Hybrid quantum systems with high-T[Formula: see text] superconducting resonators.

Superconducting microwave resonators are crucial elements of microwave circuits, offering a wide range of potential applications in modern science and technology. While conventional low-T[Formula: see text] superconductors are mainly employed, high-T[Formula: see text] cuprates could offer enhanced temperature and magnetic field operating ranges. Here, we report the realization of [Formula: see text] superconducting coplanar waveguide resonators, and demonstrate a continuous evolution from a lossy undercoupled regime, to a lossless overcoupled regime by adjusting the device geometry, in good agreement with circuit model theory. A high-quality factor resonator was then used to perform electron spin resonance measurements on a molecular spin ensemble across a temperature range spanning two decades. We observe spin-cavity hybridization indicating coherent coupling between the microwave field and the spins in a highly cooperative regime. The temperature dependence of the Rabi splitting and the spin relaxation time point toward an antiferromagnetic coupling of the spins below 2 K. Our findings indicate that high-Tc superconducting resonators hold great promise for the development of functional circuits. Additionally, they suggest novel approaches for achieving hybrid quantum systems based on high-T[Formula: see text] superconductors and for conducting electron spin resonance measurements over a wide range of magnetic fields and temperatures.

Superfluid stiffness of a KTaO3-based two-dimensional electron gas.

After almost twenty years of intense work on the celebrated LaAlO3/SrTiO3system, the recent discovery of a superconducting two-dimensional electron gas (2-DEG) in (111)-oriented KTaO3-based heterostructures injects new momentum to the field of oxides interface. However, while both interfaces share common properties, experiments also suggest important differences between the two systems. Here, we report gate tunable superconductivity in 2-DEGs generated at the surface of a (111)-oriented KTaO3 crystal by the simple sputtering of a thin Al layer. We extract the superfluid stiffness of the 2-DEGs and show that its temperature dependence is consistent with a node-less superconducting order parameter having a gap value larger than expected within a simple BCS weak-coupling limit model. The superconducting transition follows the Berezinskii-Kosterlitz-Thouless scenario, which was not reported on SrTiO3-based interfaces. Our finding offers innovative perspectives for fundamental science but also for device applications in a variety of fields such as spin-orbitronics and topological electronics.

Extremely long-range, high-temperature Josephson coupling across a half-metallic ferromagnet.

The Josephson effect results from the coupling of two superconductors across a spacer such as an insulator, a normal metal or a ferromagnet to yield a phase coherent quantum state. However, in junctions with ferromagnetic spacers, very long-range Josephson effects have remained elusive. Here we demonstrate extremely long-range (micrometric) high-temperature (tens of kelvins) Josephson coupling across the half-metallic manganite La0.7Sr0.3MnO3 combined with the superconducting cuprate YBa2Cu3O7. These planar junctions, in addition to large critical currents, display the hallmarks of Josephson physics, such as critical current oscillations driven by magnetic flux quantization and quantum phase locking effects under microwave excitation (Shapiro steps). The latter display an anomalous doubling of the Josephson frequency predicted by several theories. In addition to its fundamental interest, the marriage between high-temperature, dissipationless quantum coherent transport and full spin polarization brings opportunities for the practical realization of superconducting spintronics, and opens new perspectives for quantum computing.

Quasiparticle tunnel electroresistance in superconducting junctions.

The term tunnel electroresistance (TER) denotes a fast, non-volatile, reversible resistance switching triggered by voltage pulses in ferroelectric tunnel junctions. It is explained by subtle mechanisms connected to the voltage-induced reversal of the ferroelectric polarization. Here we demonstrate that effects functionally indistinguishable from the TER can be produced in a simpler junction scheme-a direct contact between a metal and an oxide-through a different mechanism: a reversible redox reaction that modifies the oxide's ground-state. This is shown in junctions based on a cuprate superconductor, whose ground-state is sensitive to the oxygen stoichiometry and can be tracked in operando via changes in the conductance spectra. Furthermore, we find that electrochemistry is the governing mechanism even if a ferroelectric is placed between the metal and the oxide. Finally, we extend the concept of electroresistance to the tunnelling of superconducting quasiparticles, for which the switching effects are much stronger than for normal electrons. Besides providing crucial understanding, our results provide a basis for non-volatile Josephson memory devices.

Gap suppression at a Lifshitz transition in a multi-condensate superconductor.

In multi-orbital materials, superconductivity can exhibit several coupled condensates. In this context, quantum confinement in two-dimensional superconducting oxide interfaces offers new degrees of freedom to engineer the band structure and selectively control the occupancy of 3d orbitals by electrostatic doping. Here, we use resonant microwave transport to extract the superfluid stiffness of the (110)-oriented LaAlO3/SrTiO3 interface in the entire phase diagram. We provide evidence of a transition from single-condensate to two-condensate superconductivity driven by continuous and reversible electrostatic doping, which we relate to the Lifshitz transition between 3d bands based on numerical simulations of the quantum well. We find that the superconducting gap is suppressed while the second band is populated, challenging Bardeen-Cooper-Schrieffer theory. We ascribe this behaviour to the existence of superconducting order parameters with opposite signs in the two condensates due to repulsive coupling. Our findings offer an innovative perspective on the possibility to tune and control multiple-orbital physics in superconducting interfaces.

Competition between electron pairing and phase coherence in superconducting interfaces.

In LaAlO3/SrTiO3 heterostructures, a gate tunable superconducting electron gas is confined in a quantum well at the interface between two insulating oxides. Remarkably, the gas coexists with both magnetism and strong Rashba spin-orbit coupling. However, both the origin of superconductivity and the nature of the transition to the normal state over the whole doping range remain elusive. Here we use resonant microwave transport to extract the superfluid stiffness and the superconducting gap energy of the LaAlO3/SrTiO3 interface as a function of carrier density. We show that the superconducting phase diagram of this system is controlled by the competition between electron pairing and phase coherence. The analysis of the superfluid density reveals that only a very small fraction of the electrons condenses into the superconducting state. We propose that this corresponds to the weak filling of high-energy dxz/dyz bands in the quantum well, more apt to host superconductivity.

Phase Separation from Electron Confinement at Oxide Interfaces.

Oxide heterostructures are of great interest for both fundamental and applicative reasons. In particular, the two-dimensional electron gas at the LaAlO_{3}/SrTiO_{3} or LaTiO_{3}/SrTiO_{3} interfaces displays many different properties and functionalities. However, there are clear experimental indications that the interface electronic state is strongly inhomogeneous and therefore it is crucial to investigate possible intrinsic mechanisms underlying this inhomogeneity. Here, the electrostatic potential confining the electron gas at the interface is calculated self-consistently, finding that such confinement may induce phase separation, to avoid a thermodynamically unstable state with a negative compressibility. This provides a robust mechanism for the inhomogeneous character of these interfaces.

Interplay between density and superconducting quantum critical fluctuations.

We consider the case of a density-driven metal-superconductor transition in the proximity of an electronic phase separation. In particular, we investigate the interplay between superconducting fluctuations and density fluctuations, which become quantum critical when the electronic phase separation vanishes at zero temperature into a quantum critical point. In this situation, the critical dynamical density fluctuations strongly affect the dynamics of the Cooper-pair fluctuations, which acquire a more singular character with a z = 3 dynamical critical index. This gives rise to a scenario that possibly rules the disappearance of superconductivity when the electron density is reduced by electrostatic gating at the LaAlO3/SrTiO3 interface.

Field-effect control of superconductivity and Rashba spin-orbit coupling in top-gated LaAlO3/SrTiO3 devices.

The recent development in the fabrication of artificial oxide heterostructures opens new avenues in the field of quantum materials by enabling the manipulation of the charge, spin and orbital degrees of freedom. In this context, the discovery of two-dimensional electron gases (2-DEGs) at LaAlO3/SrTiO3 interfaces, which exhibit both superconductivity and strong Rashba spin-orbit coupling (SOC), represents a major breakthrough. Here, we report on the realisation of a field-effect LaAlO3/SrTiO3 device, whose physical properties, including superconductivity and SOC, can be tuned over a wide range by a top-gate voltage. We derive a phase diagram, which emphasises a field-effect-induced superconductor-to-insulator quantum phase transition. Magneto-transport measurements show that the Rashba coupling constant increases linearly with the interfacial electric field. Our results pave the way for the realisation of mesoscopic devices, where these two properties can be manipulated on a local scale by means of top-gates.

Limit of the electrostatic doping in two-dimensional electron gases of LaXO3(X = Al, Ti)/SrTiO3.

In LaTiO3/SrTiO3 and LaAlO3/SrTiO3 heterostructures, the bending of the SrTiO3 conduction band at the interface forms a quantum well that contains a superconducting two-dimensional electron gas (2-DEG). Its carrier density and electronic properties, such as superconductivity and Rashba spin-orbit coupling can be controlled by electrostatic gating. In this article we show that the Fermi energy lies intrinsically near the top of the quantum well. Beyond a filling threshold, electrons added by electrostatic gating escape from the well, hence limiting the possibility to reach a highly-doped regime. This leads to an irreversible doping regime where all the electronic properties of the 2-DEG, such as its resistivity and its superconducting transition temperature, saturate. The escape mechanism can be described by the simple analytical model we propose.

Freezing and thawing of artificial ice by thermal switching of geometric frustration in magnetic flux lattices.

The problem of an ensemble of repulsive particles on a potential-energy landscape is common to many physical systems and has been studied in multiple artificial playgrounds. However, the latter usually involve fixed energy landscapes, thereby impeding in situ investigations of the particles' collective response to controlled changes in the landscape geometry. Here, we experimentally realize a system in which the geometry of the potential-energy landscape can be switched using temperature as the control knob. This realization is based on a high-temperature superconductor in which we engineer a nanoscale spatial modulation of the superconducting condensate. Depending on the temperature, the flux quanta induced by an applied magnetic field see either a geometrically frustrated energy landscape that favours an ice-like flux ordering, or an unfrustrated landscape that yields a periodic flux distribution. This effect is reflected in a dramatic change in the superconductor's magneto-transport. The thermal switching of the energy landscape geometry opens new opportunities for the study of ordering and reorganization in repulsive particle manifolds.

Multiple quantum criticality in a two-dimensional superconductor.

The diverse phenomena associated with the two-dimensional electron gas (2DEG) that occurs at oxide interfaces include, among others, exceptional carrier mobilities, magnetism and superconductivity. Although these have mostly been the focus of interest for potential future applications, they also offer an opportunity for studying more fundamental quantum many-body effects. Here, we examine the magnetic-field-driven quantum phase transition that occurs in electrostatically gated superconducting LaTiO3/SrTiO3 interfaces. Through a finite-size scaling analysis, we show that it belongs to the (2+1)D XY model universality class. The system can be described as a disordered array of superconducting puddles coupled by a 2DEG and, depending on its conductance, the observed critical behaviour is single (corresponding to the long-range phase coherence in the whole array) or double (one related to local phase coherence, the other one to the array). A phase diagram illustrating the dependence of the critical field on the 2DEG conductance is constructed, and shown to agree with theoretical proposals. Moreover, by retrieving the coherence-length critical exponent ν, we show that the quantum critical behaviour can be clean or dirty according to the Harris criterion, depending on whether the phase-coherence length is smaller or larger than the size of the puddles.

Structural and electrical characterization of ultra-thin SrTiO3 tunnel barriers grown over YBa2Cu3O7 electrodes for the development of high Tc Josephson junctions.

The transport properties of ultra-thin SrTiO(3) (STO) layers grown over YBa(2)Cu(3)O(7) electrodes were studied by conductive atomic force microscopy at the nano-scale. A very good control of the barrier thickness was achieved during the deposition process. A phenomenological approach was used to obtain critical parameters regarding the structural and electrical properties of the system. The STO layers present an energy barrier of 0.9 eV and an attenuation length of 0.23 nm, indicating very good insulating properties for the development of high-quality Josephson junctions.

Two-dimensional superconducting phase in LaTiO3/SrTiO3 heterostructures induced by high-mobility carrier doping.

In this Letter, we show that a superconducting two-dimensional electron gas is formed at the LaTiO3/SrTiO3 interface whose transition temperature can be modulated by a back-gate voltage. The gas consists of two types of carriers: a majority of low-mobility carriers always present, and a few high-mobility ones that can be injected by electrostatic doping. The calculation of the electron spatial distribution in the confinement potential shows that the high-mobility electrons responsible for superconductivity set at the edge of the gas whose extension can be tuned by the field effect.

Two-mode correlation of microwave quantum noise generated by parametric down-conversion.

In this Letter, we report the observation of the correlation between two modes of microwave radiation resulting from the amplification of quantum noise by the Josephson parametric converter. This process, seen from the pump, can be viewed as parametric down-conversion. The correlation is measured by an interference experiment displaying a contrast better than 99% with a number of photons per mode greater than 250,000. Dispersive measurements of mesoscopic systems and quantum encryption can benefit from this development.

Imprinting nanoporous alumina patterns into the magneto-transport of oxide superconductors.

We used oxygen ion irradiation to transfer the nanoscale pattern of a porous alumina mask into high-T(C) superconducting thin films. This causes a nanoscale spatial modulation of superconductivity and strongly affects the magneto-transport below T(C), which shows a series of periodic oscillations reminiscent of the Little-Parks effect in superconducting wire networks. This irradiation technique could be extended to other oxide materials in order to induce ordered nanoscale phase segregation.

Two-dimensional superconductivity at a Mott insulator/band insulator interface LaTiO3/SrTiO3.

Transition metal oxides show a great variety of quantum electronic behaviours where correlations often have an important role. The achievement of high-quality epitaxial interfaces involving such materials gives a unique opportunity to engineer artificial structures where new electronic orders take place. One of the most striking result in this area is the recent observation of a two-dimensional electron gas at the interface between a strongly correlated Mott insulator LaTiO(3) and a band insulator SrTiO(3). The mechanism responsible for such a behaviour is still under debate. In particular, the influence of the nature of the insulator has to be clarified. In this article, we show that despite the expected electronic correlations, LaTiO(3)/SrTiO(3) heterostructures undergo a superconducting transition at a critical temperature T(c)(onset)~300 mK. We have found that the superconducting electron gas is confined over a typical thickness of 12 nm and is located mostly on the SrTiO(3) substrate.

Phase-preserving amplification near the quantum limit with a Josephson ring modulator.

Recent progress in solid-state quantum information processing has stimulated the search for amplifiers and frequency converters with quantum-limited performance in the microwave range. Depending on the gain applied to the quadratures of a single spatial and temporal mode of the electromagnetic field, linear amplifiers can be classified into two categories (phase sensitive and phase preserving) with fundamentally different noise properties. Phase-sensitive amplifiers use squeezing to reduce the quantum noise, but are useful only in cases in which a reference phase is attached to the signal, such as in homodyne detection. A phase-preserving amplifier would be preferable in many applications, but such devices have not been available until now. Here we experimentally realize a proposal for an intrinsically phase-preserving, superconducting parametric amplifier of non-degenerate type. It is based on a Josephson ring modulator, which consists of four Josephson junctions in a Wheatstone bridge configuration. The device symmetry greatly enhances the purity of the amplification process and simplifies both its operation and its analysis. The measured characteristics of the amplifier in terms of gain and bandwidth are in good agreement with analytical predictions. Using a newly developed noise source, we show that the upper bound on the total system noise of our device under real operating conditions is three times the quantum limit. We foresee applications in the area of quantum analog signal processing, such as quantum non-demolition single-shot readout of qubits, quantum feedback and the production of entangled microwave signal pairs.

Scanning tunneling spectroscopy on the novel superconductor CaC6.

We present scanning tunneling microscopy and spectroscopy of the newly discovered superconductor CaC6. The tunneling conductance spectra, measured between 3 and 15 K, show a clear superconducting gap in the quasiparticle density of states. The gap function extracted from the spectra is in good agreement with the conventional BCS theory with Delta0=1.6+/-0.2 meV. The possibility of gap anisotropy and two-gap superconductivity is also discussed. In a magnetic field, direct imaging of the vortices allows us to deduce a coherence length in the ab plane xiab approximately 33 nm.