  Carbon nanotubes (CNTs) are not intrinsically superconducting but they can
carry a supercurrent when connected to superconducting electrodes. This
supercurrent is mainly transmitted by discrete entangled electron-hole states
confined to the nanotube, called Andreev Bound States (ABS). These states are a
key concept in mesoscopic superconductivity as they provide a universal
description of Josephson-like effects in quantum-coherent nanostructures (e.g.
molecules, nanowires, magnetic or normal metallic layers) connected to
superconducting leads. We report here the first tunneling spectroscopy of
individually resolved ABS, in a nanotube-superconductor device. Analyzing the
evolution of the ABS spectrum with a gate voltage, we show that the ABS arise
from the discrete electronic levels of the molecule and that they reveal
detailed information about the energies of these levels, their relative spin
orientation and the coupling to the leads. Such measurements hence constitute a
powerful new spectroscopic technique capable of elucidating the electronic
structure of CNT-based devices, including those with well-coupled leads. This
is relevant for conventional applications (e.g. superconducting or normal
transistors, SQUIDs) and quantum information processing (e.g. entangled
electron pairs generation, ABS-based qubits). Finally, our device is a new type
of dc-measurable SQUID.
