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

TL;DR

This paper demonstrates that in optically thick atomic ensembles, back-action effects can exponentially narrow Ramsey resonance linewidths, significantly enhancing measurement sensitivity, confirmed experimentally with rare-earth ions in crystals.

Contribution

The study reveals and experimentally confirms that optically thick, inhomogeneously broadened atomic samples can exponentially improve Ramsey interferometry sensitivity through nonlinear interference effects.

Findings

Linewidth narrowing scales exponentially with optical depth.

Back-action causes highly enhanced resonance narrowing.

Experimental validation with $^{167}$Er$^{3+}$ ions in Y$_2$SiO$_5$ crystal.

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.