Recoil temperature

In quantum optics , the recoil temperature or recoil temperature is the lowest temperature that can be reached when atoms are cooled by absorption and emission of photons (this is also referred to as the recoil limit ). It is defined as the temperature that can be assigned to a resting atom that emits exactly one photon on the cooling transition used and thus experiences a small transfer of momentum ( recoil ).

The atom from the emitted photon has the pulse ( : Planck's constant , : Wavelength of the photon : wave number). Because of the conservation of momentum, the atom receives exactly the opposite momentum. If the atom has mass , the kinetic energy follows from this change in momentum . A temperature, the recoil temperature, can now be formally assigned to this kinetic energy: ${\displaystyle p_{\gamma }=\hbar k=h/\lambda }$ ${\displaystyle h}$ ${\displaystyle \lambda }$ ${\displaystyle k=2\pi /\lambda }$ ${\displaystyle m}$ ${\displaystyle E_{\text{kin, Atom}}=p_{\gamma }^{2}/(2m)}$

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

Here is the Boltzmann constant . The recoil temperature is typically of the order of magnitude and is therefore significantly lower than the Doppler temperature . The recoil temperature can e.g. B. can be achieved with the method of Sisyphus cooling . ${\displaystyle k_{B}}$ ${\displaystyle 1\,\mathrm {\mu K} }$

Recoil speed

Analogous to the recoil temperature, the recoil speed or recoil speed is defined as the change in speed that an atom experiences during the spontaneous emission of a photon: ${\displaystyle v_{\text{recoil}}}$

${\displaystyle v_{\text{recoil}}={\frac {\hbar k}{m}}={\frac {p_{\gamma }}{m}}}$

It is typically a few cm / s.

Individual evidence

1. ↑ ^{a b} Harold Metcalf , Peter van der Straten: Laser Cooling and Trapping . Springer-Verlag, New York 1999, ISBN 0-387-98728-2 .