  Coherent dark states in atoms, created by simultaneous interaction of two
coherent light fields with a 3-level system, are of prime importance in quantum
state manipulation. They are used extensively in quantum sensing and quantum
information applications to build atomic clocks, magnetometers, atomic
interferometers and more. Here we study the formation and decay of coherent
dark-states in an ensemble of laser-cooled free-falling atoms. We measure the
optical-pumping rate into the dark-state in the $\sigma ^+-\sigma ^-$
polarization configuration. We find that the pumping rate is linear with the
optical field intensity, but about an order-of-magnitude slower than the rate
predicted by the commonly used, but simplistic, three-level analytic formula.
Using a numerical model we demonstrate that this discrepancy is due to the
multi-level Zeeman manifold. Taking into account the slower pumping rate we
explain quantitatively the relation between the light-shift and the duration of
pumping into dark-state in Ramsey spectroscopy. We also measure the decay of
the dark-state coherence and find that in our apparatus it is dominated by the
mechanical motion of the atoms out of the probing region, while the atomic
decoherence is negligible.
