As before, the presence of a fast, radiationless decay transition results in the population of the pump band being quickly depleted (N 4 ≈ 0). In a four-level system, any atom in the lower laser level E 2 is also quickly de-excited, leading to a negligible population in that state (N 2 ≈ 0). This is important, since any appreciable population accumulating in level 3, the upper laser level, will form a population inversion with respect to level 2. That is, as long as N 3 > 0, then N 3 > N 2, and a population inversion is achieved. Thus optical amplification, and laser operation, can take place at a frequency of ν 32 (E 3 − E 2 = hν 32).