  The strength of radiative transitions in atoms is governed by selection
rules. Spectroscopic studies of allowed transitions in hydrogen and helium
provided crucial evidence for the Bohr's model of an atom. Forbidden
transitions, which are actually allowed by higher-order processes or other
mechanisms, indicate how well the quantum numbers describe the system. We apply
these tests to the quantum states in semiconductor quantum dots (QDs), which
are regarded as artificial atoms. Electrons in a QD occupy quantized states in
the same manner as electrons in real atoms. However, unlike real atoms, the
confinement potential of the QD is anisotropic, and the electrons can easily
couple with phonons of the material. Understanding the selection rules for such
QDs is an important issue for the manipulation of quantum states. Here we
investigate allowed and forbidden transitions for phonon emission in one- and
two-electron QDs (artificial hydrogen and helium atoms) by electrical
pump-and-probe experiments, and find that the total spin is an excellent
quantum number in artificial atoms. This is attractive for potential
applications to spin based information storage.
