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 State of matter, phases, that arise from electromagnetic forces between atoms and elec ...

and

atomic physics Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...

, the recoil temperature is a fundamental lower limit of

temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...

attainable by some

laser cooling Laser cooling includes several techniques where atoms, molecules, and small mechanical systems are cooled with laser light. The directed energy of lasers is often associated with heating materials, e.g. laser cutting, so it can be counterintuit ...

schemes. When an atom decays from an excited electronic state at rest to a lower energy electronic state by the

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

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 particles that can ...

, due to

conservation of momentum In Newtonian mechanics, momentum (: momenta or momentums; 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. ...

, the atom gains momentum equivalent to the momentum of the photon. This

kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...

gain corresponds to the recoil temperature of the atom. 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 photon, * is the

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

of the atom, * is the

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

, *

\hbar

is the

Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

, *

p = \hbar k

is the photon's

momentum In Newtonian mechanics, momentum (: momenta or momentums; 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. ...

. 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. In experiment implementation, Doppler cooling is limited by the broad natural linewidth of the lasers used ...

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. However, the narrow-linewidth intercombination transitions of

alkaline earth The alkaline earth metals are six chemical elements in group 2 of the periodic table. They are beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra).. The elements have very similar properties: they are al ...

atoms such as

strontium Strontium is a chemical element; it has symbol Sr and atomic number 38. An alkaline earth metal, it is a soft silver-white yellowish metallic element that is highly chemically reactive. The metal forms a dark oxide layer when it is exposed to ...

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. 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 su ...

, 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.

References

Atomic physics {{Atomic-physics-stub