Recoil temperature

In laser cooling, the Boltzmann constant times the recoil temperature is equal to the recoil energy deposited in a single atom initially at rest by the spontaneous emission of a single photon.[1] The recoil temperature is

${\displaystyle T_{recoil}={\frac {\hbar ^{2}k^{2}}{2mk_{B}}}}$,

since the photon's momentum is ${\displaystyle p=\hbar k}$ (here ${\displaystyle k}$ is the wavevector of the light, ${\displaystyle m}$ is the mass of an atom, ${\displaystyle k_{B}}$ is Boltzmann's constant and ${\displaystyle \hbar }$ is Planck's constant). The recoil temperature for the D2 lines of alkali atoms is typically on the order of 1 μK, and thus lower than the Doppler temperature.[2] An example of a process where the recoil temperature can be reached is Sisyphus cooling.[3]