What is the Lamb-Dicke regime and how does it impact ion trapping experiments?

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SUMMARY

The Lamb-Dicke regime is crucial for the creation of entangled ions in ion trapping experiments. It defines the upper limit of ion motion relative to the wavelength of light used for state manipulation, specifically requiring that the amplitude of ion motion is significantly smaller than \(\lambda/2\pi\). This regime establishes a maximum temperature for the ions, necessitating that they be cooled below the Lamb-Dicke limit prior to manipulation, as active laser cooling cannot occur during the entanglement process.

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Incidental to my research in connection with the questions I posed in https://www.physicsforums.com/showthread.php?t=279595", I found the answer to a question that has been pending in this forum for some time.

The Lamb-Dicke limit is a necessary condition for creation of entangled ions (i.e. the ions must be within the Lamb-Dicke range while their internal and motional states are being manipulated to create the entanglement). The Lamb-Dicke limit defines the upper limit of a range where the ion motion is much smaller than the wavelength of light that is used to excite the desired transition (i.e. the amplitude of the ion motion in the propagation direction of the state manipulating radiation is much less than \lambda/2 Pi, where\lambda is the radiation wavelength). In other words, the Lamb-Dicke limit functionally establishes a maximum temperature for the ions that are to be manipulated. Further, because the ions generally cannot be actively laser cooled while the state manipulations are being performed, the ions must initially be cooled below the Lamb-Dicke limit such that the Lamb-Dicke limit will not be exceeded during the entire manipulation process that creates the entanglement.
\pi
 
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Man... if this had been asked in General Discussion, I would have had something to say about Welshmen and their sheep... :rolleyes:
 

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