Quantum theory of Josephson junction for a quantum bit

Abstract

Josephson junction is one of the promising devices to be used as a quantum bit or known as qubit in a quantum computer. The dynamics of current-bias Josephson junction can be described by using the Resistively and Capacitively Shunted Junction (RCSJ) model which is analogous to the classical motion of a particle in a tilted washboard potential. In this work, quantum theory and approximation methods are used to calculate and explain quantum properties of the Josepson junction. We found that the energy levels in the washboard potential can be quantum mechanically quantized, and thus used as a qubit in quantum computation. The tunneling rate from the n[superscript th] energy level exponentially increases with bias current and the first excited state is three orders of magnitude more than the ground state. The wave function of the state in the potential well is relatively similar to the harmonic oscillator wave function because of the shape of the washboard potential. The transition rate between the energy levels due to an electromagnetic radiation depends on the amplitude and the frequency of microwave current. The period of the oscillation is in the order of nanoseconds. Finally the decoherence time in Josephson junction can be observed by considering the Rabi's oscillation in the presence of current noise. The decoherence time depends on the magnitude of the current noise. This result can be used to determine the feasibility of using Josephson Junction as a qubit