Recoil temperature

In condensed matter physics and atomic physics, the recoil temperature is a fundamental lower limit of temperature attainable by some laser cooling schemes. When an atom decays from an excited electronic state at rest to a lower energy electronic state by the spontaneous emission of a photon, due to conservation of momentum, the atom gains momentum equivalent to the momentum of the photon. This kinetic energy gain corresponds to the recoil temperature of the atom. ^[1] 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 photon,
• 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^[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] However, the narrow-linewidth intercombination transitions of alkaline earth atoms such as strontium can have Doppler limits that are below their recoil limits, allowing laser cooling in narrow-line magneto-optical traps to the recoil limit without sub-Doppler cooling.^[4]

Cooling beyond the recoil limit is possible using specific schemes such as Raman cooling.^[5] Sub-recoil temperatures can also occur in the Lamb Dicke regime, where the recoil energy of a photon is smaller than a motional energy quantum; therefore the atom's state is effectively unchanged by recoil photons. ^[6]

See also: Doppler cooling, sub-Doppler cooling, Raman cooling, and Mössbauer effect