We study a modified Ramsey spectroscopy technique employing slowly decaying
states for quantum metrology applications using dense ensembles. While closely
positioned atoms exhibit superradiant collective decay and dipole-dipole
induced frequency shifts, recent results [Ostermann, Ritsch and Genes, Phys.
Rev. Lett. \textbf{111}, 123601 (2013)] suggest the possibility to suppress
such detrimental effects and achieve an even better scaling of the frequency
sensitivity with interrogation time than for noninteracting particles. Here we
present an in-depth analysis of this 'protected subspace Ramsey technique'
using improved analytical modeling and numerical simulations including larger
3D samples. Surprisingly we find that using sub-radiant states of N particles
to encode the atomic coherence yields a scaling of the optimal sensitivity
better than 1/N​. Applied to ultracold atoms in 3D optical lattices we
predict a precision beyond the single atom linewidth.Comment: 9 pages, 7 figure