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

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,
$\hbar$ 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 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]

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.

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[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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