Supercurrent Spectroscopy of Andreev States

We measure the excitation spectrum of a superconducting atomic contact. In addition to the usual continuum above the superconducting gap, the single particle excitation spectrum contains discrete, spin-degenerate Andreev levels inside the gap. Quasiparticle excitations are induced by a broadband on-chip microwave source and detected by measuring changes in the supercurrent flowing through the atomic contact. Since microwave photons excite quasiparticles in pairs, two types of transitions are observed: Andreev transitions, which consists of putting two quasiparticles in an Andreev level, and transitions to odd states with a single quasiparticle in an Andreev level and the other one in the continuum. In contrast to absorption spectroscopy, supercurrent spectroscopy allows detection of long-lived odd states.Comment: typos correcte

Theory of microwave spectroscopy of Andreev bound states with a Josephson junction

We present a microscopic theory for the current through a tunnel Josephson junction coupled to a non-linear environment, which consists of an Andreev two-level system coupled to a harmonic oscillator. It models a recent experiment [Bretheau, Girit, Pothier, Esteve, and Urbina, Nature (London) 499, 312 (2013)] on photon spectroscopy of Andreev bound states in a superconducting atomic-size contact. We find the eigenenergies and eigenstates of the environment and derive the current through the junction due to inelastic Cooper pair tunneling. The current-voltage characteristic reveals the transitions between the Andreev bound states, the excitation of the harmonic mode that hybridizes with the Andreev bound states, as well as multi-photon processes. The calculated spectra are in fair agreement with the experimental data.Comment: 8 pages, 6 figure

Exciting Andreev pairs in a superconducting atomic contact

The Josephson effect describes the flow of supercurrent in a weak link, such as a tunnel junction, nanowire, or molecule, between two superconductors. It is the basis for a variety of circuits and devices, with applications ranging from medicine to quantum information. Currently, experiments using Josephson circuits that behave like artificial atoms are revolutionizing the way we probe and exploit the laws of quantum physics. Microscopically, the supercurrent is carried by Andreev pair states, which are localized at the weak link. These states come in doublets and have energies inside the superconducting gap. Existing Josephson circuits are based on properties of just the ground state of each doublet and so far the excited states have not been directly detected. Here we establish their existence through spectroscopic measurements of superconducting atomic contacts. The spectra, which depend on the atomic configuration and on the phase difference between the superconductors, are in complete agreement with theory. Andreev doublets could be exploited to encode information in novel types of superconducting qubits.Comment: Submitted to Natur

Superconducting atomic contacts inductively coupled to a microwave resonator

We describe and characterize a microwave setup to probe the Andreev levels of a superconducting atomic contact. The contact is part of a superconducting loop inductively coupled to a superconducting coplanar resonator. By monitoring the resonator reflection coefficient close to its resonance frequency as a function of both flux through the loop and frequency of a second tone we perform spectroscopy of the transition between two Andreev levels of highly transmitting channels of the contact. The results indicate how to perform coherent manipulation of these states.Comment: 14 pages, 10 figures, to appear in special issue on break-junctions in JOPC

Dynamics of quasiparticle trapping in Andreev levels

We present a theory describing the trapping and untrapping of quasiparticles in the Andreev bound level of a single-channel weak link between two superconductors. We calculate the rates of the transitions between even and odd occupations of the Andreev level induced by absorption and emission of both photons and phonons. We apply the theory to a recent experiment [Phys. Rev. Lett. 106, 257003 (2011)] in which the dynamics of the trapping of quasiparticles in the Andreev levels of superconducting atomic contacts coupled to a Josephson junction was measured. We show that the plasma energy $h\nu_p$ of the Josephson junction defines a rather abrupt transition between a fast relaxation regime dominated by coupling to photons and a slow relaxation regime dominated by coupling to phonons. With realistic parameters the theory provides a semi-quantitative description of the experimental results.Comment: 11 pages, 9 figures. Accepted for publication in Physical Review

Dynamics of quasiparticle trapping in Andreev levels

International audienceWe present a theory describing the trapping of a quasiparticle in a prototypical Josephson junction , a single-channel superconducting weak link. We calculate the trapping and untrapping rates associated to absorption and emission of both photons and phonons. We show that the presence of an electromagnetic mode with frequency smaller than the gap gives rise to a rather abrupt transition between a fast relaxation regime dominated by coupling to photons and a slow relaxation regime dominated by coupling to phonons. This conclusion is illustrated by the analysis of a recent experiment 1 measuring the dynamics of quasiparticle trapping in a superconducting atomic contact coupled to a Josephson junction. With realistic parameters the theory provides a semi-quantitative description of the experimental results

The two-dimensional phase of boron nitride: Few-atomic-layer sheets and suspended membranes

We describe the synthesis of very thin sheets (between a few and ten atomic layers) of hexagonal boron nitride (h-BN), prepared either on a SiO2 substrate or freely suspended. Optical microscopy, atomic force microscopy, and transmission electron microscopy have been used to characterize the morphology of the samples and to distinguish between regions of different thicknesses. Comparison is made to previous studies on single- and few-layer graphene. This synthesis opens the door to experimentally accessing the two-dimensional phase of boron nitride

Low Energy Electron Point Projection Microscopy of Suspended Graphene, the Ultimate "Microscope Slide"

Point Projection Microscopy (PPM) is used to image suspended graphene using low-energy electrons (100-200eV). Because of the low energies used, the graphene is neither damaged or contaminated by the electron beam. The transparency of graphene is measured to be 74%, equivalent to electron transmission through a sheet as thick as twice the covalent radius of sp^2-bonded carbon. Also observed is rippling in the structure of the suspended graphene, with a wavelength of approximately 26 nm. The interference of the electron beam due to the diffraction off the edge of a graphene knife edge is observed and used to calculate a virtual source size of 4.7 +/- 0.6 Angstroms for the electron emitter. It is demonstrated that graphene can be used as both anode and substrate in PPM in order to avoid distortions due to strong field gradients around nano-scale objects. Graphene can be used to image objects suspended on the sheet using PPM, and in the future, electron holography

Instability of two dimensional graphene: Breaking sp2 bonds with soft X-rays

We study the stability of various kinds of graphene samples under soft X-ray irradiation. Our results show that in single layer exfoliated graphene (a closer analogue to two dimensional material), the in-plane carbon-carbon bonds are unstable under X-ray irradiation, resulting in nanocrystalline structures. As the interaction along the third dimension increases by increasing the number of graphene layers or through the interaction with the substrate (epitaxial graphene), the effect of X-ray irradiation decreases and eventually becomes negligible for graphite and epitaxial graphene. Our results demonstrate the importance of the interaction along the third dimension in stabilizing the long range in-plane carbon-carbon bonding, and suggest the possibility of using X-ray to pattern graphene nanostructures in exfoliated graphene.Comment: 4 pages, 3 figures, Phys. Rev. B rapid communication, in pres

Quark--hadron duality in lepton scattering off nuclei

A phenomenological study of quark--hadron duality in electron and neutrino scattering on nuclei is performed. We compute the structure functions $F_2$ and $xF_3$ in the resonance region within a framework that includes the Dortmund-group model for the production of the {f}{i}rst four lowest-lying baryonic resonances and a relativistic mean-field model for nuclei. We consider four-momentum transfers between 0.2 and 2.5 GeV$^2$. The results indicate that nuclear effects play a different role in the resonance and DIS region. We find that global but not local duality works well. In the studied range of four-momentum transfers, the integrated strength of the computed nuclear structure functions in the resonance region, is considerably lower than the DIS one.Comment: 18 pages, 11 figure