We have seen that an atom can jump from a lower-energy level $E_1$ to a higher-energy level $E_2$ by absorbing a photon. FIGURE 41.30a illustrates the basic absorption process, with a photon of frequency $f=\text{Δ}{E}_{\text{atom}}\text{/}h$ disappearing as the atom jumps from level 1 to level 2. Once in level 2, as shown in FIGURE 41.30b, the atom can emit a photon of the same frequency as it jumps back to level 1. This transition is called spontaneous emission.

FIGURE 41.30 Three types of radiative transitions.

In 1917, four years after Bohr’s proposal of stationary states in atoms but still prior to de Broglie and Schrödinger, Einstein was puzzled by how quantized atoms reach thermodynamic equilibrium in the presence of electromagnetic radiation. Einstein found that absorption and spontaneous emission were not sufficient to allow a collection of atoms to reach thermodynamic equilibrium. To resolve this difficulty, Einstein proposed a third mechanism for the interaction of atoms with light.

The left half of FIGURE 41.30c shows a photon with frequency $f=\text{Δ}{E}_{\text{atom}}\text{/}h$ approaching an excited atom. If a photon can induce the $1\to 2$ transition of absorption, then Einstein proposed that it should also be able to induce a $2\to 1$ transition. In a sense, this transition is a reverse absorption. But to undergo a reverse absorption, the atom must emit a photon of frequency $f=\text{Δ}{E}_{\text{atom}}\text{/}h$. The end result, as seen in the right half of Figure 41.30c, is an atom in level 1 plus two photons! Because the first photon induced the atom to emit the second photon, this process is called stimulated emission.

Stimulated emission occurs only if the first photon’s frequency exactly matches the $E_2-E_1$ energy difference of the atom. This is precisely the same condition that absorption has to satisfy. More interesting, the emitted photon is identical to the incident photon. This means that as the two photons leave the atom they have exactly the same frequency and wavelength, are traveling in exactly the same direction, and are exactly in phase with each other. In other words, stimulated emission produces a second photon that is an exact clone of the first.

Stimulated emission is of no importance in most practical situations. Atoms typically spend only a few nanoseconds in an excited state before undergoing spontaneous emission, so the atom would need to be in an extremely intense light wave for stimulated emission to occur prior to spontaneous emission. Ordinary light sources are not nearly intense enough for stimulated emission to be more than a minor effect; hence it was many years before Einstein’s prediction was confirmed. No one had doubted Einstein because he had clearly demonstrated that stimulated emission was necessary to make the energy equations balance, but it seemed no more important than would pennies to a millionaire balancing her checkbook. At least, that is, until 1960, when a revolutionary invention appeared that made explicit use of stimulated emission: the laser.