechanical resonators made from multilayered two-dimensional (2D) materials are the better fit for this role because of their comparable electrostatic tunability and potential for larger optomechanical responsivity. To show this, we first demonstrate the electrostatic tunability of mechanical modes of a multilayered nanomechanical resonator made from graphite. We also show that the optimal values of optomechanical responsivities are obtained for multilayered devices, particularly when the Fabry−Perot gap is close to half the detection wavelength. Finally, by using the multilayered model and comparing this device with the reported ones, we find that the electrostatic tunability of devices of intermediate thickness is not significantly lower than that of ultrathin ones. Together with the practicality in terms of fabrication ease and design predictability, we contend that multilayered 2D nanomechanical resonators are the optimal choice for the electromagnetic interface in integrated quantum systems.

One of the challenges in integrating nanomechanical resonators made from van der Waals materials in optoelectromechanical technologies is characterizing their dynamic properties from vibrational displacement. Multiple calibration schemes using optical interferometry have tackled this challenge. However, these techniques are limited only to optically thin resonators with an optimal vacuum gap height and substrate for interferometric detection. Here, we address this limitation by implementing a modeling-based approach via multilayer thin-film interference for in situ, non-invasive determination of the resonator thickness, gap height, and motional amplitude. This method is demonstrated on niobium diselenide drumheads that are electromotively driven in their linear regime of motion. The laser scanning confocal configuration enables a resolution of hundreds of picometers in motional amplitude for circular and elliptical devices. The measured thickness and spacer height, determined to be in the order of tens and hundreds of nanometers, respectively, are in excellent agreement with profilometric measurements. Moreover, the transduction factor estimated from our method agrees with the result of other studies that resolved Brownian motion. This characterization method, which applies to both flexural and acoustic wave nanomechanical resonators, is robust because of its scalability to thickness and gap height, and any form of reflecting substrate.

Since we still lack a theory of classical turbulence, attention has focused on the conceptually simpler turbulence in quantum fluids. Reaching a better understanding of the quantum case may provide additional insight into the classical counterpart. That said, we have hitherto lacked detectors capable of the real-time, non-invasive probing of the wide range of length scales involved in quantum turbulence. Here we demonstrate the real-time detection of quantum vortices by a nanoscale resonant beam in superfluid 4He at 10mK. Essentially, we trap a single vortex along the length of a nanobeam and observe the transitions as a vortex is either trapped or released, detected through the shift in the beam resonant frequency. By exciting a tuning fork, we control the ambient vortex density and follow its influence on the vortex capture and release rates demonstrating that these devices are capable of probing turbulence on the micron scale.

Superconducting quantum devices offer numerous applications, from electrical metrology and magnetic sensing to energy-efficient high-end computing and advanced quantum information processing. The key elements of quantum circuits are (single and double) Josephson junctions controllable either by electric current or magnetic field. The voltage control, commonly used in semiconductor-based devices via the electrostatic field effect, would be far more versatile and practical. Hence, the field effect recently reported in superconducting devices may revolutionise the whole field of superconductor electronics provided it is confirmed. Here we show that the suppression of the critical current attributed to the field effect, can be explained by quasiparticle excitations in the constriction of superconducting devices. Our results demonstrate that a miniscule leakage current between the gate and the constriction of devices perfectly follows the Fowler-Nordheim model of electron field emission from a metal electrode and injects quasiparticles with energies sufficient to weaken or even suppress superconductivity.

A cryogenic quantum dot thermometer is calibrated and operated using only a single nongalvanic gate connection. The thermometer is probed with radio-frequency reflectometry and calibrated by fitting a physical model to the phase of the reflected radio-frequency signal taken at temperatures across a small range. Thermometry of the source and drain reservoirs of the dot is then performed by fitting the calibrated physical model to new phase data. The thermometer can operate at the transition between thermally broadened and lifetime-broadened regimes and outside the temperatures used in calibration. Electron thermometry is performed at temperatures between 3.0K and 1.0K, in both a 1-K cryostat and a dilution refrigerator. In principle, the experimental setup enables fast electron-temperature readout with a sensitivity of 4.0±0.3mK/√Hz, at kelvin temperatures. The nongalvanic calibration process gives a readout of physical parameters, such as the quantum dot lever arm. The demodulator used for reflectometry readout is readily available at relatively low cost.

Flexural mode vibrations of miniature piezoelectric tuning forks (TF) are known to be highly sensitive to superfluid excitations and quantum turbulence in 3He and 4He quantum fluids, as well as to the elastic properties of solid 4He, complementing studies by large scale torsional resonators. Here we explore the sensitivity of a TF, capable of simultaneously operating in both the flexural and torsional modes, to excitations in the normal and superfluid 4He. The torsional mode is predominantly sensitive to shear forces at the sensor - fluid interface and much less sensitive to changes in the density of the surrounding fluid when compared to the flexural mode. Although we did not reach the critical velocity for quantum turbulence onset in the torsional mode, due to its order of magnitude higher frequency and increased acoustic damping, the torsional mode was directly sensitive to fluid excitations, linked to quantum turbulence created by the flexural mode. The combination of two dissimilar modes in a single TF sensor can provide a means to study the details of elementary excitations in quantum liquids, and at interfaces between solids and quantum fluid.

Cooling electrons in a nanoelectronic device to a few milikelvin, and further into the microkelvin regime, is a longstanding challenge. Weak electron-phonon coupling at low temperatures creates a bottleneck in traditional cooling techniques. Here we will present our approach to solving the problem: nuclear demagnetization refrigeration of on-chip copper to directly cool the electrons without intervening phonons. Our method has achieved a base electron temperature below 1.3 mK, held for several 1000s. On-chip refrigeration could potentially provide improvements in the operation of quantum simulators, computers and metrology standards, and open a new regime for the study of electron transport in nanostructures and 2D materials. However, it will be necessary to couple the copper refrigerant to the system of interest and to employ non-invasive thermometry techniques. We will discuss our progress towards these goals, including the development of a single-electron thermometer that is measured by RF reflectometry and does not require galvanic connection between the cooled electron gas and the outside world. This research is supported by the U.K. EPSRC (EP/N019199/1).

Nanomechanical resonators have recently been studied as high-sensitivity probes of fluid dynamics in superfluid helium. When turbulence is introduced to such a system, quantum vortices may form and become trapped by the resonator, either completely surrounding the oscillating beam (a fully trapped vortex) or surrounding only part of it (a partially trapped vortex). Fully trapped vortices have been studied using the model of a linear harmonic oscillator behaviour with great success. However, in the presence of a partially trapped vortex, the oscillators have been found to behave non-linearly. We analysed the non-linear response of a doubly clamped nanobeam resonator submerged in helium-4 at 10 mK in the presence of a partially trapped vortex. Our analysis demonstrates that the observed non-linearities are caused by the dynamics of the vortex line. N. M. acknowledges the financial support of the US-UK Fulbright Program.

Lateral superconductor/graphene structures can be used to make Josephson junctions with low contact resistances and gate-tuneable critical currents. These junctions have the potential to provide new functionality for superconducting devices. For most devices, e.g. transmon qubits and SQUID sensors, it is important to quantify the intrinsic noise of the junctions. The voltage noise of low resistance junctions is typically below the noise floor of room temperature amplifiers. By cross-correlating the signals from two parallel amplifiers, we can detect signals down to 100 pV/√Hz, well below the noise floor of each amplifier. Using this technique, we characterise the voltage noise of a NbTi DC SQUID with graphene junctions in a frequency range from Hz to kHz. Combined with measurements of the SQUID's gain, we map its sensitivity across a range of operating conditions and find that the best-case sensitivity of the device is similar to traditional low temperature SQUIDs with oxide tunnel junctions. This project has received funding from the European Union's Horizon 2020 research and innovation programme under Grant agreement No 785219.

Superfluids, such as superfluid 3He and 4He, exhibit a broad range of quantum phenomena and excitations which are unique to these systems. Nanoscale mechanical resonators are sensitive and versatile force detectors with the ability to operate over many orders of magnitude in damping. Using nanomechanical-doubly clamped beams of extremely high-quality factors Q>106, we probe superfluid 4He from the superfluid transition temperature down to mK temperatures at frequencies up to 11.6 MHz. Our studies show that nanobeam damping is dominated by hydrodynamic viscosity of the normal component of 4He above 1K. In the temperature range 0.3-0.8K, the ballistic quasiparticles (phonons and rotons) determine the beams' behavior. At lower temperatures, damping saturates and is determined either by magnetomotive losses or acoustic emission into helium. It is remarkable that all these distinct regimes can be extracted with just a single device, despite damping changing over six orders of magnitude.

Cooling electrons in a nanoelectronic device to a few milikelvin, and further into the microkelvin regime, is a longstanding challenge. Weak electron-phonon coupling at low temperatures creates a bottleneck in traditional cooling techniques. Here we will present our approach to solving the problem: nuclear demagnetization refrigeration of on-chip copper to directly cool the electrons without intervening phonons. Our method has achieved a base electron temperature below 1.3 mK, held for several 1000s. On-chip refrigeration could potentially provide improvements in the operation of quantum simulators, computers and metrology standards, and open a new regime for the study of electron transport in nanostructures and 2D materials. However, it will be necessary to couple the copper refrigerant to the system of interest and to employ non-invasive thermometry techniques. We will discuss our progress towards these goals, including the development of a single-electron thermometer that is measured by RF reflectometry and does not require galvanic connection between the cooled electron gas and the outside world. This research is supported by the U.K. EPSRC (EP/N019199/1).

We present a new technique for on-chip cooling of electrons in a nanostructure: nuclear demagnetisation of on-chip, thin-film copper refrigerant. We are motivated by the potential improvement in the operation of nanoelectronic devices below 10 mK . At these temperatures, weak electron-phonon coupling hinders traditional cooling, yet here gives the advantage of thermal isolation between the environment and the on-chip electrons, enabling cooling significantly below the base temperature of the host lattice. To demonstrate this we electroplate copper onto the metallic islands of a Coulomb blockade thermometer (CBT), and hence provide a direct thermal link between the cooled copper nuclei and the device electrons. The CBT provides primary thermometry of its internal electron temperature, and we use this to monitor the cooling. Using an optimised demagnetisation profile we observe the electrons being cooled from 9 mK to 4 . 5 mK , and remaining below 5 mK for an experimentally useful time of 1200 seconds. We also suggest how this technique can be used to achieve sub- 1 mK electron temperatures without the use of elaborate bulk demagnetisation stages.

We report the single-electron tunneling behaviour of a silicon nanobridge where the effective island is a single As dopant atom. The device is a gated silicon nanobridge with a thickness and width of ∼20 nm, fabricated from a commercially available silicon-on-insulator wafer, which was first doped with As atoms and then patterned using a unique CMOS-compatible technique. Transport measurements reveal characteristic Coulomb diamonds whose size decreases with gate voltage. Such a dependence indicates that the island of the single-electron transistor created is an individual arsenic dopant atom embedded in the silicon lattice between the source and drain electrodes, and furthermore, can be explained by the increase of the localisation region of the electron wavefunction when the higher energy levels of the dopant As atom become occupied. The charge stability diagram of the device shows features which can be attributed to adjacent dopants, localised in the nanobridge, acting as charge traps. From the measured device transport, we have evaluated the tunnel barrier properties and obtained characteristic device capacitances. The fabrication, control and understanding of such “single-atom” devices marks a further step towards the implementation of single-atom electronics.

We show that a weak external magnetic field affects significantly nonequilibrium quasiparticle (QP) distributions under the conditions of the inverse proximity effect, using the single-electron hybrid turnstile as a generic example. Inverse proximity suppresses the superconducting gap in superconducting leads in the vicinity of turnstile junctions, thus, trapping hot QPs in this region. An external magnetic field creates additional QP traps in the leads in the form of vortices or regions with a reduced superconducting gap resulting in the release of QPs away from the junctions. We present clear experimental evidence of the interplay of the inverse proximity effect and magnetic field revealing itself in the superconducting gap enhancement and significant improvement of the turnstile characteristics. The observed interplay and its theoretical explanation in the context of QP overheating are important for various superconducting and hybrid nanoelectronic devices, which find applications in quantum computation, photon detection, and quantum metrology.

The superconducting proximity effect in graphene can be used to create Josephson junctions with critical currents that can be tuned using local field-effect gates. These junctions have the potential to add functionality to existing technologies; for example, superconducting quantum interference device (SQUID) magnetometers with adaptive dynamic range and superconducting qubits with fast electrical control. Here, we present measurements of graphene-based superconducting quantum interference devices incorporating ballistic Josephson junctions that can be controlled individually. We investigate the magnetic field response of the SQUIDs as the junctions are gated and as the device is tuned between symmetric and asymmetric configurations. We find a highest transfer function 300 lV/U0, which compares favorably with conventional, low temperature DC SQUIDs. With low noise readout electronics and optimised geometries, devices based on ballistic graphene Josephson junctions have the potential to match the sensitivity of traditional SQUIDs while also providing additional functionality.