AC Josephson effect and resonant Cooper pair tunneling emission of a Cooper Pair Transistor

We measure the high-frequency emission of a single Cooper pair transistor(SCPT) in the regime where transport is only due to tunneling of Cooper pairs. This is achieved by coupling on-chip the SCPT to a superconductor-insulator-superconductor junction and by measuring the photon assisted tunneling current of quasiparticles across the junction. This technique allows a direct detection of the AC Josephson effect of the SCPT and provides evidence of Landau-Zener transitions for proper gate voltage. The emission in the regime of resonant Cooper pair tunneling is also investigated. It is interpreted in terms of transitions between charge states coupled by the Josephson effect.Comment: Revtex4, 5 pages, 4 figures, final versio

The Gross-Pitaevskii Equation for Bose Particles in a Double Well Potential: Two Mode Models and Beyond

There have been many discussions of two-mode models for Bose condensates in a double well potential, but few cases in which parameters for these models have been calculated for realistic situations. Recent experiments lead us to use the Gross-Pitaevskii equation to obtain optimum two-mode parameters. We find that by using the lowest symmetric and antisymmetric wavefunctions, it is possible to derive equations for a more exact two-mode model that provides for a variable tunneling rate depending on the instantaneous values of the number of atoms and phase differences. Especially for larger values of the nonlinear interaction term and larger barrier heights, results from this model produce better agreement with numerical solutions of the time-dependent Gross-Pitaevskii equation in 1D and 3D, as compared with previous models with constant tunneling, and better agreement with experimental results for the tunneling oscillation frequency [Albiez et al., cond-mat/0411757]. We also show how this approach can be used to obtain modified equations for a second quantized version of the Bose double well problem.Comment: RevTeX, 14 pages, 14 figure

Electronic transport in a series of multiple arbitrary tunnel junctions

Monte Carlo simulations and an analytical approach within the framework of a semiclassical model are presented which permit the determination of Coulomb blockade and single electron charging effects for multiple tunnel junctions coupled in series. The Coulomb gap in the I(V) curves can be expressed as a simple function of the capacitances in the series. Furthermore, the magnitude of the differential conductivity at current onset is calculated in terms of the model. The results are discussed with respect to the number of junctions.Comment: 3 figures, revte

Observation of quantum capacitance in the Cooper-pair transistor

We have fabricated a Cooper-pair transistor (CPT) with parameters such that for appropriate voltage biases, the sub-gap charge transport takes place via slow tunneling of quasiparticles that link two Josephson-coupled charge manifolds. In between the quasiparticle tunneling events, the CPT behaves essentially like a single Cooper-pair box (SCB). The effective capacitance of a SCB can be defined as the derivative of the induced charge with respect to gate voltage. This capacitance has two parts, the geometric capacitance, C_geom, and the quantum capacitance C_Q. The latter is due to the level anti-crossing caused by the Josephson coupling. It depends parametrically on the gate voltage and is dual to the Josephson inductance. Furthermore, it's magnitude may be substantially larger than C_geom. We have been able to detect C_Q in our CPT, by measuring the in-phase and quadrature rf-signal reflected from a resonant circuit in which the CPT is embedded. C_Q can be used as the basis of a charge qubit readout by placing a Cooper-pair box in such a resonant circuit.Comment: 3 figure

Single-charge devices with ultrasmall Nb/AlOx/Nb trilayer Josephson junctions

Josephson junction transistors and 50-junction arrays with linear junction dimensions from 200 nm down to 70 nm were fabricated from standard Nb/AlOx/Nb trilayers. The fabrication process includes electron beam lithography, dry etching, anodization, and planarization by chemical-mechanical polishing. The samples were characterized at temperatures down to 25 mK. In general, all junctions are of high quality and their I-U characteristics show low leakage currents and high superconducting energy gap values of 1.35 meV. The characteristics of the transistors and arrays exhibit some features in the subgap area, associated with tunneling of Cooper pairs, quasiparticles and their combinations due to the redistribution of the bias voltage between the junctions. Total island capacitances of the transistor samples ranged from 1.5 fF to 4 fF, depending on the junction sizes. Devices made of junctions with linear dimensions below 100 nm by 100 nm demonstrate a remarkable single-electron behavior in both superconducting and normal state. We also investigated the area dependence of the junction capacitances for transistor and array samples.Comment: 19 pages incl. 2 tables and 11 figure

Coherent photon assisted cotunneling in a Coulomb blockade device

We study cotunneling in a double junction Coulomb blockade device under the influence of time dependent potentials. It is shown that the ac-bias leads to photon assisted cotunneling which in some cases may dominate the transport. We derive a general non-perturbative expression for the tunneling current in the presence of oscillating potentials and give a perturbative expression for the photon assisted cotunneling current.Comment: Replaced with a longer paper which includes a non-perturbative calculation. 13 pages with 1 figure. To be published in Physical Review

Coherent oscillations in a Cooper-pair box

This paper is devoted to an analysis of the experiment by Nakamura {\it et al.} (Nature {\bf 398}, 786 (1999)) on the quantum state control in Josephson junctions devices. By considering the relevant processes involved in the detection of the charge state of the box and a realistic description of the gate pulse we are able to analyze some aspects of the experiment (like the amplitude of the measurement current) in a quantitative way

Enhancement of Josephson phase diffusion by microwaves

We report an experimental and theoretical study of the phase diffusion in small Josephson junctions under microwave irradiation. A peculiar enhancement of the phase diffusion by microwaves is observed. The enhancement manifests itself by a pronounced current peak in the current-voltage characteristics. The voltage position $V_{\rm top}$ of the peak increases with the power $P$ of microwave radiation as $V_{\rm top}\propto\sqrt P$, while its current amplitude weakly decreases with $P$. As the microwave frequency increases, the peak feature evolves into Shapiro steps with finite slope. Our theoretical analysis taking into account the enhancement of incoherent superconducting current by multi-photon absorption is in good agreement with experimental data.Comment: 5 pages, 4 figure

The signature of a double quantum-dot structure in the I-V characteristics of a complex system

We demonstrate that by carefully analyzing the temperature dependent characteristics of the I-V measurements for a given complex system it is possible to determine whether it is composed of a single, double or multiple quantum-dot structure. Our approach is based on the orthodox theory for a double-dot case and is capable of simulating I-V characteristics of systems with any resistance and capacitance values and for temperatures corresponding to thermal energies larger than the dot level spacing. We compare I-V characteristics of single-dot and double-dot systems and show that for a given measured I-V curve considering the possibility of a second dot is equivalent to decreasing the fit temperature. Thus, our method allows one to gain information about the structure of an experimental system based on an I-V measurement.Comment: 12 pages 7 figure

Observation of Strong Coulomb Blockade in Resistively Isolated Tunnel Junctions

We report measurements of the Coulomb-blockade current in resistively isolated (R_{Isol} >> h/e^{2}) tunnel junctions for the temperature range 60mK $We report measurements of the Coulomb-blockade current in resistively isolated ($R_{Isol}\gg h/e^{2})$ tunnel junctions for the temperature range 60mK < T < 230mK where the charging energy E_{c} is much greater than the thermal energy. A zero-bias resistance R_{0} of up to 10^{4}R_{T} (the tunnel resistance of the bare junction) is obtained. For eV << E_{c}, the I-V curves for a given R_{Isol} scale as a function of V/T, with I \propto V^{\alpha (R_{Isol})} over a range of V. The data agree well with numerical calculations of the tunneling rate that include environmental effects.Comment: 13 pages, 3 eps figure