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The term '''quantum defect''' is [[ambiguity|ambiguous]]. Various meanings are discussed below. Characteristic is that the defect deals with the loss on the smallest energy scale of light: that of the [[quantum]].
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==Quantum defect in laser science==
In [[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 difference of energies goes to the heat;
this heat may carry away the excess of [[entropy]] delivered with the multimode uncoherent pump.
 
The '''quantum defect''' of a [[laser]] can be defined as part of the energy of the pumping photon, which is lost (not turned into photons at the lasing wavelength) in the [[gain medium]] at the [[lasing]].<ref name="LaserQD">{{cite journal
| url=http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=6035&arnumber=234394&count=87&index=4
| author=T.Y.Fan
| coauthors=
| title=Heat generation in Nd:YAG and Yb:YAG
| journal=[[IEEE Journal of Quantum Electronics]]
| volume=29
| issue=6
| pages=1457–1459
| year=1993
| doi=10.1109/3.234394
| format=abstract
|bibcode = 1993IJQE...29.1457F }}</ref>
At given frequency <math>~\omega_{\rm p}~</math> of [[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 '''quantum defect''' has dimension of energy; for the efficient operation, the [[temperature]] of the [[gain medium]]
(measured in units of energy) should be small compared to the '''quantum defect'''.
 
<!--
Some colleagues define the '''quantum defect''' in a different way.
At given frequency <math>~\omega_{\rm p}~</math> of [[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
.<ref>
'''[[WHO HAD PUBLISHED A PAPER WITH SUCH DEFINITION??? Reference, please!!]]'''
</ref><br><br>
!-->
At a fixed pump frequency, the higher the quantum defect, the lower is the upper bound for the power efficiency.
 
==Quantum defect in Rydberg atoms==
The '''quantum defect''' of a [[Rydberg atom]] refers to a correction applied to the equations governing Rydberg atom behavior to take into account the fact that the inner electrons do not entirely screen their associated charge in the nucleus.<ref>
http://www.phy.davidson.edu/StuHome/joesten/IntLab/final/rydberg.htm ,
Rydberg Atoms and the Quantum Defect at the site of [[Davidson College]], Physics department</ref>  It is used particularly for the alkalis that contain a single electron in their outer shell.  
 
The perfect 1/''r'' potential in the [[hydrogen atom]] leads to an [[electron]] [[binding energy]] given by
 
:<math>E_\text{B} = -\dfrac{Rhc}{n^2}</math>,
 
where ''R'' is the [[Rydberg constant]], ''h'' is Planck's constant, ''c'' is the speed of light and ''n'' is the [[principal quantum number]].
 
For multi-electron atoms in Rydberg states with a low value of the [[angular momentum operator|orbital angular momentum]], there is a high probability of finding the excited electron near the nucleus where it can [[Polarizability|polarize]] or even penetrate the ion core, modifying the potential.  The resulting shift of the energy levels is represented mathematically as an angular momentum dependent quantum defect, δ<sub>''l''</sub>:
 
:<math>E_\text{B} = -\dfrac{Rhc}{(n-\delta_l)^2}</math>.
 
The largest shifts occur when the orbital angular momentum is equal to 0 (normally labelled '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 !! n* !! δ<sub>''s''</sub>
|-
| 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==
<references/>
 
<!--  {{disambig}}  recover this as soon as we have separate articles for each of meanings mentioned
!-->
 
[[Category:Atoms]]
[[Category:Laser science]]
 
 
{{quantum-stub}}

Latest revision as of 04:02, 21 October 2014

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