  We show that continuous quantum nondemolition (QND) measurement of an atomic
ensemble is able to improve the precision of frequency estimation even in the
presence of independent dephasing acting on each atom. We numerically simulate
the dynamics of an ensemble with up to N = 150 atoms initially prepared in a
(classical) spin coherent state, and we show that, thanks to the spin squeezing
dynamically generated by the measurement, the information obtainable from the
continuous photocurrent scales superclassically with respect to the number of
atoms N. We provide evidence that such superclassical scaling holds for
different values of dephasing and monitoring efficiency. We moreover calculate
the extra information obtainable via a final strong measurement on the
conditional states generated during the dynamics and show that the
corresponding ultimate limit is nearly achieved via a projective measurement of
the spin-squeezed collective spin operator. We also briefly discuss the
difference between our protocol and standard estimation schemes, where the
state preparation time is neglected.

Quantum Physics