Laser noise imposed limitations of ensemble quantum metrology

Laser noise is a decisive limiting factor in high precision spectroscopy of narrow lines using atomic ensembles. In an idealized Doppler and differential light shift free magic wavelength lattice configuration, it remains as one distinct principal limitation beyond collective atomic decay. In this work we study the limitations originating from laser phase and amplitude noise in an idealized Ramsey pulse interrogation scheme with uncorrelated atoms. Phase noise leads to a saturation of the frequency sensitivity with increasing atom number while amplitude noise implies a scaling $1/\sqrt{\tau}$ with $\tau$ being the interrogation time. We employ a technique using decoherence free subspaces first introduced in New J. Phys. \textbf{14}, 043011 (2012) which can restore the scaling with the square root of the inverse particle number $1/\sqrt{N}$. Similar results and improvements are obtained numerically for a Rabi spectroscopy setup.