Recoil temperature

The recoil temperature is a fundamental lower limit of temperature attainable by some laser cooling schemes, and corresponds 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

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

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, ${\displaystyle k_{\text{B}}}$ is the Boltzmann constant and ${\displaystyle \hbar }$ is the Planck constant). In general, the recoil temperature is below the Doppler cooling limit for atoms and molecules, so sub-Doppler cooling techniques such as Sisyphus cooling[2] are necessary to reach it. For example, the recoil temperature for the D₂ lines of alkali atoms is typically on the order of 1 μK, in contrast with a Doppler cooling limit on the order of 100 μK.[3]

Cooling beyond the recoil limit is possible using specific schemes such as Raman cooling.[4] Sub-recoil temperatures can also occur in the Lamb Dicke regime, where an atom is so strongly confined that its motion (and thus temperature) is effectively unchanged by recoil photons. [5]