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In condensed matter physics and atomic physics, the recoil temperature is a fundamental lower limit of temperature attainable by some laser cooling schemes. It is the temperature corresponding to the kinetic energy imparted to an atom initially at rest by the spontaneous emission of a photon.^[1] The recoil temperature is

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,
$\hbar$ is the Planck constant,
$p=\hbar k$ 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 an atom is so strongly confined that its motion (and thus temperature) is effectively unchanged by recoil photons. ^[6]

References

^ Metcalf and van der Straten (1999). Laser Cooling and Trapping. New York: Springer-Verlag. ISBN 0-387-98728-2.
^ Cohen-Tannoudji, C. (2004). Atoms in electromagnetic fields (2nd ed.). Singapore: World Scientific. ISBN 978-9812560193.
^ Cohen-Tannoudji, Claude N. (1 July 1998). "Nobel Lecture: Manipulating atoms with photons". Reviews of Modern Physics. 70 (3): 707–719. Bibcode:1998RvMP...70..707C. doi:10.1103/RevModPhys.70.707.
^ Stellmer, Simon (2013). "2.7.3 The red MOT". Degenerate quantum gases of strontium (PDF) (PhD thesis). University of Innsbruck. Retrieved 2024-02-16.
^ Reichel, J.; Morice, O.; Tino, G.M.; Salomon, C. (1994). "Subrecoil Raman Cooling of Cesium Atoms". Europhysics Letters. 28 (7): 477. Bibcode:1994EL.....28..477R. doi:10.1209/0295-5075/28/7/004. S2CID 250765474.
^ Eschner, Jürgen (2003). "Laser cooling of trapped ions". J. Opt. Soc. Am. B. 20 (5): 1003–1015. Bibcode:2003JOSAB..20.1003E. doi:10.1364/JOSAB.20.001003.

[Metcalf-1] Metcalf and van der Straten (1999). Laser Cooling and Trapping. New York: Springer-Verlag. ISBN 0-387-98728-2.

[2] Cohen-Tannoudji, C. (2004). Atoms in electromagnetic fields (2nd ed.). Singapore: World Scientific. ISBN 978-9812560193.

[3] Cohen-Tannoudji, Claude N. (1 July 1998). "Nobel Lecture: Manipulating atoms with photons". Reviews of Modern Physics. 70 (3): 707–719. Bibcode:1998RvMP...70..707C. doi:10.1103/RevModPhys.70.707.

[4] Stellmer, Simon (2013). "2.7.3 The red MOT". Degenerate quantum gases of strontium (PDF) (PhD thesis). University of Innsbruck. Retrieved 2024-02-16.

[5] Reichel, J.; Morice, O.; Tino, G.M.; Salomon, C. (1994). "Subrecoil Raman Cooling of Cesium Atoms". Europhysics Letters. 28 (7): 477. Bibcode:1994EL.....28..477R. doi:10.1209/0295-5075/28/7/004. S2CID 250765474.

[eschner-6] Eschner, Jürgen (2003). "Laser cooling of trapped ions". J. Opt. Soc. Am. B. 20 (5): 1003–1015. Bibcode:2003JOSAB..20.1003E. doi:10.1364/JOSAB.20.001003.

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