Exponential Linewidth Narrowing and Enhancement of Sensitivity in Ramsey Interferometry with an Optically Thick...

Ramsey resonance is a high-resolution technique used in spectroscopy, precise measurement of time and frequency, and the creation of modern clocks. The Ramsey experiments are typically done in optically dilute samples of atoms to improve homogeneity and avoid backaction of atoms on excitation pulses. In contrast to latter belief, we predict and experimentally show that in optically thick resonant media, the backaction can lead to the highly enhanced narrowing of Ramsey resonance. The linewidth narrowing and corresponding precision of the frequency measurement scale exponentially with an increase in optical depth of a sample and can reach the limits set by homogeneous broadening. We show that this effect is caused by a nonlinear interference of multiple echoes formed inside the atomic medium, which is experimentally confirmed with ^{167}Er^{3+} ions in Y_{2}SiO_{5} crystal. Our findings open new opportunities for sensitivity enhancement of the Ramsey technique, as well as providing researchers with an additional method to investigate fundamental issues of coherent nonlinear interaction of light pulses with resonant atomic ensembles and numerous applications.