Let’s go back to a simplified picture where we have 3 atoms.
Atom 1 is at rest, atom 2 is traveling towards the laser at speed v, and atom 3 is moving away from the laser at the same speed as atom 2. For this thought experiment, each atom that experiences a Doppler shift will have |ΔfD|= 150 MHz.
What do the transmission and absorption plots look like? Spend a few moments thinking about it, make a prediction, and then read on! Hint: There are only 3 atoms, so the fraction of light lost is very, very small.
The answer is shown in Fig. 4.4. There are three spectral features. Each spectral feature is identical except for a horizontal offset determined by the Doppler shift formula. Since atom 2 is traveling towards the laser beam, it perceives a higher laser frequency compared to what we measure in the lab. Therefore, atom 2 will absorb photons when the laser frequency is below the resonance frequency. The spectral feature from atom 2 is at δ =−150 MHz. Likewise, atom 3 is traveling away from the laser, so it is seeing a lower laser frequency compared to what we measure in the lab. Therefore, atom 3 will absorb photons when the laser frequency is above the resonance frequency. The spectral feature for atom 3 is at δ =+150 MHz. This important information is summarized in Table 1.
Fig.1 A simulated transmission plot (left) and absorption plot (right) for the three atoms
Table .1 A table summarizing the Doppler shifts for the 3 atoms
In a real vapor cell, atoms are moving with all sorts of different velocities. Unlike energy levels in an atom, velocity is a continuous variable. In the next two sections, we are going to discuss the distributions of velocities inside a real vapor cell (Sect. 4.4) and use that information to develop what the transmission and absorption plots look like for a vapor cell of atoms at a given temperature (Sect. 4.5).
