  Natural orbital theory is a computationally useful approach to the few and
many-body quantum problem. While natural orbitals are known and applied since
many years in electronic structure applications, their potential for
time-dependent problems is being investigated only since recently. Correlated
two-particle systems are of particular importance because the structure of the
two-body reduced density matrix expanded in natural orbitals is known exactly
in this case. However, in the time-dependent case the natural orbitals carry
time-dependent phases that allow for certain time-dependent gauge
transformations of the first kind. Different phase conventions will, in
general, lead to different equations of motion for the natural orbitals. A
particular phase choice allows us to derive the exact equations of motion for
the natural orbitals of any (laser-) driven two-electron system explicitly,
i.e., without any dependence on quantities that, in practice, require further
approximations. For illustration, we solve the equations of motion for a model
helium system. Besides calculating the spin-singlet and spin-triplet ground
states, we show that the linear response spectra and the results for resonant
Rabi flopping are in excellent agreement with the benchmark results obtained
from the exact solution of the time-dependent Schr\"odinger equation.
