Ultimate quantum limits for noisy magnetometry via time-continuous measurements. (arXiv:1706.00485v2 [quant-ph] UPDATED)
We address the estimation of the magnetic field B acting on an ensemble of
atoms with total spin J subjected to collective transverse noise. By preparing
an initial spin coherent state, for any measurement performed after the
evolution, the mean-square error of the estimate is known to scale as 1/J, i.e.
no quantum enhancement is obtained. Here, we consider the possibility of
continuously monitoring the atomic environment, and conclusively show that
strategies based on time-continuous non-demolition measurements followed by a
final strong measurement may achieve Heisenberg-limited scaling 1/J 2 and also
a quantum-enhanced scaling in terms of the interrogation time. We also find
that time-continuous schemes are robust against detection losses, as we prove
that the quantum enhancement can be recovered also for finite measurement
efficiency. Finally, we analytically prove the optimality of our strategy.