The Josephson heat interferometer

Microwave quantum diode

The fragile nature of quantum circuits is a major bottleneck to scalable quantum applications. Operating at cryogenic temperatures, quantum circuits are highly vulnerable to amplifier backaction and external noise. Non-reciprocal microwave devices such as circulators and isolators are used for this purpose. These devices have a considerable footprint in cryostats, limiting the scalability of quantum circuits. As a proof-of-concept, here we report a compact microwave diode architecture, which exploits the non-linearity of a superconducting flux qubit. At the qubit degeneracy point we experimentally demonstrate a significant difference between the power levels transmitted in opposite directions. The observations align with the proposed theoretical model. At - 99 dBm input power, and near the qubit-resonator avoided crossing region, we report the transmission rectification ratio exceeding 90% for a 50 MHz wide frequency range from 6.81 GHz to 6.86 GHz, and over 60% for the 250 MHz range from 6.67 GHz to 6.91 GHz. The presented architecture is compact, and easily scalable towards multiple readout channels, potentially opening up diverse opportunities in quantum information, microwave read-out and optomechanics.

Bolometric detection of Josephson inductance in a highly resistive environment

The Josephson junction is a building block of quantum circuits. Its behavior, well understood when treated as an isolated entity, is strongly affected by coupling to an electromagnetic environment. In 1983, Schmid predicted that a Josephson junction shunted by a resistance exceeding the resistance quantum RQ = h/4e2 ≈ 6.45 kΩ for Cooper pairs would become insulating since the phase fluctuations would destroy the coherent Josephson coupling. However, recent microwave measurements have questioned this interpretation. Here, we insert a small Josephson junction in a Johnson-Nyquist-type setup where it is driven by weak current noise arising from thermal fluctuations. Our heat probe minimally perturbs the junction's equilibrium, shedding light on features not visible in charge transport. We find that the Josephson critical current completely vanishes in DC charge transport measurement, and the junction demonstrates Coulomb blockade in agreement with the theory. Surprisingly, thermal transport measurements show that the Josephson junction acts as an inductor at high frequencies, unambiguously demonstrating that a supercurrent survives despite the Coulomb blockade observed in DC measurements.

Thermophase Seebeck Coefficient in Hybridized Superconductor-Quantum-Dot-Superconductor Josephson Junction Side-Coupled to Majorana Nanowire

The dc Josephson current is generated from phase difference between two superconductors separated by a mesoscopic thin film (Josephson junction) without external bias voltage. In the presence of a temperature gradient across the superconductors, a thermal phase is induced under the condition of open circuit. This is very similar to the Seebeck effect in the usual thermoelectric effect, and the thermal phase is thus named as thermophase Seebeck coefficient (TPSC). Here we find obvious enhancement and sign change of the TPSC unique to the Josephson junction composing of two superconductors connected to a semiconductor quantum dot (QD), which is additionally side-coupled to a nanowire hosting Majorana bound states (MBSs), the system denoted by S-MQD-S. These result arise from the newly developed states near the Fermi level of the superconductors due to the QD-MBS hybridization when the dot level is within the superconducting gap. The sign change of the TPSC provides a strong evidence of the existence of MBSs, and is absent if the QD is coupled to regular fermion, such as another QD (system denoted by S-DQD-S). We show that the magnitude and sign of the TPSC are sensitive to the physical quantities including interaction strength between the QD and MBSs, direct overlap between the MBSs, system equilibrium temperature, as well as hopping amplitude between the QD and the superconductors. The obtained results are explained with the help of the current-carrying density of the states (CCDOS), and may be useful in interdisciplinary research areas of Josephson and Majorana physics.

Top-ranked cycle flux network analysis of molecular photocells

We introduce a top-ranked cycle flux ranking scheme of network analysis to assess the performance of molecular junction solar cells. By mapping the Lindblad master equation to the quantum-transition network, we propose a microscopic Hamiltonian description underpinning the rate equations commonly used to characterize molecular photocells. Our approach elucidates the paramount significance of edge flux and unveils two pertinent electron transfer pathways that play equally important roles in robust photocurrent generation. Furthermore, we demonstrate that nonradiative loss processes impede the maximum power efficiency of photocells, which may otherwise be above the Curzon-Ahlborn limit. These findings shed light on the intricate functionalities that govern molecular photovoltaics and offer a comprehensive approach to address them in a systematic way.

Energy dynamics, heat production and heat-work conversion with qubits: toward the development of quantum machines

We present an overview of recent advances in the study of energy dynamics and mechanisms for energy conversion in qubit systems with special focus on realizations in superconducting quantum circuits. We briefly introduce the relevant theoretical framework to analyze heat generation, energy transport and energy conversion in these systems with and without time-dependent driving considering the effect of equilibrium and non-equilibrium environments. We analyze specific problems and mechanisms under current investigation in the context of qubit systems. These include the problem of energy dissipation and possible routes for its control, energy pumping between driving sources and heat pumping between reservoirs, implementation of thermal machines and mechanisms for energy storage. We highlight the underlying fundamental phenomena related to geometrical and topological properties, as well as many-body correlations. We also present an overview of recent experimental activity in this field.

Josephson quantum spin thermodynamics

A 1D Josephson junction (JJ) loop, doped with a spin-flipper and attached to two thermal reservoirs is shown to operate as a heat engine, or a refrigerator, or a Joule pump or even as a cold pump. When operating as a quantum heat engine, the efficiency of this device exceeds that of some recent Josephson heat engine proposals. Further, as a quantum refrigerator, the coefficient of performance of this device is much higher than previously proposed JJ based refrigerators. In addition, this device can be tuned from engine mode to refrigerator mode or to any other mode, i.e., Joule pump or cold pump by either tuning the temperature of reservoirs, or via the flux enclosed in the JJ loop. In presence of spin flip scattering we can tune our device from engine mode to other operating modes by only changing the enclosed flux in JJ loop without changing the temperatures of the reservoirs. This is potentially an advantage with respect to other proposals. This makes the proposed device much more versatile as regards possible applications.

Photonic heat transport in three terminal superconducting circuit

We report an experimental realization of a three-terminal photonic heat transport device based on a superconducting quantum circuit. The central element of the device is a flux qubit made of a superconducting loop containing three Josephson junctions, which can be tuned by magnetic flux. It is connected to three resonators terminated by resistors. By heating one of the resistors and monitoring the temperatures of the other two, we determine photonic heat currents in the system and demonstrate their tunability by magnetic field at the level of 1 aW. We determine system parameters by performing microwave transmission measurements on a separate nominally identical sample and, in this way, demonstrate clear correlation between the level splitting of the qubit and the heat currents flowing through it. Our experiment is an important step towards realization of heat transistors, heat amplifiers, masers pumped by heat and other quantum heat transport devices.

Quantum heat transport devices are currently intensively studied. Here, the authors report the photonic heat transport modulated by superconducting qubit in a three-terminal device. Flux dependent heat power correlates with microwave measurements.

Cycle Flux Ranking of Network Analysis in Quantum Thermal Devices

Manipulating quantum thermal transport relies on uncovering the principle working cycles of quantum devices. Here we introduce the cycle flux ranking of network analysis to nonequilibrium thermal devices characterized as a quantum-transition network. To excavate the principal mechanism out of complex transport behaviors, we decompose the network into cycle trajectories, collect the cycle fluxes by algebraic graph theory, and select top-ranked cycle fluxes, i.e., the cycle trajectories with highest probabilities. We exemplify the cycle flux ranking in typical quantum device models, e.g., a thermal-drag spin-Seebeck pump and a quantum thermal transistor. Top-ranked cycle trajectories indeed elucidate the principal working mechanisms. Therefore, cycle flux ranking provides an alternative perspective that naturally describes the working cycle corresponding to the main functionality of quantum thermal devices, which would further guide the device optimization with desired performance.

Micrometer Sized Hexagonal Chromium Selenide Flakes for Cryogenic Temperature Sensors

Nanoscale thermometers with high sensitivity are needed in domains which study quantum and classical effects at cryogenic temperatures. Here, we present a micrometer sized and nanometer thick chromium selenide cryogenic temperature sensor capable of measuring a large domain of cryogenic temperatures down to tenths of K. Hexagonal Cr-Se flakes were obtained by a simple physical vapor transport method and investigated using scanning electron microscopy, energy dispersive X-ray spectrometry and X-ray photoelectron spectroscopy measurements. The flakes were transferred onto Au contacts using a dry transfer method and resistivity measurements were performed in a temperature range from 7 K to 300 K. The collected data have been fitted by exponential functions. The excellent fit quality allowed for the further extrapolation of resistivity values down to tenths of K. It has been shown that the logarithmic sensitivity of the sensor computed over a large domain of cryogenic temperature is higher than the sensitivity of thermometers commonly used in industry and research. This study opens the way to produce Cr-Se sensors for classical and quantum cryogenic measurements.

Quantum Transport of Particles and Entropy

A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric effects, and connects the various transport coefficients to certain thermodynamic susceptibilities and a diffusion coefficient. In the second part of the paper, the connection between macroscopic thermodynamics and quantum statistics is discussed. It is proposed to employ not particles, but elementary Fermi- or Bose-systems as the elementary building blocks of ideal quantum gases. In this way, the transport not only of particles but also of entropy can be derived in a concise way, and is illustrated both for ballistic quantum wires, and for diffusive conductors. In particular, the quantum interference of entropy flow is in close correspondence to that of electric current.

Gate-Controlled Supercurrent in Epitaxial Al/InAs Nanowires

Gate-controlled supercurrent (GCS) in superconducting nanobridges has recently attracted attention as a means to create superconducting switches. Despite the clear advantages for applications, the microscopic mechanism of this effect is still under debate. In this work, we realize GCS for the first time in a highly crystalline superconductor epitaxially grown on an InAs nanowire. We show that the supercurrent in the epitaxial Al layer can be switched to the normal state by applying ≃±23 V on a bottom gate insulated from the nanowire by a crystalline hBN layer. Our extensive study of the temperature and magnetic field dependencies suggests that the electric field is unlikely to be the origin of GCS in our device. Though hot electron injection alone cannot explain our experimental findings, a very recent non-equilibrium phonons based picture is compatible with most of our results.

Heat Modulation on Target Thermal Bath via Coherent Auxiliary Bath

We study a scheme of thermal management where a three-qubit system assisted with a coherent auxiliary bath (CAB) is employed to implement heat management on a target thermal bath (TTB). We consider the CAB/TTB being ensemble of coherent/thermal two-level atoms (TLAs), and within the framework of collision model investigate the characteristics of steady heat current (also called target heat current (THC)) between the system and the TTB. It demonstrates that with the help of the quantum coherence of ancillae the magnitude and direction of heat current can be controlled only by adjusting the coupling strength of system-CAB. Meanwhile, we also show that the influences of quantum coherence of ancillae on the heat current strongly depend on the coupling strength of system—CAB, and the THC becomes positively/negatively correlated with the coherence magnitude of ancillae when the coupling strength below/over some critical value. Besides, the system with the CAB could serve as a multifunctional device integrating the thermal functions of heat amplifier, suppressor, switcher and refrigerator, while with thermal auxiliary bath it can only work as a thermal suppressor. Our work provides a new perspective for the design of multifunctional thermal device utilizing the resource of quantum coherence from the CAB.

Gate Control of Superconductivity in Mesoscopic All-Metallic Devices

The possibility to tune, through the application of a control gate voltage, the superconducting properties of mesoscopic devices based on Bardeen-Cooper-Schrieffer metals was recently demonstrated. Despite the extensive experimental evidence obtained on different materials and geometries, a description of the microscopic mechanism at the basis of such an unconventional effect has not been provided yet. This work discusses the technological potential of gate control of superconductivity in metallic superconductors and revises the experimental results, which provide information regarding a possible thermal origin of the effect: first, we review experiments performed on high-critical-temperature elemental superconductors (niobium and vanadium) and show how devices based on these materials can be exploited to realize basic electronic tools, such as a half-wave rectifier. Second, we discuss the origin of the gating effect by showing gate-driven suppression of the supercurrent in a suspended titanium wire and by providing a comparison between thermal and electric switching current probability distributions. Furthermore, we discuss the cold field-emission of electrons from the gate employing finite element simulations and compare the results with experimental data. In our view, the presented data provide a strong indication regarding the unlikelihood of the thermal origin of the gating effect.

Single-Quantum-Dot Heat Valve

We demonstrate gate control of electronic heat flow in a thermally biased single-quantum-dot junction. Electron temperature maps taken in the immediate vicinity of the junction, as a function of the gate and bias voltages applied to the device, reveal clearly defined Coulomb diamond patterns that indicate a maximum heat transfer at the charge degeneracy point. The nontrivial bias and gate dependence of this heat valve results from the quantum nature of the dot at the heart of device and its strong coupling to leads.

Near-field radiative heat transfer between high-temperature superconductors

Near-field radiative heat transfer (NFRHT) management can be achieved using high-temperature superconductors. In this work, we present a theoretical study of the radiative heat transfer between two [Formula: see text] (YBCO) slabs in three different scenarios: Both slabs either in the normal or superconducting state, and only one of them below the superconductor critical temperature [Formula: see text]. The radiative heat transfer is calculated using Rytov's theory of fluctuating electrodynamics, while a two-fluid model describes the dielectric function of the superconducting materials. Our main result is the significant suppression of the NFRHT when one or both of the slabs are superconducting, which is explained in terms of the detailed balance of the charge carriers density together with the sudden reduction of the free electron scattering rate. A critical and unique feature affecting the radiative heat transfer between high-temperature superconductors is the large damping of the mid-infrared carriers which screens the surface plasmon excitation.

Electric field control of radiative heat transfer in a superconducting circuit

Heat is detrimental for the operation of quantum systems, yet it fundamentally behaves according to quantum mechanics, being phase coherent and universally quantum-limited regardless of its carriers. Due to their robustness, superconducting circuits integrating dissipative elements are ideal candidates to emulate many-body phenomena in quantum heat transport, hitherto scarcely explored experimentally. However, their ability to tackle the underlying full physical richness is severely hindered by the exclusive use of a magnetic flux as a control parameter and requires complementary approaches. Here, we introduce a dual, magnetic field-free circuit where charge quantization in a superconducting island enables thorough electric field control. We thus tune the thermal conductance, close to its quantum limit, of a single photonic channel between two mesoscopic reservoirs. We observe heat flow oscillations originating from the competition between Cooper-pair tunnelling and Coulomb repulsion in the island, well captured by a simple model. Our results highlight the consequences of charge-phase conjugation on heat transport, with promising applications in thermal management of quantum devices and design of microbolometers.

Electronic heat flow and thermal shot noise in quantum circuits

When assembling individual quantum components into a mesoscopic circuit, the interplay between Coulomb interaction and charge granularity breaks down the classical laws of electrical impedance composition. Here we explore experimentally the thermal consequences, and observe an additional quantum mechanism of electronic heat transport. The investigated, broadly tunable test-bed circuit is composed of a micron-scale metallic node connected to one electronic channel and a resistance. Heating up the node with Joule dissipation, we separately determine, from complementary noise measurements, both its temperature and the thermal shot noise induced by the temperature difference across the channel. The thermal shot noise predictions are thereby directly validated, and the electronic heat flow is revealed. The latter exhibits a contribution from the channel involving the electrons' partitioning together with the Coulomb interaction. Expanding heat current predictions to include the thermal shot noise, we find a quantitative agreement with experiments.

Thermodynamics of a Phase-Driven Proximity Josephson Junction

We study the thermodynamic properties of a superconductor/normal metal/superconductor Josephson junction in the short limit. Owing to the proximity effect, such a junction constitutes a thermodynamic system where phase difference, supercurrent, temperature and entropy are thermodynamical variables connected by equations of state. These allow conceiving quasi-static processes that we characterize in terms of heat and work exchanged. Finally, we combine such processes to construct a Josephson-based Otto and Stirling cycles. We study the related performance in both engine and refrigerator operating mode.

Strong system-bath coupling induces negative differential thermal conductance and heat amplification in nonequilibrium two-qubit systems

Quantum heat transfer is analyzed in nonequilibrium two-qubits systems by applying the nonequilibrium polaron-transformed Redfield equation combined with full counting statistics. Steady-state heat currents with weak and strong qubit-bath couplings are clearly unified. Within the two-terminal setup, the negative differential thermal conductance is unraveled with strong qubit-bath coupling and finite qubit splitting energy. The partially strong spin-boson interaction is sufficient to show the negative differential thermal conductance. Based on the three-terminal setup, in which two qubits are asymmetrically coupled to three thermal baths, a giant heat amplification factor is observed with strong qubit-bath coupling. Moreover, the strong interaction of either the left or right spin-boson coupling is able to exhibit the apparent heat amplification effect.

Thermal transport of Josephson junction based on two-dimensional electron gas

We study the phase-dependent thermal transport of a short temperature-biased Josephson junction based on two-dimensional electron gas (2DEG) with both Rashba and Dresselhaus couplings. Except for thermal equilibrium temperature T, characters of thermal transport can also be manipulated by interaction parameter h0 and the parameter [Formula: see text] . A larger value and a sharper switching behavior of thermal conductance can be obtained if h0 takes suitable values and [Formula: see text] is larger. Finally, we propose a possible experimental setup based on the discussed Josephson junction and find that the temperature of the right superconducting electrode TR is influenced by the same three parameters in a similar way with thermal conductance. This setup may provide a valid method to select moderately-doped 2DEG materials and superconducting electrodes to control the change of temperature and obtain an efficient temperature regulator.

A Brief Review on the Recent Experimental Advances in Thermal Rectification at the Nanoscale

The concept of thermal rectification was put forward decades ago. It is a phenomenon in which the heat flux along one direction varies as the sign of temperature gradient changes. In bulk materials, thermal rectification has been realized at contact interfaces by manufacturing asymmetric effective contact areas, electron transport, temperature dependence of thermal conductivity and so on. The mechanism of thermal rectification has been studied intensively by using both experimental and theoretical methods. In recent years, with the rapid development of nanoscience and technology, the active control and management of heat transport at the nanoscale has become an important task and has attracted much attention. As the most fundamental component, the development and utilization of a nanothermal rectifier is the key technology. Although many research papers have been published in this field, due to the significant challenge in manufacturing asymmetric nanostructures, most of the publications are focused on molecular dynamics simulation and theoretical analysis. Great effort is urgently required in the experimental realization of thermal rectification at the nanoscale, laying a solid foundation for computation and theoretical modeling. The aim of this brief review is to introduce the most recent experimental advances in thermal rectification at the nanoscale and discuss the physical mechanisms. The new nanotechnology and method can be used to improve our ability to further design and produce efficient thermal devices with a high rectification ratio.

Breakdown of the Wiedemann-Franz law in a unitary Fermi gas

We report on coupled heat and particle transport measurements through a quantum point contact (QPC) connecting two reservoirs of resonantly interacting, finite temperature Fermi gases. After heating one of them, we observe a particle current flowing from cold to hot. We monitor the temperature evolution of the reservoirs and find that the system evolves after an initial response into a nonequilibrium steady state with finite temperature and chemical potential differences across the QPC. In this state any relaxation in the form of heat and particle currents vanishes. From our measurements we extract the transport coefficients of the QPC and deduce a Lorenz number violating the Wiedemann-Franz law by one order of magnitude, a characteristic persisting even for a wide contact. In contrast, the Seebeck coefficient takes a value close to that expected for a noninteracting Fermi gas and shows a smooth decrease as the atom density close to the QPC is increased beyond the superfluid transition. Our work represents a fermionic analog of the fountain effect observed with superfluid helium and poses challenges for microscopic modeling of the finite temperature dynamics of the unitary Fermi gas.

Phase-coherent solitonic Josephson heat oscillator

Since its recent foundation, phase-coherent caloritronics has sparkled continuous interest giving rise to numerous concrete applications. This research field deals with the coherent manipulation of heat currents in mesoscopic superconducting devices by mastering the Josephson phase difference. Here, we introduce a new generation of devices for fast caloritronics able to control local heat power and temperature through manipulation of Josephson vortices, i.e., solitons. Although most salient features concerning Josephson vortices in long Josephson junctions were comprehensively hitherto explored, little is known about soliton-sustained coherent thermal transport. We demonstrate that the soliton configuration determines the temperature profile in the junction, so that, in correspondence of each magnetically induced soliton, both the flowing thermal power and the temperature significantly enhance. Finally, we thoroughly discuss a fast solitonic Josephson heat oscillator, whose frequency is in tune with the oscillation frequency of the magnetic drive. Notably, the proposed heat oscillator can effectively find application as a tunable thermal source for nanoscale heat engines and coherent thermal machines.

Andreev bound states and their signatures

Many of the properties of superconductors related to quantum coherence are revealed when the superconducting state is forced to vary in space in response to an external magnetic field, a proximity contact, an interface to a ferromagnet or to impurities embedded in the superconductor. Among the earliest examples is Andreev reflection of an electron into a retro-reflected hole at a normal-superconducting interface. In regions of strong inhomogeneity, multiple Andreev reflection leads to the formation of sub-gap states, Andreev bound states, with excitation energies below the superconducting gap. These states play a central role in our understanding of inhomogeneous superconductors. The discoveries of unconventional superconductivity in many classes of materials, advances in fabrication of superconducting/ferromagnetic hybrids and nanostructures for confining superfluid ³ He, combined with theoretical developments in topological quantum matter have dramatically expanded the significance of branch conversion scattering and Andreev bound state formation. This collection of articles highlights developments in inhomogeneous superconductivity, unconventional superconductivity and topological phases of superfluid ³ He, in which Andreev scattering and bound states underpin much of the physics of these systems. This article provides an introduction to the basic physics of Andreev scattering, bound-state formation and their signatures. The goal is both an introduction for interested readers who are not already experts in the field, and to highlight examples in which branch conversion scattering and Andreev bound states provide unique signatures in the transport properties of superconductors.This article is part of the theme issue 'Andreev bound states'.

Phase-Tunable Josephson Thermal Router

A fundamental aspect of electronics is the ability to distribute a charge current among different terminals. On the other hand, despite the great interest in dissipation, storage, and conversion of heat in solid state structures, the control of thermal currents at the nanoscale is still in its infancy. Here, we show the experimental realization of a phase-tunable thermal router able to control the spatial distribution of an incoming heat current, thus providing the possibility of tuning the electronic temperatures of two output terminals. This ability is obtained thanks to a direct current superconducting quantum interference device (dc SQUID), which can tune the coherent component of the electronic heat currents flowing through its Josephson junctions. By varying the external magnetic flux and the bath temperature, the SQUID allows us to regulate the size and the direction of the thermal gradient between two drain electrodes. Our results offer new opportunities for all microcircuits requiring an accurate energy management, including electronic coolers, quantum information architectures, and thermal logic components.

Thermal transport in topological-insulator-based superconducting hybrid structures with mixed singlet and triplet pairing states

In the framework of the Bogoliubov-de Gennes equation, we investigate the thermal transport properties in topological-insulator-based superconducting hybrid structures with mixed spin-singlet and spin-triplet pairing states, and emphasize the different manifestations of the spin-singlet and spin-triplet pairing states in the thermal transport signatures. It is revealed that the temperature-dependent differential thermal conductance strongly depends on the components of the pairing state, and the negative differential thermal conductance only occurs in the spin-singlet pairing state dominated regime. It is also found that the thermal conductance is profoundly sensitive to the components of the pairing state. In the spin-singlet pairing state controlled regime, the thermal conductance obviously oscillates with the phase difference and junction length. With increasing the proportion of the spin-triplet pairing state, the oscillating characteristic of the thermal conductance fades out distinctly. These results suggest an alternative route for distinguishing the components of pairing states in topological-insulator-based superconducting hybrid structures.

Towards phase-coherent caloritronics in superconducting circuits

The emerging field of phase-coherent caloritronics (from the Latin word calor, heat) is based on the possibility of controlling heat currents by using the phase difference of the superconducting order parameter. The goal is to design and implement thermal devices that can control energy transfer with a degree of accuracy approaching that reached for charge transport by contemporary electronic components. This can be done by making use of the macroscopic quantum coherence intrinsic to superconducting condensates, which manifests itself through the Josephson effect and the proximity effect. Here, we review recent experimental results obtained in the realization of heat interferometers and thermal rectifiers, and discuss a few proposals for exotic nonlinear phase-coherent caloritronic devices, such as thermal transistors, solid-state memories, phase-coherent heat splitters, microwave refrigerators, thermal engines and heat valves. Besides being attractive from the fundamental physics point of view, these systems are expected to have a vast impact on many cryogenic microcircuits requiring energy management, and possibly lay the first stone for the foundation of electronic thermal logic.

High operating temperature in V-based superconducting quantum interference proximity transistors

Here we report the fabrication and characterization of fully superconducting quantum interference proximity transistors (SQUIPTs) based on the implementation of vanadium (V) in the superconducting loop. At low temperature, the devices show high flux-to-voltage (up to 0.52 mV/Φ₀) and flux-to-current (above 12 nA/Φ₀) transfer functions, with the best estimated flux sensitivity ~ 2.6 μΦ₀/(Hz)^1/2 reached under fixed voltage bias, where Φ₀ is the flux quantum. The interferometers operate up to T_bath  \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\simeq $$\end{document}≃ 2 K, with an improvement of 70% of the maximal operating temperature with respect to early SQUIPTs design. The main features of the V-based SQUIPT are described within a simplified theoretical model. Our results open the way to the realization of SQUIPTs that take advantage of the use of higher-gap superconductors for ultra-sensitive nanoscale applications that operate at temperatures well above 1 K.

Quantum-circuit refrigerator

Quantum technology promises revolutionizing applications in information processing, communications, sensing and modelling. However, efficient on-demand cooling of the functional quantum degrees of freedom remains challenging in many solid-state implementations, such as superconducting circuits. Here we demonstrate direct cooling of a superconducting resonator mode using voltage-controllable electron tunnelling in a nanoscale refrigerator. This result is revealed by a decreased electron temperature at a resonator-coupled probe resistor, even for an elevated electron temperature at the refrigerator. Our conclusions are verified by control experiments and by a good quantitative agreement between theory and experimental observations at various operation voltages and bath temperatures. In the future, we aim to remove spurious dissipation introduced by our refrigerator and to decrease the operational temperature. Such an ideal quantum-circuit refrigerator has potential applications in the initialization of quantum electric devices. In the superconducting quantum computer, for example, fast and accurate reset of the quantum memory is needed.

Efficient on-demand cooling of the functional degrees of freedom in solid-state implementations of quantum information processing devices remains a challenge. Here the authors demonstrate direct cooling of a photonic mode of a superconducting resonator using voltage-controllable electron tunnelling.

0-π phase-controllable thermal Josephson junction

Two superconductors coupled by a weak link support an equilibrium Josephson electrical current that depends on the phase difference ϕ between the superconducting condensates. Yet, when a temperature gradient is imposed across the junction, the Josephson effect manifests itself through a coherent component of the heat current that flows opposite to the thermal gradient for |ϕ| < π/2 (refs 2-4). The direction of both the Josephson charge and heat currents can be inverted by adding a π shift to ϕ. In the static electrical case, this effect has been obtained in a few systems, for example via a ferromagnetic coupling or a non-equilibrium distribution in the weak link. These structures opened new possibilities for superconducting quantum logic and ultralow-power superconducting computers. Here, we report the first experimental realization of a thermal Josephson junction whose phase bias can be controlled from 0 to π. This is obtained thanks to a superconducting quantum interferometer that allows full control of the direction of the coherent energy transfer through the junction. This possibility, in conjunction with the completely superconducting nature of our system, provides temperature modulations with an unprecedented amplitude of ∼100 mK and transfer coefficients exceeding 1 K per flux quantum at 25 mK. Then, this quantum structure represents a fundamental step towards the realization of caloritronic logic components such as thermal transistors, switches and memory devices. These elements, combined with heat interferometers and diodes, would complete the thermal conversion of the most important phase-coherent electronic devices and benefit cryogenic microcircuits requiring energy management, such as quantum computing architectures and radiation sensors.

Spin manipulation in nanoscale superconductors

The interplay of superconductivity and magnetism in nanoscale structures has attracted considerable attention in recent years due to the exciting new physics created by the competition of these antagonistic ordering phenomena, and the prospect of exploiting this competition for superconducting spintronics devices. While much of the attention is focused on spin-polarized supercurrents created by the triplet proximity effect, the recent discovery of long range quasiparticle spin transport in high-field superconductors has rekindled interest in spin-dependent nonequilibrium properties of superconductors. In this review, the experimental situation on nonequilibrium spin injection into superconductors is discussed, and open questions and possible future directions of the field are outlined.

Observation of Thermoelectric Currents in High-Field Superconductor-Ferromagnet Tunnel Junctions

We report on the experimental observation of spin-dependent thermoelectric currents in superconductor-ferromagnet tunnel junctions in high magnetic fields. The thermoelectric signals are due to a spin-dependent lifting of the particle-hole symmetry, and are found to be in excellent agreement with recent theoretical predictions. The maximum Seebeck coefficient inferred from the data is about -100  μV/K, much larger than commonly found in metallic structures. Our results directly prove the coupling of spin and heat transport in high-field superconductors.

Nanoscale phase engineering of thermal transport with a Josephson heat modulator

Macroscopic quantum phase coherence has one of its pivotal expressions in the Josephson effect, which manifests itself both in charge and energy transport. The ability to master the amount of heat transferred through two tunnel-coupled superconductors by tuning their phase difference is the core of coherent caloritronics, and is expected to be a key tool in a number of nanoscience fields, including solid-state cooling, thermal isolation, radiation detection, quantum information and thermal logic. Here, we show the realization of the first balanced Josephson heat modulator designed to offer full control at the nanoscale over the phase-coherent component of thermal currents. Our device provides magnetic-flux-dependent temperature modulations up to 40 mK in amplitude with a maximum of the flux-to-temperature transfer coefficient reaching 200 mK per flux quantum at a bath temperature of 25 mK. Foremost, it demonstrates the exact correspondence in the phase engineering of charge and heat currents, breaking ground for advanced caloritronic nanodevices such as thermal splitters, heat pumps and time-dependent electronic engines.

Thermal electron-tunneling devices as coolers and amplifiers

Nanoscale thermal systems that are associated with a pair of electron reservoirs have been previously studied. In particular, devices that adjust electron tunnels relatively to reservoirs' chemical potentials enjoy the novelty and the potential. Since only two reservoirs and one tunnel exist, however, designers need external aids to complete a cycle, rendering their models non-spontaneous. Here we design thermal conversion devices that are operated among three electron reservoirs connected by energy-filtering tunnels and also referred to as thermal electron-tunneling devices. They are driven by one of electron reservoirs rather than the external power input, and are equivalent to those coupling systems consisting of forward and reverse Carnot cycles with energy selective electron functions. These previously-unreported electronic devices can be used as coolers and thermal amplifiers and may be called as thermal transistors. The electron and energy fluxes of devices are capable of being manipulated in the same or oppsite directions at our disposal. The proposed model can open a new field in the application of nano-devices.

Energetics of an rf SQUID Coupled to Two Thermal Reservoirs

We study energetics of a Josephson tunnel junction connecting a superconducting loop pierced by an external magnetic flux (an rf SQUID) and coupled to two independent thermal reservoirs of different temperature. In the framework of the theory of quantum dissipative systems, we analyze energy currents in stationary states. The stationary energy flow can be periodically modulated by the external magnetic flux exemplifying the rf SQUID as a quantum heat interferometer. We also consider the transient regime and identify three distinct regimes: monotonic decay, damped oscillations and pulse-type behavior of energy currents. The first two regimes can be controlled by the external magnetic flux while the last regime is robust against its variation.

Temperature-Dependent Transformation Thermotics: From Switchable Thermal Cloaks to Macroscopic Thermal Diodes

The macroscopic control of ubiquitous heat flow remains poorly explored due to the lack of a fundamental theoretical method. Here, by establishing temperature-dependent transformation thermotics for treating materials whose conductivity depends on temperature, we show analytical and simulation evidence for switchable thermal cloaking and a macroscopic thermal diode based on the cloaking. The latter allows heat flow in one direction but prohibits the flow in the opposite direction, which is also confirmed by our experiments. Our results suggest that the temperature-dependent transformation thermotics could be a fundamental theoretical method for achieving macroscopic heat rectification, and it could provide guidance both for the macroscopic control of heat flow and for the design of the counterparts of switchable thermal cloaks or macroscopic thermal diodes in other fields like seismology, acoustics, electromagnetics, and matter waves.

A Josephson radiation comb generator

We propose the implementation of a Josephson Radiation Comb Generator (JRCG) based on a dc superconducting quantum interference device (SQUID) driven by an external magnetic field. When the magnetic flux crosses a diffraction node of the critical current interference pattern, the superconducting phase undergoes a jump of π and a voltage pulse is generated at the extremes of the SQUID. Under periodic drive this allows one to generate a sequence of sharp, evenly spaced voltage pulses. In the frequency domain, this corresponds to a comb-like structure similar to the one exploited in optics and metrology. With this device it is possible to generate up to several hundreds of harmonics of the driving frequency. For example, a chain of 50 identical high-critical-temperature SQUIDs driven at 1 GHz can deliver up to a 0.5 nW at 200 GHz. The availability of a fully solid-state radiation comb generator such as the JRCG, easily integrable on chip, may pave the way to a number of technological applications, from metrology to sub-millimeter wave generation.

Rectification of electronic heat current by a hybrid thermal diode

Thermal diodes--devices that allow heat to flow preferentially in one direction--are one of the key tools for the implementation of solid-state thermal circuits. These would find application in many fields of nanoscience, including cooling, energy harvesting, thermal isolation, radiation detection and quantum information, or in emerging fields such as phononics and coherent caloritronics. However, both in terms of phononic and electronic heat conduction (the latter being the focus of this work), their experimental realization remains very challenging. A highly efficient thermal diode should provide a difference of at least one order of magnitude between the heat current transmitted in the forward temperature (T) bias configuration (Jfw) and that generated with T-bias reversal (Jrev), leading to ℛ = Jfw/Jrev ≫ 1 or ≪ 1. So far, ℛ ≈ 1.07-1.4 has been reported in phononic devices, and ℛ ≈ 1.1 has been obtained with a quantum-dot electronic thermal rectifier at cryogenic temperatures. Here, we show that unprecedentedly high ratios of ℛ ≈ 140 can be achieved in a hybrid device combining normal metals tunnel-coupled to superconductors. Our approach provides a high-performance realization of a thermal diode for electronic heat current that could be successfully implemented in true low-temperature solid-state thermal circuits.

Coherent energy transport in classical nonlinear oscillators: An analogy with the Josephson effect

By means of a simple theoretical model and numerical simulations, we demonstrate the presence of persistent energy currents in a lattice of classical nonlinear oscillators with uniform temperature and chemical potential. In analogy with the well-known Josephson effect, the currents are proportional to the sine of the phase differences between the oscillators. Our results elucidate general aspects of nonequilibrium thermodynamics and point towards a way to practically control transport phenomena in a large class of systems. We apply the model to describe the phase-controlled spin-wave current in a bilayer nanopillar.

Very large thermophase in ferromagnetic Josephson junctions

The concept of thermophase refers to the appearance of a phase gradient inside a superconductor originating from the presence of an applied temperature bias across it. The resulting supercurrent flow may, in suitable conditions, fully counterbalance the temperature-bias-induced quasiparticle current therefore preventing the formation of any voltage drop, i.e., a thermovoltage, across the superconductor. Yet, the appearance of a thermophase is expected to occur in Josephson-coupled superconductors as well. Here, we theoretically investigate the thermoelectric response of a thermally biased Josephson junction based on a ferromagnetic insulator. In particular, we predict the occurrence of a very large thermophase that can reach π/2 across the contact for suitable temperatures and structure parameters; i.e., the quasiparticle thermal current can reach the critical current. Such a thermophase can be several orders of magnitude larger than that predicted to occur in conventional Josephson tunnel junctions. In order to assess experimentally the predicted very large thermophase, we propose a realistic setup realizable with state-of-the-art nanofabrication techniques and well-established materials, based on a superconducting quantum interference device. This effect could be of strong relevance in several low-temperature applications, for example, for revealing tiny temperature differences generated by coupling the electromagnetic radiation to one of the superconductors forming the junction.

Superconductive quantum interference magnetometer with high sensitivity achieved by an induced resonance

A fully integrated low noise superconducting quantum interference device (SQUID) in a magnetometer configuration is presented. An intrinsic high voltage responsivity as high as 500 μV/Φ0 has been obtained by introducing a resonance in the voltage - magnetic flux characteristic. This resonance is induced by an integrated superconducting coil surrounding the pick-up coil and connected to one end of the SQUID output. The SQUID magnetometer exhibits a spectral density of magnetic field noise as low as 3 fT/Hz(1/2). In order to verify the suitability of the magnetometer, measurements of bandwidth and slew rate have been performed and compared with those of the same device without the resonance and with additional positive feedback. Due to their good characteristics such devices can be employed in a large number of applications including biomagnetism.

A quantum diffractor for thermal flux

Macroscopic phase coherence between weakly coupled superconductors leads to peculiar interference phenomena. Among these, magnetic flux-driven diffraction might be produced, in full analogy to light diffraction through a rectangular slit. This can be experimentally revealed by the electric current and, notably, also by the heat current transmitted through the circuit. The former was observed more than 50 years ago and represented the first experimental evidence of the phase-coherent nature of the Josephson effect, whereas the second one was still lacking. Here we demonstrate the existence of heat diffraction by measuring the modulation of the electronic temperature of a small metallic electrode nearby-contacted to a thermally biased short Josephson junction subjected to an in-plane magnetic field. The observed temperature dependence exhibits symmetry under magnetic flux reversal, and clear resemblance with a Fraunhofer-like modulation pattern. Our approach, joined to widespread methods for phase-biasing superconducting circuits, might represent an effective tool for controlling the thermal flux in nanoscale devices.

A ballistic quantum ring Josephson interferometer

We report the realization of a ballistic Josephson interferometer. The interferometer is made from a quantum ring etched in a nanofabricated two-dimensional electron gas confined in an InAs-based heterostructure laterally contacted to superconducting niobium leads. The Josephson current flowing through the structure shows oscillations with h/e flux periodicity when threading the loop with a perpendicular magnetic field. This periodicity, in sharp contrast with the h/2e one observed in conventional dc superconducting quantum interference devices, confirms the ballistic nature of the device in agreement with theoretical predictions. This system paves the way for the implementation of interferometric Josephson π-junctions, and for the investigation of Majorana fermions.