  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.
