I analyze a metrological strategy for improving the precision of frequency estimation via Ramsey interferometry with strings of atoms in the presence of correlated dephasing. This strategy does not employ entangled states, but rather a product state
which evolves into a stationary state under the influence of correlated dephasing. It is shown that by using this state an improvement in precision compared to standard Ramsey interferometry can be gained. This improvement is not an improvement in scaling, i.e. the estimation precision has the same scaling with the number of atoms as the standard quantum limit, but an improvement proportional to the free evolution time in the Ramsey interferometer. Since a stationary state is used, this evolution time can be substantially larger than in standard Ramsey interferometry which is limited by the coherence time of the atoms.
We discuss strategies for quantum enhanced estimation of atomic transition frequencies with ions stored in Paul traps or neutral atoms trapped in optical lattices. We show that only marginal quantum improvements can be achieved using standard Ramsey
interferometry in the presence of collective dephasing, which is the major source of noise in relevant experimental setups. We therefore analyze methods based on decoherence free subspaces and prove that quantum enhancement can readily be achieved even in the case of significantly imperfect state preparation and faulty detections.
By using a systematic optimization approach we determine quantum states of light with definite photon number leading to the best possible precision in optical two mode interferometry. Our treatment takes into account the experimentally relevant situa
tion of photon losses. Our results thus reveal the benchmark for precision in optical interferometry. Although this boundary is generally worse than the Heisenberg limit, we show that the obtained precision beats the standard quantum limit thus leading to a significant improvement compared to classical interferometers. We furthermore discuss alternative states and strategies to the optimized states which are easier to generate at the cost of only slightly lower precision.
