Non-equilibrium supercurrent through a quantum dot: current harmonics and proximity effect due to a normal metal lead

We consider a Hamiltonian model for a quantum dot which is placed between two superconducting leads with a constant bias imposed between these leads. Using the non-equilibrium Keldysh technique, we focus on the subgap current, where it is known that multiple Andreev reflections (MAR) are responsible for charge transfer through the dot. Attention is put on the DC current and on the first harmonics of the supercurrent. Varying the energy and width of the resonant level on the dot, we first investigate a cross-over from a quantum dot regime to a quantum point contact regime when there is zero coupling to the normal probe. We then study the effect on the supercurrent of the normal probe which is attached to the dot. This normal probe is understood to lead to dephasing, or alternatively to induce reverse proximity effect. We describe the full crossover from zero dephasing to the incoherent case. We also compute the Josephson current in the presence of the normal lead, and find it in excellent agreement with the values of the non-equlibrium current extrapolated at zero voltage

Quantum phase transition of dynamical resistance in a mesoscopic capacitor

We study theoretically dynamic response of a mesoscopic capacitor, which consists of a quantum dot connected to an electron reservoir via a point contact and capacitively coupled to a gate voltage. A quantum Hall edge state with a filling factor nu is realized in a strong magnetic field applied perpendicular to the two-dimensional electron gas. We discuss a noise-driven quantum phase transition of the transport property of the edge state by taking into account an ohmic bath connected to the gate voltage. Without the noise, the charge relaxation for nu>1/2 is universally quantized at R_q=h/(2e^2), while for nu<1/2, the system undergoes the Kosterlitz-Thouless transtion, which drastically changes the nature of the dynamical resistance. The phase transition is facilitated by the noisy gate voltage, and we see that it can occur even for an integer quantum Hall edge at nu=1. When the dissipation by the noise is sufficiently small, the quantized value of R_q is shifted by the bath impedance.Comment: 5 pages, 2 figures, proceeding of the 19th International Conference on the Application of High Magnetic Fields in Semiconductor Physics and Nanotechnology (HMF-19

Colored delta-T noise in Fractional Quantum Hall liquids

Photons are emitted or absorbed by a nano-circuit under both equilibrium and non-equilibrium situations. Here, we focus on the non-equilibrium situation arising due to a temperature difference between the leads of a quantum point contact, and study the finite frequency (colored) noise. We explore this delta-$T$ noise in the finite frequency regime for two systems: conventional conductors described by Fermi liquid scattering theory and the fractional quantum Hall system at Laughlin filling fractions, described by the chiral Luttinger liquid formalism. We study the emission noise, its expansion in the temperature difference (focusing on the quadratic component) as well as the excess emission noise defined with respect to a properly chosen equilibrium situation. The behavior of these quantities are markedly different for the fractional quantum Hall system compared to Fermi liquids, signalling the role of strong correlations. We briefly treat the strong backscattering regime of the fractional quantum Hall liquid, where a behavior closer to the Fermi liquid case is observed

Observation of coherent backscattering of light by cold atoms

Coherent backscattering (CBS) of light waves by a random medium is a signature of interference effects in multiple scattering. This effect has been studied in many systems ranging from white paint to biological tissues. Recently, we have observed CBS from a sample of laser-cooled atoms, a scattering medium with interesting new properties. In this paper we discuss various effects, which have to be taken into account for a quantitative study of coherent backscattering of light by cold atoms.Comment: 25 pages LaTex2e, 17 figures, submitted to J. Opt. B: Quant. Semicl. Op

Photo-assisted Andreev reflection as a probe of quantum noise

19 pages, 11 figuresAndreev reflection, which corresponds to the tunneling of two electrons from a metallic lead to a superconductor lead as a Cooper pair (or vice versa), can be exploited to measure high frequency noise. A detector is proposed, which consists of a normal lead--superconductor circuit, which is capacitively coupled to a mesoscopic circuit where noise is to be measured. We discuss two detector circuits: a single normal metal -- superconductor tunnel junction and a normal metal separated from a superconductor by a quantum dot operating in the Coulomb blockade regime. A substantial DC current flows in the detector circuit when an appropriate photon is provided or absorbed by the mesoscopic circuit, which plays the role of an environment for the junction to which it couples. Results for the current can be cast in all cases in the form of a frequency integral of the excess noise of the environment weighted by a kernel which is specific to the transport process (quasiparticle tunneling, Andreev reflection,...) which is considered. We apply these ideas to the measurement of the excess noise of a quantum point contact and we provide numerical estimates of the detector current

Fermionic Mach-Zehnder interferometer subject to a quantum bath

We study fermions in a Mach-Zehnder interferometer, subject to a quantum-mechanical environment leading to inelastic scattering, decoherence, renormalization effects, and time-dependent conductance fluctuations. Both the loss of interference contrast as well as the shot noise are calculated, using equations of motion and leading order perturbation theory. The full dependence of the shot-noise correction on setup parameters, voltage, temperature and the bath spectrum is presented. We find an interesting contribution due to correlations between the fluctuating renormalized phase shift and the output current, discuss the limiting behaviours at low and high voltages, and compare with simpler models of dephasing.Comment: 5 pages, 3 figure

Theory of non-equilibrium noise in general multi-terminal superconducting hydrid devices: application to multiple Cooper pair resonances

We consider the out-of-equilibrium behavior of a general class of mesoscopic devices composed of several superconducting or/and normal metal leads separated by quantum dots. Starting from a microscopic Hamiltonian description, we provide a non-perturbative approach to quantum electronic transport in the tunneling amplitudes between dots and leads: using the equivalent of a path integral formulation, the lead degrees of freedom are integrated out in order to compute both the current and the current correlations (noise) in this class of systems, in terms of the dressed Green's function matrix of the quantum dots. In order to illustrate the efficiency of this formalism, we apply our results to the "all superconducting Cooper pair beam splitter", a device composed of three superconducting leads connected via two quantum dots, where crossed Andreev reflection operates Cooper pair splitting. Commensurate voltage differences between the three leads allow to obtain expressions for the current and noise as a function of the Keldysh Nambu Floquet dressed Green's function of the dot system. This voltage configuration allows the occurrence of non-local processes involving multiple Cooper pairs which ultimately lead to the presence of non-zero DC currents in an out-of-equilibrium situation. We investigate in details the results for the noise obtained numerically in the specific case of opposite voltages, where the transport properties are dominated by the so called "quartet processes", involving the coherent exchange of two Cooper pairs among all three superconducting terminals. We show that these processes are noiseless in the non-resonant case, and that this property is also observed for other voltage configurations. When the dots are in a resonant regime, the noise characteristics change qualitatively, with the appearance of giant Fano factors.Comment: 18 pages, 12 figure

Conductivity in quasi two-dimensional systems

The conductivity in quasi two-dimensional systems is calculated using the quantum kinetic equation. Linearizing the Lenard-Balescu collision integral with the extension to include external field dependences allows one to calculate the conductivity with diagrams beyond the GW approximation including maximally crossed lines. Consequently the weak localization correction as an interference effect appears here from the field dependence of the collision integral (the latter dependence sometimes called intra-collisional field effect). It is shown that this weak localization correction has the same origin as the Debye-Onsager relaxation effect in plasma physics. The approximation is applied to a system of quasi two-dimensional electrons in hetero-junctions which interact with charged and neutral impurities and the low temperature correction to the conductivity is calculated analytically. It turns out that the dynamical screening due to charged impurities leads to a linear temperature dependence, while the scattering from neutral impurities leads to the usual Fermi-liquid behavior. By considering an appropriate mass action law to determine the ratio of charged to neutral impurities we can describe the experimental metal-insulator transition at low temperatures as a Mott-Hubbard transition.Comment: 7 pages 7 pages appendix 11 figure

Statistics of level spacing of geometric resonances in random binary composites

We study the statistics of level spacing of geometric resonances in the disordered binary networks. For a definite concentration $p$ within the interval $[0.2,0.7]$, numerical calculations indicate that the unfolded level spacing distribution $P(t)$ and level number variance $\Sigma^2(L)$ have the general features. It is also shown that the short-range fluctuation $P(t)$ and long-range spectral correlation $\Sigma^2(L)$ lie between the profiles of the Poisson ensemble and Gaussion orthogonal ensemble (GOE). At the percolation threshold $p_c$, crossover behavior of functions $P(t)$ and $$ is obtained, giving the finite size scaling of mean level spacing $\delta$ and mean level number $n$, which obey the scaling laws, $$ and $n=0.911L^{1.970}$.Comment: 11 pages, 7 figures,submitted to Phys. Rev.