Session K38: Superconductivity-Mesoscopics and Theory

Charge dynamics in a single electron trap

We report on measurements made using a radio frequency single electron transistor (RF-SET) capacitively coupled to a small metallic island to study the dynamics of single tunneling events. A circuit consisting of two small metallic islands and two tunnel junctions provides an architecture with which to tune the tunneling rates of single electrons up to the micro-second time scale. Thermal and cotunneling (quantum tunneling) events as well as the cross-over between the two regimes can be studied with this system. Characterization of devices will be shown including stability diagrams and the dependence of tunneling rates on bias conditions.   

Measuring the Quantum Capacitance of a Differential Single Cooper-Pair Box

We present a simple method for measuring the quantum capacitance (QC) of a charge qubit based on a Differential Single Cooper-Pair Box using a Differential Radio-Frequency Single Electron Transistor. Measurement of the QC, which is proportional to the second derivative of the energy bands, can in principle be used for state readout at the degeneracy point, where decoherence due to charge fluctuations is at a minimum. The QC is measured by examining the response of the qubit to a small-amplitude AC excitation. Using this technique, we make an independent measurement of the qubit energy relaxation time. Although we have performed this experiment with a differential SCB and differential charge readout, the technique can easily be applied to a conventional SCB.   

A solid-state refrigerator for cooling cm-scale payloads below 300 mK

State-of-the-art x-ray and infrared sensors require bath temperatures near 100 mK. Currently, the two main options for cooling devices below 300 mK are the dilution refrigerator and adiabatic demagnetization refrigerator. We have developed a compact, lightweight alternative. Solid-state refrigerators based on Normal metal/Insulator/Superconductor (NIS) tunnel junctions can cool from temperatures near 300 mK to below 100 mK. The physical cooling mechanism is the preferential tunneling of the highest energy (hottest) electrons through a biased NIS junction. Recently, we have cooled both thin-film and bulk thermistors from 320 to 240 mK. Here, we present progress towards NIS refrigerators capable of cooling user-supplied payloads. In particular, we demonstrate a NIS-based refrigerator capable of cooling 6 x 6 mm$^{2}$ silicon chips. This refrigerator, in combination with a $^{3}$He cryostat (base temperature $\sim $300 mK), forms a simple, compact cooling platform for ultralow temperature x-ray and infrared sensors. NIS refrigerators are fabricated lithographically on wafers, making the technology inherently scaleable to wafer-sized detector arrays.   

Quantum Calorimetry for Nonproliferation

High resolution $\gamma$-ray spectroscopy is an important tool for non-destructive analysis of nuclear materials and is often used by safeguards inspectors to help verify the inventories of nuclear materials held around the world. The energy spectrum of photons emitted from isotopes of uranium or plutonium in the $40-1000$ keV energy range give unique signatures that, if accurately measured, give inspectors important information about the age and enrichment of the material and therefore its intended purpose. In this talk I will describe our recent demonstration of a $\gamma$-ray spectrometer based on a superconducting transition-edge sensor microcalorimeter detector. This device has more than an order of magnitude better energy resolution than standard high resolution $\gamma$-ray detectors. We present high-resolution $\gamma$-ray spectra of Pu isotopic mixtures, describe the physics of the microcalorimeter and overview our plans for a realistic spectrometer for meeting real-world challenges such as measuring the mass of plutonium in spent nuclear fuel.   

Tunable magnetic coupler for a superconducting adiabatic quantum computer

We report on measurements of a superconducting sign-tunable magnetic coupling element. This device could be used as part of a programmable adiabatic quantum computer utilizing flux qubits. The sign-tunability is achieved by mediating the coupling between two flux qubits through a third rf SQUID device [1]. We are able to tune the resulting coupling from antiferromagnetic through zero to ferromagnetic. [1] A. Maassen van den Brink, A. J. Berkley, M. Yalowsky, New J. Phys. 7 230 (2005).   

Giant oscillations of energy levels in mesoscopic superconductors

The interplay of geometrical and Andreev quantization in mesoscopic superconductors leads to giant mesoscopic oscillations of energy levels as functions of the Fermi momentum and/or sample size. Quantization rules are formulated for closed quasiparticle trajectories in the presence of normal scattering at the sample boundaries. Two generic examples of mesoscopic systems are studied: (i) one dimensional Andreev states in a quantum box, (ii) a single vortex in a mesoscopic cylinder.   

Dynamics of a Nanomechanical Resonator Coupled to a Superconducting Single Electron Transistor

We present an analysis of the dynamics of a nanomechanical resonator coupled to a superconducting single electron transistor (SSET) in the vicinity of the Josephson quasiparticle (JQP) and double Josephson quasiparticle (DJQP) resonances. For weak coupling and wide separation of dynamical timescales, we find that for either superconducting resonances the dynamics of the resonator are given by a Fokker-Planck equation, i.e., the SSET behaves effectively as an equilibrium heat bath, characterised by an effective temperature, which also damps the resonator and renormalizes its frequency.Depending on the gate and drain-source voltage bias points with respect to the superconducting resonance, the SSET can also give rise to an instability in the mechanical resonator marked by negative damping and temperature within the appropriate Fokker-Planck equation. Furthermore, sufficiently close to a resonance, we find that the Fokker-Planck description breaks down. We also point out that there is a close analogy between coupling a nanomechanical resonator to a SSET in the vicinity of the JQP resonance and Doppler cooling of atoms by means of lasers.   

Dipolon Theory of Superconducting Regular and Pseudo- Energy Gap Parameters at Finite Temperature and Transition Temperatures $T_C$ and $T^*$ in High-Temperature Superconductors

First temperature dependent regular and pseudo- energy gap parameters and regular ($T_C$)and pseudo-($T^*$)transition temperatures have been obtained arising from the same physical origin by developing many-body field-theoretic techniques making use of dipolon propagator and electron Green's function with dressed dipolons as mediators of superconductivity, screened Coulomb repulsion, nonrigid electron energy bands, retardation and damping effects and electron-hole asymmetry, as an extention of our previous zero temperature formalism [1]. The theory contains all essential and important electron correlations.The Migdal vertex correction is found to be small ($\sim 1 \%$). Our calculated results of temperature dependent regular and pseudo- energy gap parameters and regular ($T_C$) and pseudo- ($T^*$) transition temperatures for Bi-cuprates agree well with available experimental data. In comparison it is concluded that the models (such as the Hubbard and t-j models) should contain additionally electron correlations due to dipolons to visualize superconductivity. \\ 1. R.R. Sharma, Phys. Rev. {\bf B 63}, 054506, (2001).   

Bad Screening and Applicability of Migdal's Theorem to Layered Cuprates

A proof is presented, that in the model of high-T$_{c }$layered cuprates with long- range phonon-mediated attraction, due to bad screening of Coulomb forces, the ``Migdal's theorem,'' permitting to neglect vertex corrections, still holds, despite the absence of the small ``adiabatic parameter.'' The calculation of the superconducting critical temperature for this model permits to explain the high values of T$_{c}$ observed in experiment. This work was supported by the Department of Energy under the contracts {\#} W-31-109-ENG-38.