A general method is given to determine the steady-state level populations for $N$-level systems interacting with $N-1\mathrm{}$ strong resonant laser beams. For a three-level system it reproduces recent results of Whitley and Stroud. For a four-level system it leads to simple conditions for the population inversion between the highest and the lowest level. However, the population of the highest level can never exceed 0.5.

• Received 9 February 1977

DOI:https://doi.org/10.1103/PhysRevA.16.1318