277 research outputs found

### 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

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