  Ramsey spectroscopy in large, dense ensembles of ultra-cold atoms trapped in
optical lattices suffers from dipole-dipole interaction induced shifts and
collective superradiance limiting its precision and accuracy. We propose a
novel geometry implementing fast signal readout with minimal heating for large
atom numbers at lower densities via an optical cavity operated in the weak
single atom but strong collective coupling regime. The key idea is controlled
collective transverse $\pi/2$-excitation of the atoms to prepare a macroscopic
collective spin protected from cavity superradiance. This requires that the two
halves of the atomic ensemble are coupled to the cavity mode with opposite
phase, which is naturally realized for a homogeneously filled volume covering
odd and even sites of the cavity mode along the cavity axis. The origin of the
superior precision can be traced back to destructive interference among
sub-ensembles in the complex nonlinear collective atom field dynamics. In the
same configuration we find surprising regular self-pulsing of the cavity output
for suitable continuous illumination. Our simulations for large atom numbers
employing a cumulant expansion are qualitatively confirmed by a full quantum
treatment of smaller ensembles.
