BCS model of Cooper Pair Box

TL;DR

This paper introduces a new BCS-based model for Cooper Pair Boxes that highlights the role of excited Cooper pairs and multi-level dynamics, offering fresh insights into dissipation and experimental phenomena in Josephson junctions.

Contribution

A novel BCS Hamiltonian model for Cooper Pair Boxes that incorporates individual tunneling and excited pairs, providing a multi-level perspective beyond standard approaches.

Findings

Identifies a highly degenerated level between ground and excited states.

Shows excited Cooper pairs significantly influence system dynamics.

Proposes alternative explanations for experimental observations.

Abstract

The standard phenomenological Hamiltonian of a small superconducting Josephson junction in the charge regime (Cooper Pair Box) produces a model of the effective charge qubit with possible applications to quantum information processing. In this note a new model based on the BCS Hamiltonian with individual tunneling yields an effective multi-level picture with a highly degenerated level placed between the ground state and the excited state. Unlike in the standard approach, the excited Cooper pairs play here an important role. For such a system coupled to a zero temperature bath the additional levels act as a probability sink. In contrast to the standard large-spin model the coupling to phonons can be an effective source of dissipation. This model provides also alternative explanations of various effects observed in experiments and sheds new light on the issue of Josephson junctions as macroscopic quantum systems.