Interplay of Andreev Reflection and Coulomb Blockade in Hybrid Superconducting Single-Electron Transistors.

We study the interplay between Coulomb blockade and superconductivity in a tunable superconductor-superconductor-normal-metal single-electron transistor. The device is realized by connecting the superconducting island via an oxide barrier to the normal-metal lead and with a break junction to the superconducting lead. The latter enables Cooper pair transport and (multiple) Andreev reflection. We show that these processes are relevant also far above the superconducting gap and that signatures of Coulomb blockade may reoccur at high bias while they are absent for small bias in the strong-coupling regime. Our experimental findings agree with simulations using a rate equation approach in combination with the full counting statistics of multiple Andreev reflection.

Demonstration of the Nonlocal Josephson Effect in Andreev Molecules.

We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current-phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates the nonlocal Josephson effect, and the implementation of a φ0-junction which is tunable both electrostatically and magnetically. The anomalous phase shift is larger for shorter distances between the JJs and vanishes for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of Andreev bound states, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source and could enable new coupling schemes for hybrid quantum devices.

Magnetic Field-Induced "Mirage" Gap in an Ising Superconductor.

Superconductivity is commonly destroyed by a magnetic field due to orbital or Zeeman-induced pair breaking. Surprisingly, the spin-valley locking in a two-dimensional superconductor with spin-orbit interaction makes the superconducting state resilient to large magnetic fields. We investigate the spectral properties of such an Ising superconductor in a magnetic field taking into account disorder. The interplay of the in-plane magnetic field and the Ising spin-orbit coupling leads to noncollinear effective fields. We find that the emerging singlet and triplet pairing correlations manifest themselves in the occurrence of "mirage" gaps: at (high) energies of the order of the spin-orbit coupling strength, a gaplike structure in the spectrum emerges that mirrors the main superconducting gap. We show that these mirage gaps are signatures of the equal-spin triplet finite-energy pairing correlations and due to their odd parity are sensitive to intervalley scattering.

Persistent Response in an Ultrastrongly Driven Mechanical Membrane Resonator.

We study experimentally and theoretically the phenomenon of "persistent response" in ultrastrongly driven membrane resonators. The term persistent response denotes the development of a vibrating state with nearly constant amplitude over an extreme wide frequency range. We reveal the underlying mechanism by directly imaging the vibrational state using advanced optical interferometry. We argue that this state is related to the nonlinear interaction between higher-order flexural modes and higher-order overtones of the driven mode. Finally, we propose a stability diagram for the different vibrational states that the membrane can adopt.

Prediction of a Paramagnetic Meissner Effect in Voltage-Biased Superconductor-Normal-Metal Bilayers.

Conventional superconductors respond to external magnetic fields by generating diamagnetic screening currents. However, theoretical work has shown that one can engineer systems where the screening current is paramagnetic, causing them to attract magnetic flux-a prediction that has recently been experimentally verified. In contrast to previous studies, we show that this effect can be realized in simple superconductor-normal-metal structures with no special properties, using only a simple voltage bias to drive the system out of equilibrium. This is of fundamental interest, since it opens up a new avenue of research, and at the same time highlights how one can realize paramagnetic Meissner effects without having odd-frequency states at the Fermi level. Moreover, a voltage-tunable electromagnetic response in such a simple system may be interesting for future device design.

Dynamical Coulomb Blockade as a Local Probe for Quantum Transport.

Quantum fluctuations are imprinted with valuable information about transport processes. Experimental access to this information is possible, but challenging. We introduce the dynamical Coulomb blockade (DCB) as a local probe for fluctuations in a scanning tunneling microscope (STM) and show that it provides information about the conduction channels. In agreement with theoretical predictions, we find that the DCB disappears in a single-channel junction with increasing transmission following the Fano factor, analogous to what happens with shot noise. Furthermore we demonstrate local differences in the DCB expected from changes in the conduction channel configuration. Our experimental results are complemented by ab initio transport calculations that elucidate the microscopic nature of the conduction channels in our atomic-scale contacts. We conclude that probing the DCB by STM provides a technique complementary to shot noise measurements for locally resolving quantum transport characteristics.

Continuous-Variable Entanglement Test in Driven Quantum Contacts.

The standard entanglement test using the Clauser-Horne-Shimony-Holt inequality is known to fail in mesoscopic junctions at finite temperatures. Since this is due to the bidirectional particle flow, a similar failure is expected to occur in an ac-driven contact. We develop a continuous-variable entanglement test suitable for electrons and holes that are created by the ac drive. At low enough temperatures the generalized Bell inequality is violated in junctions with low conductance or a small number of transport channels and with ac voltages which create few electron-hole pairs per cycle. Our ac-entanglement test depends on the total number of electron-hole pairs and on the distribution of probabilities of pair creations similar to the Fano factor.

Spin Current Cross-Correlations as a Probe of Magnon Coherence.

Motivated by the important role of the normalized second-order coherence function, often called g^{(2)}, in the field of quantum optics, we propose a method to determine magnon coherence in solid-state devices. Namely, we show that the cross-correlations of pure spin currents injected by a ferromagnet into two metal leads, normalized by their dc value, replicate the behavior of g^{(2)} when magnons are driven far from equilibrium. We consider two scenarios: driving by ferromagnetic resonance, which leads to the coherent occupation of a single mode, and driving by heating of the magnons, which leads to an excess of incoherent magnons. We find an enhanced normalized cross-correlation in the latter case, thereby demonstrating bunching of nonequilibrium thermal magnons due to their bosonic statistics. Our results contribute to the burgeoning field of quantum magnonics, which seeks to explore and exploit the quantum nature of magnons.

Exchange-Enhanced Ultrastrong Magnon-Magnon Coupling in a Compensated Ferrimagnet.

We experimentally study the spin dynamics in a gadolinium iron garnet single crystal using broadband ferromagnetic resonance. Close to the ferrimagnetic compensation temperature, we observe ultrastrong coupling of clockwise and counterclockwise magnon modes. The magnon-magnon coupling strength reaches almost 40% of the mode frequency and can be tuned by varying the direction of the external magnetic field. We theoretically explain the observed mode coupling as arising from the broken rotational symmetry due to a weak magnetocrystalline anisotropy. The effect of this anisotropy is exchange enhanced around the ferrimagnetic compensation point.

Spin Splitting Induced in a Superconductor by an Antiferromagnetic Insulator.

Inspired by recent feats in exchange coupling antiferromagnets to an adjacent material, we demonstrate the possibility of employing them for inducing spin splitting in a superconductor, thereby avoiding the detrimental, parasitic effects of ferromagnets employed to this end. We derive the Gor'kov equation for the matrix Green's function in the superconducting layer, considering a microscopic model for its disordered interface with a two-sublattice magnetic insulator. We find that an antiferromagnetic insulator with effectively uncompensated interface induces a large, disorder-resistant spin splitting in the adjacent superconductor. In addition, we find contributions to the self-energy stemming from the interfacial disorder. Within our model, these mimic impurity and spin-flip scattering, while another breaks the symmetries in particle-hole and spin spaces. The latter contribution, however, drops out in the quasiclassical approximation and thus, does not significantly affect the superconducting state.

Model Prediction of Self-Rotating Excitons in Two-Dimensional Transition-Metal Dichalcogenides.

Using the quasiclassical concept of Berry curvature we demonstrate that a Dirac exciton-a pair of Dirac quasiparticles bound by Coulomb interactions-inevitably possesses an intrinsic angular momentum making the exciton effectively self-rotating. The model is applied to excitons in two-dimensional transition metal dichalcogenides, in which the charge carriers are known to be described by a Dirac-like Hamiltonian. We show that the topological self-rotation strongly modifies the exciton spectrum and, as a consequence, resolves the puzzle of the overestimated two-dimensional polarizability employed to fit earlier spectroscopic measurements.

Noninvasive Quantum Measurement of Arbitrary Operator Order by Engineered Non-Markovian Detectors.

The development of solid-state quantum technologies requires the understanding of quantum measurements in interacting, nonisolated quantum systems. In general, a permanent coupling of detectors to a quantum system leads to memory effects that have to be taken into account in interpreting the measurement results. We analyze a generic setup of two detectors coupled to a quantum system and derive a compact formula in the weak-measurement limit that interpolates between an instantaneous (text-book type) and almost continuous-detector dynamics-dependent-measurement. A quantum memory effect that we term "system-mediated detector-detector interaction" is crucial to observe noncommuting observables simultaneously. Finally, we propose a mesoscopic double-dot detector setup in which the memory effect is tunable and that can be used to explore the transition to non-Markovian quantum measurements experimentally.

Spin Pumping and Shot Noise in Ferrimagnets: Bridging Ferro- and Antiferromagnets.

A combination of novel technological and fundamental physics prospects has sparked a huge interest in pure spin transport in magnets, starting with ferromagnets and spreading to antiferro- and ferrimagnets. We present a theoretical study of spin transport across a ferrimagnet-nonmagnetic conductor interface, when a magnetic eigenmode is driven into a coherent state. The obtained spin current expression includes intra- as well as cross-sublattice terms, both of which are essential for a quantitative understanding of spin pumping. The dc current is found to be sensitive to the asymmetry in interfacial coupling between the two sublattice magnetizations and the mobile electrons, especially for antiferromagnets. We further find that the concomitant shot noise provides a useful tool for probing the quasiparticle spin and interfacial coupling.

Quantum Coherent Multielectron Processes in an Atomic Scale Contact.

The light emission from a scanning tunneling microscope operated on a Ag(111) surface at 6 K is analyzed from low conductances to values approaching the conductance quantum. Optical spectra recorded at sample voltages V reveal emission with photon energies hν>2eV. A model of electrons interacting coherently via a localized plasmon-polariton mode reproduces the experimental data, in particular, the kinks in the spectra at eV and 2eV as well as the scaling of the intensity at low and intermediate conductances.

Super-Poissonian Shot Noise of Squeezed-Magnon Mediated Spin Transport.

The magnetization of a ferromagnet (F) driven out of equilibrium injects pure spin current into an adjacent conductor (N). Such F|N bilayers have become basic building blocks in a wide variety of spin-based devices. We evaluate the shot noise of the spin current traversing the F|N interface when F is subjected to a coherent microwave drive. We find that the noise spectrum is frequency independent up to the drive frequency, and increases linearly with frequency thereafter. The low frequency noise indicates super-Poissonian spin transfer, which results from quasiparticles with effective spin ℏ^{*}=ℏ(1+δ). For typical ferromagnetic thin films, δ∼1 is related to the dipolar interaction-mediated squeezing of F eigenmodes.

Flux-Tunable Josephson Diode Effect in a Hybrid Four-Terminal Josephson Junction.

We investigate the direction-dependent switching current in a flux-tunable four-terminal Josephson junction defined in an InAs/Al two-dimensional heterostructure. The device exhibits the Josephson diode effect with switching currents that depend on the sign of the bias current. The superconducting diode efficiency, reaching a maximum of |η| ≈ 34%, is widely tunable─both in amplitude and sign─as a function of magnetic fluxes and gate voltages. Our observations are supported by a circuit model of three parallel Josephson junctions with nonsinusoidal current-phase relation. With respect to conventional Josephson interferometers, phase-tunable multiterminal Josephson junctions enable large diode efficiencies in structurally symmetric devices, where local magnetic fluxes generated on the chip break both time-reversal and spatial symmetries. Our work presents an approach for developing Josephson diodes with wide-range tunability that do not rely on exotic materials.

Nonsymmetrized correlations in quantum noninvasive measurements.

A long-standing problem in quantum mesoscopic physics is which operator order corresponds to noise expressions like , where I(ω) is the measured current at frequency ω. Symmetrized order describes a classical measurement while nonsymmetrized order corresponds to a quantum detector, e.g., one sensitive to either emission or absorption of photons. We show that both order schemes can be embedded in quantum weak-measurement theory taking into account measurements with memory, characterized by a memory function which is independent of a particular experimental detection scheme. We discuss the resulting quasiprobabilities for different detector temperatures and how their negativity can be tested on the level of second-order correlation functions already. Experimentally, this negativity can be related to the squeezing of the many-body state of the transported electrons in an ac-driven tunnel junction.

Phase-engineering the Andreev band structure of a three-terminal Josephson junction.

In hybrid Josephson junctions with three or more superconducting terminals coupled to a semiconducting region, Andreev bound states may form unconventional energy band structures, or Andreev matter, which are engineered by controlling superconducting phase differences. Here we report tunnelling spectroscopy measurements of three-terminal Josephson junctions realised in an InAs/Al heterostructure. The three terminals are connected to form two loops, enabling independent control over two phase differences and access to a synthetic Andreev band structure in the two-dimensional phase space. Our results demonstrate a phase-controlled Andreev molecule, originating from two discrete Andreev levels that spatially overlap and hybridise. Signatures of hybridisation are observed in the form of avoided crossings in the spectrum and band structure anisotropies in the phase space, all explained by a numerical model. Future extensions of this work could focus on addressing spin-resolved energy levels, ground state fermion parity transitions and Weyl bands in multiterminal geometries.

Microwave-induced conductance replicas in hybrid Josephson junctions without Floquet-Andreev states.

Light-matter coupling allows control and engineering of complex quantum states. Here we investigate a hybrid superconducting-semiconducting Josephson junction subject to microwave irradiation by means of tunnelling spectroscopy of the Andreev bound state spectrum and measurements of the current-phase relation. For increasing microwave power, discrete levels in the tunnelling conductance develop into a series of equally spaced replicas, while the current-phase relation changes amplitude and skewness, and develops dips. Quantitative analysis of our results indicates that conductance replicas originate from photon assisted tunnelling of quasiparticles into Andreev bound states through the tunnelling barrier. Despite strong qualitative similarities with proposed signatures of Floquet-Andreev states, our study rules out this scenario. The distortion of the current-phase relation is explained by the interaction of Andreev bound states with microwave photons, including a non-equilibrium Andreev bound state occupation. The techniques outlined here establish a baseline to study light-matter coupling in hybrid nanostructures and distinguish photon assisted tunnelling from Floquet-Andreev states in mesoscopic devices.