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By modifying the field configuration, can we trap atoms by the static electric field (DC Stark Shift)? If not, is it due to the lack of permanent dipole moment? Is there any rigorous mathematical proof for this (like the Earnshaw theorem for ion trap)?

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The potential of a neutral but polarizable atom in an electric field is given by

$$U=-\frac{\alpha}{2}E^2,$$

where $\alpha$ is the polarizability, and $E$ the electric field. From this, we can see that atoms influenced by such a potential are drawn towards higher magnitude electric fields where the potential minimum exists. And as there are no electric field maximums from Earnshaw's theorem, atoms can not be trapped by such a static field. However, in the quasi-static regime where the electric field is rotated or manipulated faster than the atomic motion but not fast enough to internally excite the atoms, localised potential minimum can exist in the time average, see ac electric trapping of neutral atoms. This type of trap is similar to an ion Paul trap.

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  • $\begingroup$ Thanks for the helpful answer! I also found that there is a generalization of the Earnshaw's theorem to neutral polarizable objects arxiv.org/abs/physics/0701277. $\endgroup$
    – sh2233
    Nov 11 at 5:12

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