  An artifcial two-atomic molecule, also called a double quantum dot (DQD), is
an ideal system for exploring few electron physics. Spin-entanglement between
just two electrons can be explored in such systems where singlet and triplet
states are accessible. These two spin-states can be regarded as the two states
in a quantum two-state system, a so-called singlet-triplet qubit. A very
attractive material for realizing spin based qubits is the carbon nanotube
(CNT), because it is expected to have a very long spin coherence time. Here we
show the existence of a gate-tunable singlet-triplet qubit in a CNT DQD. We
show that the CNT DQD has clear shell structures of both four and eight
electrons, with the singlet-triplet qubit present in the four-electron shells.
We furthermore observe inelastic cotunneling via the singlet and triplet
states, which we use to probe the splitting between singlet and triplet, in
good agreement with theory.
