Doppler Elimination?

When an atom emits or absorbs a photon, there is always a recoil of the atom and a Doppler shift in the photon frequency. Is it possible to have recoilless atomic emission or absorption?

Answer

Yes. First consider the emission process. Normally, a typical electric dipole emission occurs with a single photon exiting the atom as a result of an allowed transition within the atom that conserves energy and angular momentum that is, the angular momentum of the atom changes by ±1 unit of Planck’s constant h/2π. The probability for all other emission processes is lower by a factor of 1/137, or by a higher power of this factor.

A two-photon electric quadrupole emission process is possible between two atomic states with angular momentum quantum numbers differing by zero or two units of h/2π. There is a broad continuous spectrum of possible energies for the two photons emitted in this quadrupole emission process. A very small fraction of these two-photon emissions will spit out two photons of the same energy, go off in opposite directions, and produce no recoil of the atom. The two-photon emission from hydrogen was the first atom to be measured and the first to be calculated by quantum electrodynamics (QED) in the 1940s. Two-photon emissions after laser excitations have become commonplace for many uses in today’s optics research.

Likewise, simultaneous two-photon absorption is possible. A container of single atoms is placed between two counter propagating laser sources, shining two identical frequency laser beams on an atom so that energy and angular momentum will be conserved and recoilless absorption can occur. First achieved in the 1970s, the precise energy-spacing values within atoms have been determined. Today, two photon absorption with non-identical energies plays a critical role in the up conversion of laser light to higher frequencies to achieve coherent beams in the UV and for providing light sources of precise frequencies.

At the nuclear level, recoilless gamma-ray emission and absorption are possible if the whole crystal recoils simultaneously with the photon emission or absorption. This Mossbauer Effect transition, discovered in the 1950s, relies on the inability in principle of identifying the single nucleus involved and includes an exponential factor proportional to the negative ratio of the temperature of the crystal to its Debye temperature.

As an interesting historical note, Albert Einstein in 1917 was among the first to recognize that classical electromagnetism cannot explain spontaneous emission of light from atoms. In particular, he inferred that an atom must recoil upon spontaneous emission, in conflict with the symmetric field distributions produced by electromagnetic theory based on Maxwell’s equations. According to Einstein, “. . . outgoing radiation in the form of spherical waves does not exist . . .” for if an atom radiated a classical spherical wave it could not recoil.