condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the sub ...

, the recoil temperature is a fundamental lower limit of

temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...

attainable by some

laser cooling Laser cooling includes a number of techniques in which atoms, molecules, and small mechanical systems are cooled, often approaching temperatures near absolute zero. Laser cooling techniques rely on the fact that when an object (usually an atom) ...

schemes, and corresponds to the

kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...

imparted in an

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...

initially at rest by the

spontaneous emission Spontaneous emission is the process in which a quantum mechanical system (such as a molecule, an atom or a subatomic particle) transits from an excited energy state to a lower energy state (e.g., its ground state) and emits a quantized amount of ...

of a

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...

. The recoil temperature is :

T_\text = \frac = \frac,

where * is the magnitude of the

wavevector In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), ...

of the light, * is the

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...

of the atom, * is the

Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...

, *

\hbar

is the

Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...

, *

p = \hbar k

is the photon's

momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...

. In general, the recoil temperature is below the Doppler cooling limit for atoms and molecules, so

sub-Doppler cooling Sub-Doppler cooling is a class of laser cooling techniques that reduce the temperature of atoms and molecules below the Doppler cooling limit. Doppler cooling processes have a cooling limit that is characterized by the momentum recoil from the emiss ...

techniques such as

Sisyphus cooling In ultra-low-temperature physics, Sisyphus cooling, the Sisyphus effect, or polarization gradient cooling involves the use of specially selected laser light, hitting atoms from various angles to both cool and trap them in a potential well, effect ...

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. Cooling beyond the recoil limit is possible using specific schemes such as

Raman cooling In atomic physics, Raman cooling is a sub-recoil cooling technique that allows the cooling of atoms using optical methods below the limitations of Doppler cooling, Doppler cooling being limited by the recoil energy of a photon given to an atom. This ...

. Sub-recoil temperatures can also occur in the

Lamb Dicke regime In ion trapping and atomic physics experiments, the Lamb Dicke regime (or Lamb Dicke limit) is a quantum regime in which the coupling (induced by an external light field) between an ion or atom's internal qubit states and its motional states is suf ...

, where an atom is so strongly confined that its motion (and thus temperature) is effectively unchanged by recoil photons.

References

Atomic physics {{Atomic-physics-stub