  The Cooper-pair transistor (CPT), a small superconducting island enclosed
between two Josephson weak links, is the atomic building block of various
superconducting quantum circuits. Utilizing gate-tunable semiconductor channels
as weak links, the energy scale associated with the Josephson tunneling can be
changed with respect to the charging energy of the island, tuning the extent of
its charge fluctuations. Here, we directly demonstrate this control by mapping
the energy level structure of a CPT made of an indium arsenide nanowire (NW)
with a superconducting aluminum shell. We extract the device parameters based
on the exhaustive modeling of the quantum dynamics of the phase-biased nanowire
CPT and directly measure the even-odd parity occupation ratio as a function of
the device temperature, relevant for superconducting and prospective
topological qubits.
