Quantized current steps due to the a.c. coherent quantum phase-slip effect.

The a.c. Josephson effect predicted in 19621 and observed experimentally in 19632 as quantized 'voltage steps' (the Shapiro steps) from photon-assisted tunnelling of Cooper pairs is among the most fundamental phenomena of quantum mechanics and is vital for metrological quantum voltage standards. The physically dual effect, the a.c. coherent quantum phase slip (CQPS), photon-assisted tunnelling of magnetic fluxes through a superconducting nanowire, is envisaged to reveal itself as quantized 'current steps'3,4. The basic physical significance of the a.c. CQPS is also complemented by practical importance in future current standards, a missing element for closing the quantum metrology triangle5,6. In 2012, the CQPS was demonstrated as superposition of magnetic flux quanta in superconducting nanowires 7. However, the direct flat current steps in superconductors, the only unavailable basic effect of superconductivity to date, was unattainable due to lack of appropriate materials and challenges in circuit engineering. Here we report the direct observation of the dual Shapiro steps in a superconducting nanowire. The sharp steps are clear up to 26 GHz frequency with current values 8.3 nA and limited by the present set-up bandwidth. The current steps were theoretically predicted in small Josephson junctions 30 years ago5. However, unavoidable broadening in Josephson junctions prevents their direct experimental observation8,9. We solve this problem by placing a thin NbN nanowire in an inductive environment.

Local and Nonlocal Two-Electron Tunneling Processes in a Cooper Pair Splitter.

We measure the rates and coupling coefficients for local Andreev, nonlocal Andreev, and elastic cotunneling processes. The nonlocal Andreev process, giving rise to Cooper pair splitting, exhibits the same coupling coefficient as the elastic cotunneling whereas the local Andreev process is more than 2 orders of magnitude stronger than the corresponding nonlocal one. Theory estimates describe the findings and explain the large difference in the nonlocal and local coupling arising from competition between electron diffusion in the superconductor and tunnel junction transparency.

Universal First-Passage-Time Distribution of Non-Gaussian Currents.

We investigate the fluctuations of the time elapsed until the electric charge transferred through a conductor reaches a given threshold value. For this purpose, we measure the distribution of the first-passage times for the net number of electrons transferred between two metallic islands in the Coulomb blockade regime. Our experimental results are in excellent agreement with numerical calculations based on a recent theory describing the exact first-passage-time distributions for any nonequilibrium stationary Markov process. We also derive a simple analytical approximation for the first-passage-time distribution, which takes into account the non-Gaussian statistics of the electron transport, and show that it describes the experimental distributions with high accuracy. This universal approximation describes a wide class of stochastic processes, and can be used beyond the context of mesoscopic charge transport. In addition, we verify experimentally a fluctuation relation between the first-passage-time distributions for positive and negative thresholds.

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.

Cooper pair splitting controlled by a temperature gradient.

Electrons in two different normal metallic electrodes attached to a sufficiently thin superconducting island may become entangled due to the effect of Cooper pair splitting. This phenomenon is of fundamental importance and may also have serious implications for developing quantum communication technologies. One way to identify Cooper pair splitting is to analyze long-range cross correlations of fluctuating currents in three-terminal hybrid normal-superconducting-normal nanostructures. Here, we theoretically investigate non-trivial behavior of cross-correlated non-local shot noise in the presence of a temperature gradient. We suggest that applying a temperature gradient may serve as an extra tool to control the phenomenon of Cooper pair splitting.

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.

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.

An electron turnstile for frequency-to-power conversion.

Single-electron transport relates an operation frequency f to the emitted current I through the electron charge e as I = ef (refs. 1-5). Similarly, direct frequency-to-power conversion (FPC) links both quantities through a known energy. FPC is a natural candidate for a power standard resorting to the most basic definition of the watt: energy emitted per unit of time. The energy is traceable to Planck's constant and the time is in turn traceable to the unperturbed ground state hyperfine transition frequency of the caesium 133 atom. Hence, FPC comprises a simple and elegant way to realize the watt6. In this spirit, single-photon emission7,8 and detection9 at known rates have been proposed as radiometric standards and experimentally realized10-14. However, power standards are so far only traceable to electrical units, that is, to the volt and the ohm6,15-17. In this Letter, we demonstrate an alternative proposal based on solid-state direct FPC using a hybrid single-electron transistor (SET). The SET injects n (integer) quasi-particles (QPs) per cycle into the two superconducting leads with discrete energies close to their superconducting gap Δ, even at zero source-drain voltage. Furthermore, the application of a bias voltage can vary the distribution of the power among the two leads, allowing for an almost equal power injection nΔf into the two. While in single-electron transport current is related to a fixed universal constant (e), in our approach Δ is a material-dependent quantity. We estimate that under optimized conditions errors can be well below 1%.

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.

Bacterial Nanocellulose Nitrates.

Bacterial nanocellulose (BNC) whose biosynthesis fully conforms to green chemistry principles arouses much interest of specialists in technical chemistry and materials science because of its specific properties, such as nanostructure, purity, thermal stability, reactivity, high crystallinity, etc. The functionalization of the BNC surface remains a priority research area of polymers. The present study was aimed at scaled production of an enlarged BNC sample and at synthesizing cellulose nitrate (CN) therefrom. Cyclic biosynthesis of BNC was run in a semisynthetic glucose medium of 10-72 L in volume by using the Medusomyces gisevii Sa-12 symbiont. The most representative BNC sample weighing 6800 g and having an α-cellulose content of 99% and a polymerization degree of 4000 was nitrated. The nitration of freeze-dried BNC was performed with sulfuric-nitric mixed acid. BNC was examined by scanning electron microscopy (SEM) and infrared spectroscopy (IR), and CN was explored to a fuller extent by SEM, IR, thermogravimetric analysis/differential scanning analysis (TGA/DTA) and 13C nuclear magnetic resonance (NMR) spectroscopy. The three-cycle biosynthesis of BNC with an increasing volume of the nutrient medium from 10 to 72 L was successfully scaled up in nonsterile conditions to afford 9432 g of BNC gel-films. CNs with a nitrogen content of 10.96% and a viscosity of 916 cP were synthesized. It was found by the SEM technique that the CN preserved the 3D reticulate structure of initial BNC fibers a marginal thickening of the nanofibers themselves. Different analytical techniques reliably proved the resultant nitration product to be CN. When dissolved in acetone, the CN was found to form a clear high-viscosity organogel whose further studies will broaden application fields of the modified BNC.