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“It’s a trap!” - Admiral Ackbar

<Star Wars: Episode VI - Return of the Jedi> (1983), R. Marquand.

$$ U = \frac{\hbar \Omega^2}{4\Delta} = \frac{\hbar \Gamma}{8} \frac{I/I_{\rm sat}}{\Delta/\Gamma} $$

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Dipole trap (Far off resonance trap; FORT)

Under the dressed state picture, far-off detuned light ($|\Delta| \gg \Omega$) generates potential (AC-Stark shift),

• Red detuned case ($\Delta < 0$)

$$ \left|g\right>: E_g=0 \rightarrow -\frac{\hbar \Omega^2}{4|\Delta|} $$

• Blue detuned case ($\Delta > 0$)

$$ \left|g\right>: E_g=0 \rightarrow +\frac{\hbar \Omega^2}{4|\Delta|} $$

Under the red detuned light, atoms are attracted to the potential center, however, under the blue detuned light, atoms are repulsed to the potential center.

• A. Ashkin developed a dipole trap for capturing the atom, however, at that time the laser cooling technique was not developed so capturing the atom was difficult. One of his colleagues who developed a dipole trap with Ashkin is S. Chu, who developed the MOT.

S. Chu, Nobel Lecture: The Manipulation of Neutral Particles, Rev. Mod. Phys. 70, 685 (1998).

• In fact, the captured state is a dressed state, $\left|g'\right>=\left|g\right>+\epsilon \left|e\right>$, not a bare atomic state, $\left|g\right>$.

The depth of the dipole trap is

$$ U = \frac{\hbar \Omega^2}{4\Delta} = \frac{\hbar \Gamma}{8} \frac{I/I_{\rm sat}}{\Delta/\Gamma} $$

where $I_{\rm sat}$ is saturation intensity, $I/I_{\rm sat} = 2\Omega^2/\Gamma^2$.

XXX

$w_0$ is a beam size, $z_R$ is Reyleigh length, and $\lambda$ is wavelength of the light. By assuming the Gaussian beam under the assumption $r,z\ll 1$, the intensity of the light is

$$ I(r,z) \sim I_0 \left(1-\left(\frac{z}{z_R}\right)^2-2\left(\frac{r}{w_0}\right)^2\right) $$