In Einstein's derivation of the Einstein coefficients, he applied the condition for equilibrium on the two populations of atoms in processes of absorption, stimulated and spontaneous emission.

In doing that, he made compatible blackbody radiation with his mathematical description of the three processes, by setting the rate of change of one of the population zero to encode the state equilibrium in his physics.

My question is: what justifies that the two populations of atoms will reach equilibrium in the first place?


If I correctly understood your question you want to ask if (for simplicity let us assume a two level system) you excite an atom with a (resonant) radiation the ground state atom will absorb the radiation and will reach to excited state and if some how the transition from excited state to ground state is forbidden (switch off the spontaneous emission) all the population must transfer into the excited state.

Answer to your question is (based on my textbook knowledge) that Einstein postulated that if an atom is in ground state then it can be excited by the interaction with a photon. The same process can be reversed i.e. if the atom is in excited state, it can interact with a photon and deexcite with same probability. The argument seems plausible (indeed ingenious) because the transition frequency from ground state to excited state is same as from excited state to ground state (looks trivial to me).

Usually more atoms are in ground state hence the chances of stimulated absorption is much higher than the stimulated emission. In a two level system no matter how hard you excite the medium the population of the excited level can not exceed the ground level because same light is exciting and deexciting through stimulated absorption/emission with an added channel of spontaneous emission.

If you try to shift the equilibrium in one direction then the reverse process will get stronger and brings back the equilibrium. For example if you make absorption more than emission then the population in the excited state increases which enhance the probability of stimulated emission and de-excitation rate increases and the process will again hit equilibrium.

Upon thinking over this argument you will find out that it does not matter if we excite slightly or very strongly after a certain time the equilibrium in absorption and emission is established.

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  • $\begingroup$ Thanks! Exactly what I was looking for. However, does the probability property of the processes mean that reaching equilibrium in a finite time is not certain? Also, with your point about the triviality of stimulated emission and absorption, why do you think that it is particularly ingenious? I would think that stimulated emission is counterintuitive compared with absorption, since stimulated absorption seems like some energy exchange between the photon and the atom. $\endgroup$ – kfs Aug 1 '16 at 18:24
  • $\begingroup$ There are time scales of spontaneous process and stimulated process. The time scale of spontaneous process is the atomic property whereas for stimulated process it also depends on the excitation flux. If the excitation continued for times appreciably larger than (smaller of two) these times then equilibrium is obtained. The triviality is for the equality of frequency of the two transitions. $\endgroup$ – hsinghal Aug 1 '16 at 18:33

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