  We demonstrate several new electron transport phenomena mediated by Andreev
bound states (ABSs) that form on three-terminal carbon nanotube (CNT) QDs, with
one superconducting (S) contact in the center and two adjacent normal metal (N)
contacts. Three-terminal spectroscopy allows us to identify the coupling to the
N contacts as the origin of the Andreev resonance (AR) linewidths and to
determine the critical coupling strengths to S, for which a ground state
transition S-QD systems can occur. We ascribe replicas of the lowest-energy ABS
resonance to transitions between the ABS and odd-parity excited QD states, a
process called excited state ABS resonances. In the conductance between the two
N contacts we find a characteristic pattern of positive and negative
differential subgap conductance, which we explain by considering two nonlocal
processes, the creation of Cooper pairs in S by electrons from both N
terminals, and a novel mechanism called resonant ABS tunneling. In the latter,
electrons are transferred via the ABS without creating Cooper pairs in S. The
three-terminal geometry also allows spectroscopy experiments with different
boundary conditions, for example by leaving S floating. Surprisingly, we find
that, depending on the boundary conditions, the experiments either show
single-particle Coulomb blockade resonances, ABS characteristics, or both in
the same measurements, seemingly contradicting the notion of ABSs replacing the
single particle states as eigenstates of the QD. We qualitatively explain these
results as originating from the finite time scale required for the coherent
oscillations between the superposition states after a single electron tunneling
event. These experiments demonstrate that three-terminal experiments on a
single complex quantum object can also be useful to investigate charge dynamics
otherwise not accessible due to the very high frequencies.
