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We consider a current-biased dc SQUID in the presence of an applied time-dependent bias current or magnetic flux. The phase dynamics of such a Josephson device is equivalent to that of a quantum particle trapped in a $1-$D anharmonic potential, subject to external time-dependent control fields, {it i.e.} a driven multilevel quantum system. The problem of finding the required time-dependent control field that will steer the system from a given initial state to a desired final state at a specified final time is formulated in the framework of optimal control theory. Using the spectral filter technique, we show that the selected optimal field which induces a coherent population transfer between quantum states is represented by a carrier signal having a constant frequency but which is time-varied both in amplitude and phase. The sensitivity of the optimal solution to parameter perturbations is also addressed.
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Despite metals are believed to be insensitive to field-effect and conventional Bardeen-Cooper-Schrieffer (BCS) theories predict the electric field to be ineffective on conventional superconductors, a number of gating experiments showed the possibility of modulating the conductivity of metallic thin films and the critical temperature of conventional superconductors. All these experimental features have been explained by simple charge accumulation/depletion. In 2018, electric field control of supercurrent in conventional metallic superconductors has been demonstrated in a range of electric fields where the induced variation of charge carrier concentration in metals is negligibly small. In fact, no changes of normal state resistance and superconducting critical temperature were reported. Here, we review the experimental results obtained in the realization of field-effect metallic superconducting devices exploiting this unexplained phenomenon. We will start by presenting the seminal results on superconducting BCS wires and nano-constriction Josephson junctions (Dayem bridges) made of different materials, such as titanium, aluminum and vanadium. Then, we show the mastering of the Josephson supercurrent in superconductor-normal metal-superconductor proximity transistors suggesting that the presence of induced superconducting correlations are enough to see this unconventional field-effect. Later, we present the control of the interference pattern in a superconducting quantum interference device indicating the coupling of the electric field with thesuperconducting phase. Among the possible applications of the presented phenomenology, we conclude this review by proposing some devices that may represent a breakthrough in superconducting quantum and classical computation.
The act of measurement bridges the quantum and classical worlds by projecting a superposition of possible states into a single, albeit probabilistic, outcome. The time-scale of this instantaneous process can be stretched using weak measurements so that it takes the form of a gradual random walk towards a final state. Remarkably, the interim measurement record is sufficient to continuously track and steer the quantum state using feedback. We monitor the dynamics of a resonantly driven quantum two-level system -- a superconducting quantum bit --using a near-noiseless parametric amplifier. The high-fidelity measurement output is used to actively stabilize the phase of Rabi oscillations, enabling them to persist indefinitely. This new functionality shows promise for fighting decoherence and defines a path for continuous quantum error correction.
Spectroscopy is a powerful tool to probe physical, chemical, and biological systems. Recent advances in microfabrication have introduced novel, intriguing mesoscopic quantum systems including superconductor-semiconductor hybrid devices and topologically non-trivial electric circuits. A sensitive, general purpose spectrometer to probe the energy levels of these systems is lacking. We propose an on-chip absorption spectrometer functioning well into the millimeter wave band which is based on a voltage-biased superconducting quantum interference device. We demonstrate the capabilities of the spectrometer by coupling it to a variety of superconducting systems, probing phenomena such as quasiparticle and plasma excitations. We perform spectroscopy of a microscopic tunable non-linear resonator in the 40-50 GHz range and measure transitions to highly excited states. The Josephson junction spectrometer, with unprecedented frequency range, sensitivity, and coupling strength will enable new experiments in linear and non-linear spectroscopy of novel mesoscopic systems.
A spatially oscillating pair potential $Delta(r)=Delta_0 e^{2i Kcdot r}$ with momentum $K>Delta_0/hbar v$ drives a deconfinement transition of the Majorana bound states in the vortex cores of a Fu-Kane heterostructure (a 3D topological insulator with Fermi velocity $v$, on a superconducting substrate with gap $Delta_0$, in a perpendicular magnetic field). In the deconfined phase at zero chemical potential the Majorana fermions form a dispersionless Landau level, protected by chiral symmetry against broadening due to vortex scattering. The coherent superposition of electrons and holes in the Majorana Landau level is detectable as a local density of states oscillation with wave vector $sqrt{K^2-(Delta_0/hbar v)^2}$. The striped pattern also provides a means to measure the chirality of the Majorana fermions.
We measure the non-dissipative supercurrent in a single InAs self-assembled quantum dot (QD) coupled to superconducting leads. The QD occupation is both tuned by a back-gate electrode and lateral side-gate. The geometry of the side-gate allows tuning of the QD-lead tunnel coupling in a region of constant electron number with appropriate orbital state. Using the side-gate effect we study the competition between Kondo correlations and superconducting pairing on the QD, observing a decrease in the supercurrent when the Kondo temperature is reduced below the superconducting energy gap in qualitative agreement with theoretical predictions.
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