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{{Refimprove|date=December 2009}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


[[Image:Resolved sideband cooling.jpg|400px|right|Resolved sideband cooling]]
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
'''Resolved sideband cooling''' is a [[laser cooling]] technique that can be used to cool strongly trapped atoms to the quantum [[ground state]] of their motion. The atoms are usually precooled using the [[Doppler cooling|Doppler]] [[laser cooling]]. Subsequently the resolved [[sideband]] cooling is used to cool the atoms beyond the [[Doppler cooling limit]].
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


A cold trapped atom can be treated to a good approximation as a [[quantum mechanical]] [[harmonic oscillator]]. If the spontaneous decay rate is much smaller than the vibrational frequency of the atom in the trap, the [[energy level]]s of the system can be resolved as consisting of internal levels each corresponding to a ladder of vibrational states.
Registered users will be able to choose between the following three rendering modes:


Suppose a two-level atom whose ground state is shown by ''g'' and excited state by ''e''. Efficient laser cooling occurs when the frequency of the laser beam is tuned to the red sideband i.e.
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


<math>\omega = \omega_{0} - \nu</math>,
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


where <math>\omega_{0}</math> is the internal atomic transition frequency and <math>\nu</math> is the harmonic oscillation frequency of the atom.  In this case the atom undergoes the transition
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


<math>\vert g, n \rangle \rightarrow \vert e, n-1 \rangle</math>,
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


where <math>\vert a, m \rangle</math> represents the state of an ion whose internal atomic state is ''a'' and the motional state is ''m''.  This process is labeled '1' in the image to the right.
==Demos==


Subsequent [[spontaneous emission]] occurs predominantly at the carrier frequency if the recoil energy of the atom is negligible compared with the vibrational quantum energy i.e.
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


<math>\vert e, n-1 \rangle \rightarrow \vert g, n-1 \rangle.</math>


This process is labeled '2' in the image to the right.
* accessibility:
The average effect of this mechanism is cooling the ion by one vibrational energy level. When these steps are repeated a sufficient number of times <math>\vert g,0 \rangle</math> is reached with a high probability.<ref>A.SCHLIESSER,R. RIVIÈRE, G. ANETSBERGER, O. ARCIZET,T. J. KIPPENBERG [http://www.nature.com/nphys/journal/v4/n5/full/nphys939.html "Resolved-sideband cooling of a micromechanical oscillator"], nature physics, Vol 4 MAY 2008.</ref>
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


==References==
==Test pages ==
    {{Reflist}}


==See also==
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
* [[Laser cooling]]
*[[Displaystyle]]
* [[Amplitude modulation]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


{{DEFAULTSORT:Resolved Sideband Cooling}}
*[[Inputtypes|Inputtypes (private Wikis only)]]
[[Category:Atomic physics]]
*[[Url2Image|Url2Image (private Wikis only)]]
[[Category:Plasma physics]]
==Bug reporting==
[[Category:Cooling technology]]
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
 
[[ru:Охлаждение методом боковой полосы]]

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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