Superconducting charge qubits from a microscopic many-body perspective

TL;DR

This paper derives the quantised Josephson equation for superconducting charge qubits directly from a microscopic many-body Hamiltonian, revealing finite-size effects beyond the traditional mean field approximation.

Contribution

It introduces a microscopic derivation of the Josephson equation for charge qubits, including finite-size corrections, from a strongly coupled many-body Hamiltonian.

Findings

Derived Josephson equation from microscopic Hamiltonian

Predicted finite-size effects in charge qubits

Extended beyond mean field approximation

Abstract

The quantised Josephson junction equation that underpins the behaviour of charge qubits and other tunnel devices is usually derived through cannonical quantisation of the classical macroscopic Josephson relations. However, this approach may neglect effects due to the fact that the charge qubit consists of a superconducting island of finite size connected to a large superconductor. We show that the well known quantised Josephson equation can be derived directly and simply from a microscopic many-body Hamiltonian. By choosing the appropriate strong coupling limit we produce a highly simplified Hamiltonian that nevertheless allows us to go beyond the mean field limit and predict further finite-size terms in addition to the basic equation.