Exponential enhancement of sensitivity in Ramsey interferometry with optically thick ensemble of atoms

Abstract

Ramsey interferometry is a cornerstone technique for precise measurement of time and frequency in modern clocks. The Ramsey experiments are typically done in optically dilute samples of atoms to improve homogeneity and avoid back-action of atoms on excitation pulses. In contrast to later belief, we predict and experimentally show that in optically thick samples with inhomogeneous broadening of resonant transition, the back-action 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 ${}^{167}{\text{Er}}^{3+}$ ions in ${\text{Y}}_2{\text{SiO}}_5$ crystal. Our findings open new opportunities for nonlinear high-resolution spectroscopy of resonant media and sensitivity enhancement in a new generation of solid state clocks.

10 pages, 5 figures

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