Connecting Berry's phase and the pumped charge in a Cooper pair pump

The properties of the tunnelling-charging Hamiltonian of a Cooper pair pump are well understood in the regime of weak and intermediate Josephson coupling, i.e. when $E_{\mathrm{J}}\lesssim E_{\mathrm{C}}$. It is also known that Berry's phase is related to the pumped charge induced by the adiabatical variation of the eigenstates. We show explicitly that pumped charge in Cooper pair pump can be understood as a partial derivative of Berry's phase with respect to the phase difference $\phi$ across the array. The phase fluctuations always present in real experiments can also be taken into account, although only approximately. Thus the measurement of the pumped current gives reliable, yet indirect, information on Berry's phase. As closing remarks, we give the differential relation between Berry's phase and the pumped charge, and state that the mathematical results are valid for any observable expressible as a partial derivative of the Hamiltonian.Comment: 5 pages, 5 figures, RevTeX, Presentation has been clarifie

New Limit for the Half-Life of 2K(2neutrino)-Capture Decay Mode of 78Kr

Features of data accumulated at 1817 hours in the experimental search for 2K(2 \nu)-capture decay mode of Kr-78 are discussed. The new limit for this decay half-life is found to be T_{1/2} > 2.3 *10^{20} yr. (90% C.L.).Comment: 7 pages, 4 figures, submitted to Phys. of Atom. Nuc

The discretised harmonic oscillator: Mathieu functions and a new class of generalised Hermite polynomials

We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansatz defines a new class of generalised Hermite polynomials which are explicit functions of the coupling parameter and tend to ordinary Hermite polynomials in the limit of vanishing coupling constant. The polynomials become orthogonal as parts of the eigenvectors of a Hermitian matrix and, consequently, the exponential part of the solution can not be excluded. We have conjectured the general structure of the solution, both with respect to the quantum number and the order of the expansion. An explicit proof is given for the three leading orders of the asymptotical solution and we sketch a proof for the asymptotical convergence of eigenvectors with respect to norm. From a more practical point of view, we can estimate the required effort for improving the known solution and the accuracy of the eigenvectors. The applied method can be generalised in order to accommodate several variables.Comment: 18 pages, ReVTeX, the final version with rather general expression

Arrays of Josephson junctions in an environment with vanishing impedance

The Hamiltonian operator for an unbiased array of Josephson junctions with gate voltages is constructed when only Cooper pair tunnelling and charging effects are taken into account. The supercurrent through the system and the pumped current induced by changing the gate voltages periodically are discussed with an emphasis on the inaccuracies in the Cooper pair pumping. Renormalisation of the Hamiltonian operator is used in order to reliably parametrise the effects due to inhomogeneity in the array and non-ideal gating sequences. The relatively simple model yields an explicit, testable prediction based on three experimentally motivated and determinable parameters.Comment: 13 pages, 9 figures, uses RevTeX and epsfig, Revised version, Better readability and some new result

Pulse Shape Analysis and Identification of Multipoint Events in a Large-Volume Proportional Counter in an Experimental Search for 2K Capture Kr-78

A pulse shape analysis algorithm and a method for suppressing the noise component of signals from a large copper proportional counter in the experiment aimed at searching for 2K capture of Kr-78 are described. These signals correspond to a compound event with different numbers of charge clusters due to from primary ionization is formed by these signals. A technique for separating single- and multipoint events and determining the charge in individual clusters is presented. Using the Daubechies wavelets in multiresolutional signal analysis, it is possible to increase the sensitivity and the resolution in extraction of multipoint events in the detector by a factor of 3-4.Comment: 10 pages, 8 figures. submitted to Instruments and Experimental Techniques; ISSN 0020/441

Decoherence in circuits of small Josephson junctions

We discuss dephasing by the dissipative electromagnetic environment and by measurement in circuits consisting of small Josephson junctions. We present quantitative estimates and determine in which case the circuit might qualify as a quantum bit. Specifically, we analyse a three junction Cooper pair pump and propose a measurement to determine the decoherence time $\tau_\phi$.Comment: 4 pages, 4 figure