Floquet theory of Cooper pair pumping

In this work we derive a general formula for the charge pumped in a superconducting nanocircuit. Our expression generalizes previous results in several ways, it is applicable both in the adiabatic and in the non-adiabatic regimes and it takes into account also the effect of an external environment. More specifically, by applying Floquet theory to Cooper pair pumping, we show that under a cyclic evolution the total charge transferred through the circuit is proportional to the derivative of the associated Floquet quasi-energy with respect to the superconducting phase difference. In the presence of an external environment the expression for the transferred charge acquires a transparent form in the Floquet representation. It is given by the weighted sum of the charge transferred in each Floquet state, the weights being the diagonal components of the stationary density matrix of the system expressed in the Floquet basis. In order to test the power of this formulation we apply it to the study of pumping in a Cooper pair sluice. We reproduce the known results in the adiabatic regime and we show new data in the non-adiabatic case.Comment: 9 page

Detection of Tiny Mechanical Motion by Means of the Ratchet Effect

We propose a position detection scheme for a nanoelectromechanical resonator based on the ratchet effect. This scheme has an advantage of being a dc measurement. We consider a three-junction SQUID where a part of the superconducting loop can perform mechanical motion. The response of the ratchet to a dc current is sensitive to the position of the resonator and the effect can be further enhanced by biasing the SQUID with an ac current. We discuss the feasibility of the proposed scheme in existing experimental setups.Comment: 8 pages, 9 figure

Electron tunneling into a quantum wire in the Fabry-Perot regime

We study a gated quantum wire contacted to source and drain electrodes in the Fabry-Perot regime. The wire is also coupled to a third terminal (tip), and we allow for an asymmetry of the tip tunneling amplitudes of right and left moving electrons. We analyze configurations where the tip acts as an electron injector or as a voltage-probe, and show that the transport properties of this three-terminal set-up exhibit very rich physical behavior. For a non-interacting wire we find that a tip in the voltage-probe configuration affects the source-drain transport in different ways, namely by suppressing the conductance, by modulating the Fabry-Perot oscillations, and by reducing their visibility. The combined effect of electron electron interaction and finite length of the wire, accounted for by the inhomogeneous Luttinger liquid model, leads to significantly modified predictions as compared to models based on infinite wires. We show that when the tip injects electrons asymmetrically the charge fractionalization induced by interaction cannot be inferred from the asymmetry of the currents flowing in source and drain. Nevertheless interaction effects are visible as oscillations in the non-linear tip-source and tip-drain conductances. Important differences with respect to a two-terminal set-up emerge, suggesting new strategies for the experimental investigation of Luttinger liquid behavior.Comment: 27 pages, 10 figure

Detecting phonon blockade with photons

Measuring the quantum dynamics of a mechanical system, when few phonons are involved, remains a challenge. We show that a superconducting microwave resonator linearly coupled to the mechanical mode constitutes a very powerful probe for this scope. This new coupling can be much stronger than the usual radiation pressure interaction by adjusting a gate voltage. We focus on the detection of phonon blockade, showing that it can be observed by measuring the statistics of the light in the cavity. The underlying reason is the formation of an entangled state between the two resonators. Our scheme realizes a phonotonic Josephson junction, giving rise to coherent oscillations between phonons and photons as well as a self-trapping regime for a coupling smaller than a critical value. The transition from the self-trapping to the oscillating regime is also induced dynamically by dissipation.Comment: 6 pages, 5 figure

dc Josephson Effect in Metallic Single-Walled Carbon Nanotubes

The dc Josephson effect is investigated in a single-walled metallic carbon nanotube connected to two superconducting leads. In particular, by using the Luttinger liquid theory, we analyze the effects of the electron-electron interaction on the supercurrent. We find that in the long junction limit the strong electronic correlations of the nanotube, together with its peculiar band structure, induce oscillations in the critical current as a function of the junction length and/or the nanotube electron filling. These oscillations represent a signature of the Luttinger liquid physics of the nanotube, for they are absent if the interaction is vanishing. We show that this effect can be exploited to reverse the sign of the supercurrent, realizing a tunable \pi-junction.Comment: 7 pages, 5 figure

Relationship between cerebrovascular reactivity and age in multiple sclerosis

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DC Josephson Effect through Metallic Carbon Nanotubes

In this work we wish to study from a theoretical point of view the transport properties of metallic carbon nanotubes coupled to superconducting leads. In particular we wish to study the Josephson effect that consists of a supercurrent flowing among two superconductors through an insulating barrier (M. Tinkham , Introduction to Superconductivity , 1996) due to coherent propagation of Cooper pairs. The current that can flow has a sine dependence on the phase difference of the two superconductors and the maximum current (or critical current) is found to decay exponentially with the separation of the superconducting systems. If the coupling among the two superconductors is realized with a onedimensional conductor (the contacts with the superconductors are treated as tunnel barriers) the critical current is found to decay as a power law of the separation at zero temperature (R. Fazio et Al. , Physical Review B 53 , 6653 (1996)), making this kind of couplings of potential technological interest. Since electron–electron interactions play a prominent role in this effect, it is interesting to study what happens when using carbon nanotubes as linking conductors; this implementation has been studied experimentally in a recent work (P. Jarillo-Herrero et Al , Nature 439 , 953 (2006))