Thermal Transport in Nanoelectronic Devices Cooled by On-Chip Magnetic Refrigeration.

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.

On the origin of the controversial electrostatic field effect in superconductors.

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.

Nanoscale real-time detection of quantum vortices at millikelvin temperatures.

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 10 mK. 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.

Operating Nanobeams in a Quantum Fluid.

Microelectromechanical (MEMS) and nanoelectromechanical systems (NEMS) are ideal candidates for exploring quantum fluids, since they can be manufactured reproducibly, cover the frequency range from hundreds of kilohertz up to gigahertz and usually have very low power dissipation. Their small size offers the possibility of probing the superfluid on scales comparable to, and below, the coherence length. That said, there have been hitherto no successful measurements of NEMS resonators in the liquid phases of helium. Here we report the operation of doubly-clamped aluminium nanobeams in superfluid 4He at temperatures spanning the superfluid transition. The devices are shown to be very sensitive detectors of the superfluid density and the normal fluid damping. However, a further and very important outcome of this work is the knowledge that now we have demonstrated that these devices can be successfully operated in superfluid 4He, it is straightforward to apply them in superfluid 3He which can be routinely cooled to below 100 µK. This brings us into the regime where nanomechanical devices operating at a few MHz frequencies may enter their mechanical quantum ground state.

On-chip magnetic cooling of a nanoelectronic device.

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 advant- age. 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.

Multiplexing Superconducting Qubit Circuit for Single Microwave Photon Generation.

We report on a device that integrates eight superconducting transmon qubits in λ / 4 superconducting coplanar waveguide resonators fed from a common feedline. Using this multiplexing architecture, each resonator and qubit can be addressed individually, thus reducing the required hardware resources and allowing their individual characterisation by spectroscopic methods. The measured device parameters agree with the designed values, and the resonators and qubits exhibit excellent coherence properties and strong coupling, with the qubit relaxation rate dominated by the Purcell effect when brought in resonance with the resonator. Our analysis shows that the circuit is suitable for generation of single microwave photons on demand with an efficiency exceeding 80%.

Single-electron tunneling through an individual arsenic dopant in silicon.

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.

Nanoelectronic primary thermometry below 4 mK.

Cooling nanoelectronic structures to millikelvin temperatures presents extreme challenges in maintaining thermal contact between the electrons in the device and an external cold bath. It is typically found that when nanoscale devices are cooled to ∼ 10 mK the electrons are significantly overheated. Here we report the cooling of electrons in nanoelectronic Coulomb blockade thermometers below 4 mK. The low operating temperature is attributed to an optimized design that incorporates cooling fins with a high electron-phonon coupling and on-chip electronic filters, combined with low-noise electronic measurements. By immersing a Coulomb blockade thermometer in the (3)He/(4)He refrigerant of a dilution refrigerator, we measure a lowest electron temperature of 3.7 mK and a trend to a saturated electron temperature approaching 3 mK. This work demonstrates how nanoelectronic samples can be cooled further into the low-millikelvin range.

Coherent quantum phase slip.

A hundred years after the discovery of superconductivity, one fundamental prediction of the theory, coherent quantum phase slip (CQPS), has not been observed. CQPS is a phenomenon exactly dual to the Josephson effect; whereas the latter is a coherent transfer of charges between superconducting leads, the former is a coherent transfer of vortices or fluxes across a superconducting wire. In contrast to previously reported observations of incoherent phase slip, CQPS has been only a subject of theoretical study. Its experimental demonstration is made difficult by quasiparticle dissipation due to gapless excitations in nanowires or in vortex cores. This difficulty might be overcome by using certain strongly disordered superconductors near the superconductor-insulator transition. Here we report direct observation of CQPS in a narrow segment of a superconducting loop made of strongly disordered indium oxide; the effect is made manifest through the superposition of quantum states with different numbers of flux quanta. As with the Josephson effect, our observation should lead to new applications in superconducting electronics and quantum metrology.

Dynamics of coherent and incoherent emission from an artificial atom in a 1D space.

We study dynamics of a two-level superconducting quantum system, analogous to a natural atom in an open space, by measuring the evolution of its coherent and incoherent emission. The emitted waves containing full information about the states of the artificial atom are efficiently collected due to strong atom-transmission-line coupling. This allows us to do simultaneous measurements of all the quantum state projections and perform a full characterization of the system. We derive coherence times and extract the two-time correlation function from the dynamics of the coherent emission.

Real-time observation of discrete Andreev tunneling events.

We provide a direct proof of two-electron Andreev transitions in a superconductor-normal-metal tunnel junction by detecting them in a real-time electron counting experiment. Our results are consistent with ballistic Andreev transport with an order of magnitude higher rate than expected for a uniform barrier, suggesting that only part of the interface is effectively contributing to the transport. These findings are quantitatively supported by our direct current measurements in single-electron transistors with similar tunnel barriers.

Electromagnetically induced transparency on a single artificial atom.

We present experimental observation of electromagnetically induced transparency (EIT) on a single macroscopic artificial "atom" (superconducting quantum system) coupled to open 1D space of a transmission line. Unlike in an optical media with many atoms, the single-atom EIT in 1D space is revealed in suppression of reflection of electromagnetic waves, rather than absorption. The observed almost 100% modulation of the reflection and transmission of propagating microwaves demonstrates full controllability of individual artificial atoms and a possibility to manipulate the atomic states. The system can be used as a switchable mirror of microwaves and opens a good perspective for its applications in photonic quantum information processing and other fields.

Environment-assisted tunneling as an origin of the Dynes density of states.

We show that the effect of a high-temperature environment in current transport through a normal metal-insulator-superconductor tunnel junction can be described by an effective density of states in the superconductor. In the limit of a resistive low-Ohmic environment, this density of states reduces into the well-known Dynes form. Our theoretical result is supported by experiments in engineered environments. We apply our findings to improve the performance of a single-electron turnstile, a potential candidate for a metrological current source.

Ultimate on-chip quantum amplifier.

We report amplification of electromagnetic waves by a single artificial atom in open 1D space. Our three-level artificial atom--a superconducting quantum circuit--coupled to a transmission line presents an analog of a natural atom in open space. The system is the most fundamental quantum amplifier whose gain is limited by a spontaneous emission mechanism. The noise performance is determined by the quantum noise revealed in the spectrum of spontaneous emission, also characterized in our experiments.

Resonance fluorescence of a single artificial atom.

An atom in open space can be detected by means of resonant absorption and reemission of electromagnetic waves, known as resonance fluorescence, which is a fundamental phenomenon of quantum optics. We report on the observation of scattering of propagating waves by a single artificial atom. The behavior of the artificial atom, a superconducting macroscopic two-level system, is in a quantitative agreement with the predictions of quantum optics for a pointlike scatterer interacting with the electromagnetic field in one-dimensional open space. The strong atom-field interaction as revealed in a high degree of extinction of propagating waves will allow applications of controllable artificial atoms in quantum optics and photonics.

Single-electronic radio-frequency refrigerator.

We demonstrate experimentally that a hybrid single-electron transistor with superconducting leads and a normal-metal island can be refrigerated by an alternating voltage applied to the gate electrode. The simultaneous measurement of the dc current induced by the rf gate through the device at a small bias voltage serves as an in situ thermometer.

Single artificial-atom lasing.

Solid-state superconducting circuits are versatile systems in which quantum states can be engineered and controlled. Recent progress in this area has opened up exciting possibilities for exploring fundamental physics as well as applications in quantum information technology; in a series of experiments it was shown that such circuits can be exploited to generate quantum optical phenomena, by designing superconducting elements as artificial atoms that are coupled coherently to the photon field of a resonator. Here we demonstrate a lasing effect with a single artificial atom--a Josephson-junction charge qubit--embedded in a superconducting resonator. We make use of one of the properties of solid-state artificial atoms, namely that they are strongly and controllably coupled to the resonator modes. The device is essentially different from existing lasers and masers; one and the same artificial atom excited by current injection produces many photons.

Temperature square dependence of the low frequency charge noise in the Josephson junction qubits.

To verify the hypothesis about the common origin of the low-frequency 1/f noise and the quantum f noise recently measured in the Josephson charge qubits, we study the temperature dependence of the 1/f noise and decay of coherent oscillations. The T2 dependence of the 1/f noise is experimentally demonstrated, which supports the hypothesis. We also show that dephasing in the Josephson charge qubits off the electrostatic energy degeneracy point is consistently explained by the same low-frequency 1/f noise that is observed in the transport measurements.