Random search for a dark resonance

TL;DR

This paper introduces a novel random search method for detecting dark resonances in a three-level quantum system, utilizing non-ergodic Lévy statistics to improve frequency estimation precision over time.

Contribution

It proposes a new scheme that employs random frequency changes and Lévy statistics to enhance dark resonance detection and frequency estimation accuracy.

Findings

The method effectively identifies dark resonances through random frequency probing.

Lévy statistical analysis describes the scaling of estimation error over time.

The approach surpasses conventional bounds by accounting for non-ergodic dynamics.

Abstract

A pair of resonant laser fields can drive a three-level system into a dark state where it seizes to absorb and emit radiation due to destructive interference. We propose a scheme to search for this resonance by randomly changing the frequency of one of the fields each time a fluorescence photon is detected. The longer the system is probed, the more likely the frequency is close to resonance and the system populates the dark state. Due to the correspondingly long waiting times between detection events, the evolution is non-ergodic and the precision of the frequency estimate does not follow from the conventional Cram\'er-Rao bound of parameter estimation. Instead, a L\'{e}vy statistical analysis yields the scaling of the estimation error with time for precision probing of this kind.