High Speed Video Measurements of a Magneto-optical Trap

We present a video method to observe the mechanical properties of a lithium magneto-optical trap. A sinusoidally amplitude-modulated laser beam perturbed a collection of trapped $\ce{^7Li}$ atoms and the oscillatory response was recorded with a NAC Memrecam GX-8 high speed camera at 10,000 frames per second. We characterized the trap by modeling the oscillating cold atoms as a damped, driven, harmonic oscillator. Matlab scripts tracked the atomic cloud movement and relative phase directly from the captured high speed video frames. The trap spring constant, with magnetic field gradient $b_{z} = 36$ G/cm, was measured to be $4.5 \pm .5\times10^{-19}$ N/m, which implies a trap resonant frequency of $988\pm55$ Hz. Additionally, at $b_{z} = 27$ G/cm the spring constant was measured to be $2.3 \pm .2\times10^{-19}$ N/m, which corresponds to a resonant frequency of $707\pm30$ Hz. These properties at $b_{z} = 18$ G/cm were found to be $8.8 \pm .5\times10^{-20}$ N/m, and $438\pm13$ Hz.