[avsteele]

Atomic physicists use mostly semiconductor diode lasers.

You need to narrow their emission wavelength to something ~ the atomic transition (MHz) and then carefully tune it as you say.

Typically diffraction grating is used to carefully feedback some of the laser's output (<10%) back into it, and this can be used to to narrow the emission from several nm to MHz, and to coarsely tune the frequency to few 10-100 Ghz.

Fine tuning is done by changing the current flowing through the laser or the temperature of the junction. These both cause a frequency shift on the MHz scale scale.

You might fine it interesting, you can also use VCOs for fine tuning, but you take the generated RF and send it into a crystal called an Austo-optic modulator. The laser light refracts from the RF phonons propagating through the crystal and this can be used to shift the laser light by the RF frequency.

[fsh]

Typical optical clock transitions have ~Hz linewidths, not MHz.

The intrinsic frequency stability of almost all lasers is by far not good enough to be able to probe such transitions. Therefore, ultra-stable optical cavities are used as a frequency reference, and the laser is constantly steered to stay on the cavity resonance by a fast electronic feedback system. In this way, laser linewidths in the sub-Hz range can be achieved. Then an acousto-optic modulator is used to scan the laser frequency across the clock transition.

[Robotbeat]

*acousto-optic, of course. (I swear, auto-incorrect is getting worse.)

To expound slightly on your (correct) explanation: The phonons impart (or remove) energy to (from) the laser light, the same way a moving mirror does: via doppler shift.

I made a differential heterodyne interferometer in undergrad using the method you describe.