  Electronic transport through nanostructures is greatly affected by the
presence of superconducting leads. If the interface between the nanostructure
and the superconductors is sufficiently transparent, a dissipationless current
(supercurrent) can flow through the device due to the Josephson effect. A
Josephson coupling, as measured via the zero-resistance supercurrent, has been
obtained via tunnel barriers, superconducting constrictions, normal metals, and
semiconductors. The coupling mechanisms vary from tunneling to Andreev
reflection. The latter process has always occurred via a normal-type system
with a continuous density of states. Here we investigate a supercurrent flowing
via a discrete density of states, i.e., the quantized single particle energy
states of a quantum dot, or artificial atom, placed in between superconducting
electrodes. For this purpose, we exploit the quantum properties of finite-sized
carbon nanotubes (CNTs). By means of a gate electrode, successive discrete
energy states are tuned ON and OFF resonance with the Fermi energy in the
superconducting leads, resulting in a periodic modulation of the critical
current and a non-trivial correlation between the conductance in the normal
state and the supercurrent. We find, in good agreement with existing theory,
that the product of the critical current and the normal state resistance
becomes an oscillating function, in contrast to being constant as in previously
explored regimes.
