Silver Stern Gerlach

We would like to optically pump into different $m_F$ levels in our Optical Dipole Trap to understand how this changes the scattering properties of our different isotopes and to get to a BEC. To do this we will do a stern Gerlach experiment where we spike the MOT coils before imaging.

A magnetic moment has energy

$U=-\mu \cdot B$

To find the force we take the gradient and find

$F=-\mu \frac{dB}{dz}$

Now in a atom $\mu =g_F{\mu }_B{m}_F$ so we have

$a=\frac{g_F{\mu }_B{m}_F\frac{dB}{dz}}{m}$

Now a reasonable gradient in this system is

$\frac{dB}{dz}=100\frac{G}{cm}=1\frac{T}{m}$

And the other parameters

$g_F=1,{\mu }_B=9.274\times 10^{-24}\frac{J}{T},m=6.656\times 10^{28}kg$

Which gives an acceleration of $\approx 51m/s^2$. Now using

$\Delta x=\frac{1}{2}a{t}^2+v_{0}t$

We find that the acceleration component contributes $625\mu m$ and during a 5 ms TOF the initial velocity contributes approximately 0.2 mm. So this is a significant movement compared to the size of a regular TOF.