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{{Quantum book backlink|Atomic and spectroscopy}}

The term '''quantum defect''' refers to two concepts: energy loss in lasers and energy levels in [[Chemistry:Alkali metal|alkali elements]]. Both deal with [[Physics:Quantum|quantum]] systems where matter interacts with light.
==In laser science==
In [[Physics:Laser|laser]] science, the term "'''quantum defect'''" refers to the fact that the energy of a pump photon is generally higher than that of a ''signal photon'' (photon of the output radiation). The energy difference is lost to heat, which may carry away the excess [[Physics:Entropy|entropy]] delivered by the multimode incoherent pump.

The quantum defect of a [[Physics:Laser|laser]] can be defined as the part of the energy of the pumping photon which is lost (not turned into photons at the lasing wavelength) in the gain medium during lasing.<ref name="LaserQD">{{cite journal | author = T.Y.Fan | title = Heat generation in Nd:YAG and Yb:YAG | journal = [[Physics:IEEE Journal of Quantum Electronics|IEEE Journal of Quantum Electronics]] | volume = 29 | issue = 6 | pages = 1457–1459 | date = 1993 | doi = 10.1109/3.234394 | bibcode = 1993IJQE...29.1457F }}</ref> At given frequency <math>\omega_{\rm p}</math> of [[Engineering:Pump|pump]] and given frequency <math>\omega_{\rm s}</math> of lasing, the quantum defect <math>q = \hbar \omega_{\rm p} - \hbar\omega_{\rm s}</math>. Such a quantum defect has dimensions of energy; for the efficient operation, the [[Physics:Temperature|temperature]] of the gain medium
(measured in units of energy) should be small compared to the quantum defect.

The quantum defect may also be defined as follows: at a given frequency <math>\omega_{\rm p}</math> of [[Engineering:Pump|pump]] and given frequency <math>\omega_{\rm s}</math> of lasing, the quantum defect <math>q = 1 - \omega_{\rm s}/\omega_{\rm p}</math>; according to this definition, '''quantum defect''' is dimensionless.{{Citation needed|date=March 2023}}
At a fixed pump frequency, the higher the quantum defect, the lower is the upper bound for the power efficiency.

==In hydrogenic atoms==

[[File:Atom-sodium.png|thumb|In an idealized [[Physics:Bohr model|Bohr model]] alkali atom (such as sodium, pictured here), the single outer-shell electron stays outside the ionic core and it would be expected to behave just as if in the same orbital of a hydrogen atom.]]

The '''quantum defect''' of an [[Chemistry:Alkali metal|alkali atom]] refers to a correction to the energy levels predicted by the classic calculation of the hydrogen wavefunction. A simple model of the potential experienced by the single valence electron of an alkali atom is that the ionic core acts as a point charge with effective charge [[Physics:Elementary charge|e]] and the wavefunctions are [[Physics:Hydrogen-like atom|hydrogenic]]. However, the structure of the ionic core alters the potential at small radii.<ref>http://www.phy.davidson.edu/StuHome/joesten/IntLab/final/rydberg.htm, Rydberg Atoms and the Quantum Defect at the site of [[Organization:Davidson College|Davidson College]], Physics department</ref>

The 1/''r'' potential in the [[Physics:Hydrogen atom|hydrogen atom]] leads to an [[Physics:Electron|electron]] [[Physics:Binding energy|binding energy]] given by
<math display="block">E_\text{B} = -\dfrac{Rhc}{n^2},</math>
where <math>R</math> is the [[Physics:Rydberg constant|Rydberg constant]], <math>h</math> is Planck's constant, <math>c</math> is the [[Physics:Speed of light|speed of light]] and <math>n</math> is the [[Physics:Principal quantum number|principal quantum number]].

For [[Chemistry:Alkali metal|alkali atoms]] with small [[Physics:Angular momentum operator|orbital angular momentum]], the wavefunction of the valence electron is non-negligible in the ion core where the screened Coulomb potential with an effective charge of [[Physics:Elementary charge|e]] no longer describes the potential. The spectrum is still described well by the [[Physics:Rydberg formula|Rydberg formula]] with an angular momentum dependent quantum defect, <math>\delta_l</math>:
<math display="block">E_\text{B} = -\dfrac{Rhc}{(n-\delta_l)^2}.</math>

The largest shifts occur when the orbital angular momentum is equal to 0 (normally labeled 's') and these are shown in the table for the alkali metals:<ref>C.J.Foot, Atomic Physics, Oxford University Press, {{ISBN|978-0-19-850695-9}}</ref>
{| class="wikitable"
|-
! Element !! Configuration !! <math>n-\delta_s</math> !! <math>\delta_s</math>
|-
| Li || 2s || 1.59 || 0.41
|-
| Na || 3s || 1.63 || 1.37
|-
| K || 4s || 1.77 || 2.23
|-
| Rb || 5s || 1.81 || 3.19
|-
| Cs || 6s || 1.87 || 4.13
|}

==See also==
*External quantum efficiency
*Quantum efficiency of a solar cell

==References==
{{Reflist}}



[[Category:Atoms]]
[[Category:Laser science]]

{{Sourceattribution|Quantum defect|1}}

Physics:Quantum defect - Revision history

imported>WikiHarold: Repair Quantum Collection B backlink template

imported>WikiHarold: Repair Quantum Collection B backlink template