Carbon nanotubes (CNTs) are not intrinsically superconducting but they can carry a supercurrent when connected to superconducting electrodes 1-4. This supercurrent is mainly transmitted by discrete entangled electron-hole states confined to the nanotube, called Andreev bound states (ABS). These states are a key concept in mesoscopic superconductivity as they provide a universal description of Josephson-like effects in quantum-coherent nanostructures (for example molecules, nanowires, magnetic or normal metallic layers) connected to superconducting leads 5. We report here the first tunnelling spectroscopy of individually resolved ABS, in a nanotubesuperconductor device. Analysing the evolution of the ABS spectrum with a gate voltage, we show that the ABS arise from the discrete electronic levels of the molecule and that they reveal detailed information about the energies of these levels, their relative spin orientation and the coupling to the leads. Such measurements hence constitute a powerful new spectroscopic technique capable of elucidating the electronic structure of CNT-based devices, including those with well-coupled leads. This is relevant for conventional applications (for example, superconducting or normal transistors, superconducting quantum interference devices 3 (SQUIDs)) and quantum information processing (for example, entangled electron pair generation 6,7 , ABS-based qubits 8). Finally, our device is a new type of d.c.measurable SQUID. First conceived of four decades ago 9 , ABS are electronic analogues of the resonant states in a Fabry-Pérot resonator. The cavity is here a nanostructure and its interfaces with superconducting leads play the role of the mirrors. Furthermore, these 'mirrors' behave similarly to optical phase-conjugate mirrors: because of the superconducting pairing, electrons in the nanostructure with energies below the superconducting gap are reflected as their time-reversed particle-a process known as Andreev reflection. As a result, the resonant standing waves-the ABS-are entangled pairs of timereversed electronic states, which have opposite spins (Fig. 1a); they form a set of discrete levels within the superconducting gap (Fig. 1b) and have fermionic character. Changing the superconducting phase difference ϕ between the leads is analogous to moving the mirrors and changes the energies E n (ϕ) of the ABS. In response, a populated ABS carries a supercurrent (2e/h)(∂E n (ϕ)/∂ϕ) through the device, whereas states in the continuous spectrum (outside the superconducting gap) have negligible or minor contributions in most common cases 5. Therefore, the finite set of ABS generically determines Josephson-like effects in such systems. As such, ABS
International audienceWe performed tunneling spectroscopy of a carbon nanotube quantum dot (QD) coupled to a metallic reservoir either in the normal or in the superconducting state. We explore how the Kondo resonance, observed when the QD's occupancy is odd and the reservoir is normal, evolves towards Andreev bound states (ABS) in the superconducting state. Within this regime, the ABS spectrum observed is consistent with a quantum phase transition from a singlet to a degenerate magnetic doublet ground state, in quantitative agreement with a single-level Anderson model with superconducting leads
Superconducting circuits and microwave signals are good candidates to realize quantum networks, which are the backbone of quantum computers. We have realized a quantum node based on a 3D microwave superconducting cavity parametrically coupled to a transmission line by a Josephson ring modulator. We first demonstrate the time-controlled capture, storage, and retrieval of an optimally shaped propagating microwave field, with an efficiency as high as 80%. We then demonstrate a second essential ability, which is the time-controlled generation of an entangled state distributed between the node and a microwave channel.
We propose the "Andreev molecule," an artificial quantum system composed of two closely spaced Josephson junctions. The coupling between Josephson junctions in an Andreev molecule occurs through the overlap and hybridization of the junction's "atomic" orbitals, Andreev Bound States. A striking consequence is that the supercurrent flowing through one junction depends on the superconducting phase difference across the other junction. Using the Bogolubiov-de-Gennes formalism, we derive the energy spectrum and non-local current-phase relation for arbitrary separation. We demonstrate the possibility of creating a ϕ-junction and propose experiments to verify our predictions. Andreev molecules may have potential applications in quantum information, metrology, sensing, and molecular simulation. 1 arXiv:1809.11011v3 [cond-mat.mes-hall] 4 Sep 2019 Keywords superconductivity, Josephson junction, Andreev bound states, superconducting circuits, quantum informationUnderstanding and exploiting the interaction between Josephson junctions is paramount for superconducting device applications in quantum information 1 , magnetometry 2 , metrology 3 , and quantum simulation 4 . In typical superconducting circuits, junctions interact indirectly via electromagnetic coupling to inductors, capacitors, transmission lines, and microwave resonators. In addition to this well understood long-range interaction 5 , there is a short range interaction via quasiparticle diffusion which can modify superconducting energy gaps and critical currents, but is only important close to T c , the superconducting transition temperature, or at large bias voltages 6 .A second short-range interaction, mediated by Cooper pairs, is relevant to the majority of applications where characteristic energies are much smaller than the gap, but is still poorly understood. It becomes significant when the distance between Josephson junctions is comparable to ξ 0 , the superconducting coherence length, and can modify the electrical properties in a dramatic way.Initially, minor effects resulting from this "order-parameter interaction" were calculated for temperatures near T c using the Ginzburg-Landau equations 7 . More recently, theorists have investigated this problem at arbitrary temperature using Green's function techniques.In the two-electrode geometry, where it is not possible to independently apply a phase difference to each junction, the overall current-phase relation and dc current were obtained 8,9 .For the more relevant three-electrode geometry, non-local out-of-equilibrium supercurrents were calculated and the existence of π shifts in the current-phase relation were demonstrated 10-15 . A remarkable phase-locking similar to Shapiro steps was predicted and subsequently measured experimentally in superconducting bi-junctions biased with commensurate voltages 16,17 . The authors attribute these phenomena to the formation of entangled Cooper pairs called "quartets."
We demonstrate a novel experimental arrangement which can rotate a 2D optical lattice at frequencies up to several kilohertz. Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields, allowing investigation of phenomena such as the fractional quantum Hall effect. Our arrangement also allows the periodicity of a 2D optical lattice to be varied dynamically, producing a 2D accordion lattice.
An Andreev molecule is a system of closely spaced superconducting weak links accommodating overlapping Andreev Bound States. Recent theoretical proposals have considered one-dimensional Andreev molecules with a single conduction channel. Here we apply the scattering formalism and extend the analysis to multiple conduction channels, a situation encountered in epitaxial superconductor/semiconductor weak links. We obtain the multi-channel bound state energy spectrum and quantify the contribution of the microscopic non-local transport processes leading to the formation of Andreev molecules.
Relativistic massless charged particles in a two-dimensional conductor can be guided by a onedimensional electrostatic potential, in an analogous manner to light guided by an optical fiber. We use a carbon nanotube to generate such a guiding potential in graphene and create a single mode electronic waveguide. The nanotube and graphene are separated by a few nanometers and can be controlled and measured independently. As we charge the nanotube, we observe the formation of a single guided mode in graphene that we detect using the same nanotube as a probe. This single electronic guided mode in graphene is sufficiently isolated from other electronic states of linear Dirac spectrum continuum, allowing the transmission of information with minimal distortion.Like a photon, an electron can be used as a carrier of information [1]. However, there is a limited number of tools to control a single electron [2] and the simple fact of guiding it coherently in a solid, like an optical fiber for light, is a technological feat [3, 4]. One-dimensional materials such as semiconducting nanowires naturally provide guidance for electrons, but in these materials, electrons can only be transmitted over short distances before losing its information [5]. Another possibility is through the edge channel of a two-dimensional electron gas in the quantum Hall regime, but a large magnetic field is required for the channel to be a single mode [6], which is crucial for the carried information not to be distorted during propagation.An alternative approach, conceptually similar to an optical fiber [7], is to use an electrostatic potential well on a two-dimensional electron gas to confine the movement of electrons along one direction ( Fig. 1a) [8][9][10][11]. Particularly, massless quasiparticles in graphene is an ideal platform for the realization of such electron guide. The quasirelativistic linear energy dispersion in graphene allows the wavefunction of the Dirac fermions travel with minimal distortion. Furthermore, it has been demonstrated that high mobility [12] allows electrons to be transmitted ballistically over several microns even at room temperature [13]. In addition, graphene can be encapsulated between thin dielectric layers of hexagonal-boron nitride (h-BN) [1], providing tunable electrostatic potential on the scale of a few nanometers, without degradation of the mobility. Electrostatic gating has produced various electron-optical elements, including lenses with negative refractive index [15] and filter-collimator switches [16].An ideal single mode electronic guide requires a deep potential well with a width much smaller than the wavelength of electrons in order to suppress scattering in the core of the waveguide [17]. The wavelength can reach around one hundred nanometers with experimentally accessible densities, and it is therefore crucial to be able to place extremely narrow gates close to the electron gas. The electronic modes generated by such a 1-dimensional -U 0 NT Au BN BN G 10µm 500nm CNT (a) (b) (c) charged CNT x y U(x,y) (d)...
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