Saturated absorption spectroscopy

In experimental atomic physics, saturated absorption spectroscopy or Doppler-free spectroscopy is a set-up that enables the precise determination of the transition frequency of an atom between its ground state and an optically excited state. The accuracy to which these frequencies can be determined is, ideally, limited only by the width of the excited state, which is the inverse of the lifetime of this state. However, the samples of atomic gas that are used for that purpose are generally at room temperature, where the measured frequency distribution is highly broadened due to the Doppler effect. Saturated absorption spectroscopy allows precise spectroscopy of the atomic levels without having to cool the sample down to temperatures at which the Doppler broadening is no longer relevant (which would be on the order of a few millikelvins). It is also used to lock the frequency of a laser to the precise wavelength of an atomic transmission in atomic physics experiments.

According to the description of an atom interacting with the electromagnetic field, the absorption of light by the atom depends on the frequency of the incident photons. More precisely, the absorption is characterized by a Lorentzian of width Γ/2 (for reference, Γ ≈ 2π×6 MHz for common Rubidium D-line transitions). If we have a cell of atomic vapour at room temperature, then the distribution of velocity will follow a Maxwell–Boltzmann distribution

where ${\displaystyle N}$ is the number of atoms, ${\displaystyle k_{B}}$ is the Boltzmann constant, and ${\displaystyle m}$ is the mass of the atom. According to the Doppler effect formula in the case of non-relativistic speeds,

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