Alternative Numerical Modeling of a Superconducting Charge Qubit as an Eigenvalue Problem

Abstract

Purpose - The purpose of this paper is to employ an alternative numerical approach to analyze the characteristics of superconducting charge qubit based on a single Cooper pair box (SCB), also to study the influence of the bias current. Design/methodology/approach - The paper starts with the circuit model of a charge qubit system based on Josephson junction using Hamiltonian formalism. Corresponding Schrodinger eigenvalue problem with periodic boundary condition is converted to the Mathieu type eigenvalue problem. By applying finite difference technique, energy spectrum of charge qubit is obtained and the solutions in the lowest band are obtained in the form of Bloch waves whose superposition provides a wave packet to investigate the effect of bias current to the Coulomb blockade. Findings - The paper identifies a periodic tridiagonal Hermitian matrix form of the eigenvalue problem that is believed to be a special eigenvalue problem. The paper emphasizes that Schrodinger formalism is very, useful to model superconducting qubits systems. The investigations indicate that the bias current strongly influences the Coulomb blockade and expectation value of supercurrent (as well as number of Cooper pairs) are affected by gate voltage and energy scale. Research limitations/implications - In the present study, Schrodinger eigenvalue problem is time independent, therefore, current-voltage characteristics of the charge qubit system could not be considered. The solution technique applied here can also be used to apply other type of Josephson junction based qubits and circuits. Practical implications - The paper includes theoretical findings for the development of superconducting qubit that can be valuable for experimentalist. The result obtained in this study is useful for the comparison of experimental study with the expectation value of number of Cooper pairs as function of gate voltage. Working parameters of a SCB can be determined from the findings. Originality/value This paper fulfils the contribution of the numerical study of Schrodinger equation for the investigation of superconducting qubits under the influence of bias current.