Trapped atom number in millimeter-scale magneto-optical traps

For compact cold-atom instruments, it is desirable to trap a large number of atoms in a small volume to maximize the signal-to-noise ratio. In MOTs with beam diameters of a centimeter or larger, the slowing force is roughly constant versus velocity and the trapped atom number scales as $d^4$. For millimeter-scale MOTs formed from pyramidal reflectors, a $d^6$ dependence has been observed [Pollack et al., Opt. Express {\bf{17}}, 14109 (2009)]. A $d^6$ scaling is expected for small MOTs, where the slowing force is proportional to the atom velocity. For a 1 mm diameter MOT, a $d^6$ scaling results in 10 atoms, and the difference between a $d^4$ and a $d^6$ dependence corresponds to a factor of 1000 in atom number and a factor of 30 in the signal-to-noise ratio. We have observed $>10^4$ atoms in 1 mm diameter MOTs, consistent with a $d^4$ dependence. We are currently performing measurements for sub-mm MOTs to determine where the $d^4$ to $d^6$ crossover occurs in our system. We are also exploring MOTs based on linear polarization, which can potentially produce stronger slowing forces due to stimulated emission [Emile et al., Europhys. Lett. {\bf{20}}, 687 (1992)]. It may be possible to trap more atoms in small volumes with this method, since high intensities can be easily achieved.