Recoil temperature

In condensed matter physics, the recoil temperature is a fundamental lower limit of temperature attainable by some laser cooling schemes, and corresponds to the kinetic energy imparted in an atom initially at rest by the spontaneous emission of a photon. The recoil temperature is

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

where

• k is the magnitude of the wavevector of the light,
• m is the mass of the atom,
• k_B is the Boltzmann constant,
• ${\displaystyle \hbar }$ is the Planck constant,
• ${\displaystyle p=\hbar k}$ is the photon's momentum.

In general, the recoil temperature is below the Doppler cooling limit for atoms and molecules, so sub-Doppler cooling techniques such as Sisyphus cooling 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.

Cooling beyond the recoil limit is possible using specific schemes such as Raman cooling. 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.