Theory - Absorption Spectroscopy

In this section, we will be exploring our very first atom-light interactions by performing absorption spectroscopy in a vapor cell of Rb.

Two spectroscopy types - Absorption and Fluorescence

In atomic physics, we typically use two types of spectroscopy:

• Absorption spectroscopy: Light with frequency close to a transition frequency is sent through a sample and the intensity of the light transmitted is detected. The absorption is related to the atomic vapor density under investigation.

• Fluorescence spectroscopy: Light with frequency close to a transition frequency is sent through a sample and the intensity of the light that is absorbed and remitted is measured.

Both techniques are used for different purposes. In previous material when we talked about energy levels and transitions between them we often refer to specific energies $\omega$. In practice when we perform spectroscopy, we will be measuring absorption lines with specific widths and shapes, depending on 3 main broadening effects:

• "Natural linewidth" - given by the Heisenberg uncertainty principle and the energy uncertainty of the transition ~MHz level (Rb natural linewidth of interest is $\Gamma = 2\pi \cdot 6 \;\text{MHz}$)
• Doppler broadening - given by the velocity distribution of the atoms at a finite temperature, and the doppler shift in the angular frequency observed across the ensemble. For a Rb atom at 300K, this would represent a broadening of ~$2\pi \cdot 80 \;\text{MHz}$
• Collisional broadening - collisions between atoms in a finite pressure gas can supply small amounts of energy during transitions, allowing atoms to absorb a broader range of frequencies (not relevant for most atomic physics experiments, but extremely relevant in astrophysics/atmospheric studies)

The actual line profile that we will observe will be a convolution of these 3 conditions that determines its final width and shape, and would be dominated by the doppler broadening in this process.

Saturated absorption spectroscopy

We can actually remove the doppler broadening using an experimental technique called the "pump-probe" scheme.

Although both are at the same frequency, they interact with different atoms with different thermal motion. If the beams are red-detuned (slightly lower freqency) with respect to the atomic transition frequency, then the pump beam will be absorbed by atoms moving towards the beam source, while the probe beam will be absorbed by atoms moving away at the same speed in the opposite direction. If they are blue-detuned (slightly higher freqency), the opposite occurs.

For atoms that have near-zero velocity in the laser direction, the atoms will be on resonance with both lasers. It is more likely that the atom will absorb photons from the strong pump beam, the power of the pump beam is higher than the saturation intensity. Thus when a photon from the probe beam passes through the same atom, it would either be invisible to it, or undergo stimulated emission, increasing the signal measured. The resulting absorption profile that we would observe would then look something like the following.