Self-consistent dynamics of a Josephson junction in presence of an arbitrary environment

We derive microscopically the dynamics associated with the d.c. Josephson effect in a superconducting tunnel junction interacting with an arbitrary electromagnetic environment. To do so, we extend to superconducting junctions the so-called P(E) theory (see e.g. Ingold and Nazarov, arXiv:cond-mat/0508728) that accurately describes the interaction of a nonsuperconducting tunnel junction with its environment. We show the dynamics of this system is described by a small set of coupled correlation functions that take into account both Cooper pair and quasiparticle tunneling. When the phase fluctuations are small the problem is fully solved self-consistently, using and providing the exact linear admittance Y({\omega}) of the interacting junction.Comment: 7 pages, 1 figur

Micro-fabricated electromagnetic filters for millikelvin experiments

In this article we report on the design, fabrication and tests of micro-fabricated broadband filters suitable for proper electromagnetic thermalization of electrical lines connected to sensitive quantum electronics experiments performed at dilution fridge temperatures. Compared to previous such miniature filters, the new design improves on performance and reliability. These filters can be packed in space-saving cases with either single or multi-contact connectors. Measured performance in the accessible range compares well to simulations. We use these simulations to discuss the effectiveness of these filters for electromagnetic thermalization at 30 mK.Comment: Available at http://www-spht.cea.fr/articles/s06/03

Interacting electrodynamics of short coherent conductors in quantum circuits

When combining lumped mesoscopic electronic components to form a circuit, quantum fluctuations of electrical quantities lead to a non-linear electromagnetic interaction between the components that is not generally understood. The Landauer-B\"uttiker formalism that is frequently used to describe non-interacting coherent mesoscopic components is not directly suited to describe such circuits since it assumes perfect voltage bias, i.e. the absence of fluctuations. Here, we show that for short coherent conductors of arbitrary transmission, the Landauer-B\"uttiker formalism can be extended to take into account quantum voltage fluctuations similarly to what is done for tunnel junctions. The electrodynamics of the whole circuit is then formally worked out disregarding the non-Gaussianity of fluctuations. This reveals how the aforementioned non-linear interaction operates in short coherent conductors: voltage fluctuations induce a reduction of conductance through the phenomenon of dynamical Coulomb blockade but they also modify their internal density of states leading to an additional electrostatic modification of the transmission. Using this approach we can account quantitatively for conductance measurements performed on Quantum Point Contacts in series with impedances of the order of $R_K = h / e^2$. Our work should enable a better engineering of quantum circuits with targeted properties

Quantum Properties of the radiation emitted by a conductor in the Coulomb Blockade Regime

We present an input-output formalism describing a tunnel junction strongly coupled to its electromagnetic environment. We exploit it in order to investigate the dynamics of the radiation being emitted and scattered by the junction. We find that the non-linearity imprinted in the electronic transport by a properly designed environment generates strongly squeezed radiation. Our results show that the interaction between a quantum conductor and electromagnetic fields can be exploited as a resource to design simple sources of non-classical radiation.Comment: 14 pages, 4 figures, includes Supplementar

Phase controlled superconducting proximity effect probed by tunneling spectroscopy

Using a dual-mode STM-AFM microscope operating below 50mK we measured the Local Density of States (LDoS) along small normal wires connected at both ends to superconductors with different phases. We observe that a uniform minigap can develop in the whole normal wire and in the superconductors near the interfaces. The minigap depends periodically on the phase difference. The quasiclassical theory of superconductivity applied to a simplified 1D model geometry accounts well for the data.Comment: Accepted for publication in Physical Review Letter

Dynamical Coulomb Blockade of Shot Noise

We observe the suppression of the finite frequency shot-noise produced by a voltage biased tunnel junction due to its interaction with a single electromagnetic mode of high impedance. The tunnel junction is embedded in a quarter wavelength resonator containing a dense SQUID array providing it with a characteristic impedance in the kOhms range and a resonant frequency tunable in the 4-6 GHz range. Such high impedance gives rise to a sizeable Coulomb blockade on the tunnel junction (roughly 30% reduction in the differential conductance) and allows an efficient measurement of the spectral density of the current fluctuations at the resonator frequency. The observed blockade of shot-noise is found in agreement with an extension of the dynamical Coulomb blockade theory

Room-temperature tunnel current amplifier and experimental setup for high resolution electronic spectroscopy in millikelvin STM experiments

The spectroscopic resolution of tunneling measurements performed with a scanning tunneling microscope is ultimately limited by the temperature at which the experiment is performed. To take advantage of the potential high spectroscopic resolution associated with operating an STM in a dilution refrigerator we have designed a room temperature tunnel current amplifier having very small back-action on the tunnel contact and allowing to nearly reach the predicted energy resolution. This design is a modification of the standard op-amp based tip-biasing current-voltage converter which implements differential voltage sensing and whose back action on the tip voltage is only ~2 $\mu$V rms for a 14 MV/A transimpedance and 22 kHz bandwidth.Comment: Available at http://www-spht.cea.fr/articles/s06/03

Effect of the Tunneling Conductance on the Coulomb Staircase

Quantum fluctuations of the charge in the single electron box are investigated. The rounding of the Coulomb staircase caused by virtual electron tunneling is determined by perturbation theory up to third order in the tunneling conductance and compared with precise Monte Carlo data computed with a new algorithm. The remarkable agreement for large conductance indicates that presently available experimental data on Coulomb charging effects in metallic nanostructures can be well explained by finite order perturbative results.Comment: 4 pages, 5 figure

Proximity Induced Josephson-Quasiparticle Process in a Single Electron Transistor

We have performed the first experiments in a superconductor - normal metal - superconductor single electron transistor in which there is an extra superconducting strip partially overlapping the normal metal island in good metal-to-metal contact. Superconducting proximity effect gives rise to current peaks at voltages below the quasiparticle threshold. We interpret these peaks in terms of the Josephson-quasiparticle process and discuss their connection with the proximity induced energy gap in the normal metal island.Comment: 4 pages + 4 figure

High Temperature Conductance of the Single Electron Transistor

The linear conductance of the single electron transistor is determined in the high temperature limit. Electron tunneling is treated nonperturbatively by means of a path integral formulation and the conductance is obtained from Kubo's formula. The theoretical predictions are valid for arbitrary conductance and found to explain recent experimental data.Comment: 4 pages, 2 figure