FORCE MEASUREMENT VIA DARK-STATE COOLING

We analyze the ''polarization-gradient-assisted velocity-selective coh erent population-trapping'' laser cooling scheme in the presence of a homogeneous force. In the limit of a slow rate of cooling this system may be treated using a set of rate equations after applying the secula r approximation. This uses a basis of states which form a band structu re resulting from the periodic optical potentials. We show that in the presence of a force the secular approximation may be retained, and de rive the required modification to the rate equations, This is a densit y operator method of treating the action of a force on a particle in a band structure, and clearly shows reflections at the band edge. We so lve for the steady-state momentum distribution, which provides informa tion on the amount to which the presence of a force limits the achieva ble temperature. We solve also for the steady-state fluorescence and s uggest that the fluorescence from atoms cooled with this scheme could be used as a force meter.