the higher energy state, and this is the normal state of the system. As T increases, the number of electrons in the high-energy state (N2) increases, but N2 never exceeds N1 for a system at thermal equilibrium; rather, at infinite temperature, the populations N2 and N1 become equal. In other words, a population inversion (N2/N1 > 1) can never exist for a system at thermal equilibrium. To achieve population inversion therefore requires pushing the system into a non-equilibrated state. The interaction of light with matter There are three types of possible interactions between a system of atoms and light that are of interest: Absorption If light (photons) of frequency ν12 passes through the group of atoms, there is a possibility of the light being absorbed by electrons which are in the ground state, which will cause them to be excited to the higher energy state. The rate of absorption is proportional to the radiation density of the light, and also to the number of atoms currently in the ground state, N1. Spontaneous emission If atoms are in the excited state, spontaneous decay events to the ground state will occur at a rate proportional to N2, the number of atoms in the excited state. The energy difference between the two states ΔE21 is emitted from the atom as a photon of frequency ν21 as given by the frequency-energy relation above. The photons are emitted stochastically, and there is no fixed phase relationship between photons emitted from a group of excited atoms; in other words, spontaneous emission is incoherent. In the absence of other processes, the number of atoms in the excited state at time t, is given by where N2(0) is the number of excited atoms at time t = 0, and τ21 is the mean lifetime of the transition between the two states. Stimulated emission If an atom is already in the excited state, it may be agitated by the passage of a photon that has a frequency ν21 corresponding to the energy gap ΔE of the excited state to ground state transition. In this case, the excited atom relaxes to the ground state, and it produces a second photon of frequency ν21. The original photon is not absorbed by the atom, and so the result is two photons of the same frequency. This process is known as stimulated emission. Specifically, an excited atom will act like a small electric