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# Doppler cooling limit

Doppler temperature is the minimum temperature achievable with Doppler cooling, one of the methods of laser cooling.

When a photon is absorbed by an atom moving in the opposite direction, its velocity is decreased according to the laws of momentum conservation. Accordingly, when a photon is emitted by this excited atom, there is an extra momentum added to the atom. But since emission is non-directional, this effect "averages" out, and on a time average, there is just a little increase in the atom's momentum due to emission. At the temperature when this effect exactly balances out the cooling effect of the laser, no further cooling is possible. It turns out that it is equal to $\hbar \gamma /2k_{B}$ where γ is the natural linewidth of the atomic transition, kB is the Boltzmann's constant and $\hbar$ is the reduced Planck constant.