A population inversion occurs while a system exists in a state in which more members of the system are in higher, excited states than in lower, unexcited energy states. It is called an "inversion" because in many familiar and commonly encountered physical systems, this is not possible.
The redistribution of atomic energy levels that takes place in a system so that laser action can occur. Normally, a system of atoms is in temperature equilibrium and there are always more atoms in low energy states than in higher ones. Although absorption and emission of energy is a continuous process, the statistical distribution of atoms in the various energy states is constant.
If there are more atoms in the upper level (N2) than in the lower level (N1), the system is not at equilibrium. In fact, at thermodynamic equilibrium, the distribution of the atoms between the levels is given by Boltzmann's Law:
N2 = N1x exp – ((E2 – E1) / kT)
N2 is always less than N1. A situation not at equilibrium must be created by adding energy via a process known as “pumping” in order to raise enough atoms to the upper level.