Technique for magnetic moment and magnetic state reconstruction of laser cooled atoms using direct imaging

We describe a simple time-of-flight technique for measuring the magnetic moment of an optically pumped magneto-optical trap. The technique relies on free-expansion imaging of a cold atom cloud in a small magnetic field gradient without the need to detect spatial separation between magnetic sublevels. We find that the effective acceleration of the cloud can be used to characterize extreme state optical pumping. In the general case, we show that the integrated displacement of the falling cloud can be accurately modeled using rate equation simulations of magnetic sublevel populations, and knowledge of local magnetic fields, field gradients, and light intensities. The agreement between the model and the data allows the reconstruction of magnetic moments and suggests that this technique may be suitable for the measurement of population distributions over a range of optical pumping conditions.