The validity of the few-level approximation is investigated in a system of two dipole-dipole interacting four-level
atoms. Each atom is modelled by two complete sets of angular momentum multiplets. We provide two
independent arguments demonstrating that the few-level approximation in general leads to incorrect predictions
if it is applied to the Zeeman sublevels of the atomic level scheme. First, we show that the artificial omission
of sublevels generally leads to incorrect eigenenergies of the system. The second counterexample involves an
external laser field and illustrates that the relevant states in each atom are not only determined by the laser
field polarization, but also by the orientation of the atomic separation vector. As the physical origin of this
outcome, we identify the dipole-dipole interaction between orthogonal dipole transitions of different atoms. Our
interpretation enables us to identify conditions on the atomic level structure as well as special geometries in
which (partial) few-level approximations are valid.
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