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Technical Physics Letters

Plasma frequency of the tunnel Josephson junctions with anharmonic current-phase relationship

I. N. Askerzade

Published Sep 1, 2007• 1 citation
Publisher

Abstract

The effect of alternating current on the plasma frequency of a tunnel Josephson junction with anharmonic current-phase relationship under the conditions of simultaneous passage of direct (dc) and alternating (ac) current has been studied. It is established that the presence of the ac component decreases, whereas the anharmonicity increases the plasma frequency of the tunnel Josephson junction.

DOI
10.1134/s1063785007090027

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The effect of alternating current on the plasma frequency of a tunnel Josephson junction with anharmonic current-phase relationship under the conditions of simultaneous passage of direct (dc) and alternating (ac) current has been studied. It is established that the presence of the ac component decreases, whereas the anharmonicity increases the plasma frequency of the tunnel Josephson junction.
The aim of this review is the analysis of dynamical properties of Josephson junctions (JJ) with anharmonic current-phase relation (CPR). Firstly, discussion of theoretical foundation of anharmonic CPR in different Josephson structures and their experimental observation are presented. The influence of anisotropy and multiband effects on CPR of JJ are analyzed. We present recent theoretical study results of the anharmonic CPR influence on I–V curve, plasma frequency, and dynamics of long JJ. Results of study of Shapiro steps in I–V curve of anharmonic JJ are also presented. Finally, CPR anharmonicity effect on characteristics of JJ-based qubits is discussed.
This study is devoted to the investigation of the Josephson phase qubit spectrum considering the anharmonic current-phase relation of the junction. The change in energy difference in the spectrum of phase qubits based on single-band/multiband Josephson junctions is also analyzed. It was shown that the presence of the anharmonic term in the current-phase relation and frustration effects in the junction electrodes leads to changing effective plasma frequencies in the different cases and results in an energy spectrum.
We find the tunneling decay rate DDD of the zero-voltage states of a Josephson junction driven by a small ac current ${I}_{1}cos(\ensuremath{\Omega}t)$, when the dc current is close to the critical one. In the high-frequency limit $\ensuremath{\Omega}\ensuremath{\gg}{\ensuremath{\omega}}_{p}$ (${\ensuremath{\omega}}_{p}$ is the plasma frequency) for a high-QQQ junction, the amplitude I1{I}_{1}I1​ enters into the tunneling exponent with a large exponential factor and $\mathrm{ln}D\ensuremath{\propto}{I}_{1}\mathrm{exp}(\frac{1.77\ensuremath{\Omega}}{{\ensuremath{\omega}}_{p}})$.
In this paper, we analyse the properties of an electrical circuit containing Josephson junctions in series. Our approach is looking at the quantum mechanical phase di erence between each pair of superconducting electrodes. Since the di erential equations modelling the behaviour of this arrangement are nonlinear, we mostly work with numerical methods in MATLAB to obtain the solutions. From this point we will proceed with investigating the IV-characteristics and frequency dependent transmission of signals in the circuit when driven by DC and AC current.