Dynamics in a two-level atom magneto-optical trap

Alkaline-earth-metal atoms present an ideal platform for exploring magneto-optic trap (MOT) dynamics, enabling unique and definitive tests of laser cooling and trapping mechanisms. We have measured the trapping beam intensity, detuning, magnetic-field gradient, trap density, and lifetime dependence of the spring constant $\kappa$ and damping coefficient $\alpha$ for a ${}^1{S}_0{-}^1{P}_1$ ${}^{88}\mathrm{Sr}$ MOT by fitting the oscillatory response of the atom cloud to a step-function force. We find that the observed behavior of $\kappa$ and $\alpha$ provide a unified and consistent picture of trap dynamics that agrees with Doppler cooling theory at the level of $10\%.$ Additionally, we demonstrate that the trapped atom temperature can be determined directly from measured value of $\kappa$ and the trap size, in excellent agreement with free-expansion temperature measurements. However, the experimentally determined temperature is much higher than Doppler cooling theory, implying significant additional heating mechanisms.