Doppler temperature

The Doppler temperature (named after the physicist Christian Doppler ) is the minimum temperature that can be achieved with Doppler cooling of an atomic two-level system .

If a photon is absorbed by an atom moving in the opposite direction, the speed of the atom is reduced due to the conservation of momentum. Analogously, an atom receives an additional impulse when a photon is spontaneously emitted . However, since the spontaneous emission is isotropic , this impulse averages to zero statistically. No further cooling is possible at the temperature at which the cooling compensates for the heating caused by the spontaneous emission.

The Doppler temperature results from

${\displaystyle T_{D}={\frac {\hbar \ \gamma }{2\ k_{\mathrm {B} }}}}$

With

• the reduced Planck constant ${\displaystyle \hbar }$
• the inverse of the lifetime of the excited state ${\displaystyle \gamma }$
• the Boltzmann constant . ${\displaystyle k_{\mathrm {B} }}$

Absorption and spontaneous emission depend critically on the speed due to the Doppler effect .

The Doppler temperature is not the lowest temperature that can be achieved with laser cooling . With the help of the polarization gradient cooling , temperatures below the Doppler temperature can be reached, reaching up to the theoretical limit, the recoil temperature .