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 ¼ 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.
DOI: 10.1103/PhysRevLett.125.200505