Statistical sensitivity of phase measurements via laser-induced fluorescence with optical cycling detection

TL;DR

This paper analyzes how optical cycling detection in laser-induced fluorescence affects phase measurement sensitivity, revealing that maximum photon detection does not always approach the quantum limit due to leakage effects.

Contribution

It derives a general formula for the signal-to-noise ratio considering photon detection efficiency and leakage, highlighting limitations in phase measurement sensitivity.

Findings

Detecting many photons per atom/molecule is necessary but not sufficient for quantum-limited sensitivity.

Leakage from the optical cycle reduces SNR by a factor of √2 compared to ideal conditions.

A general SNR expression is derived in terms of detection efficiency and leakage probability.

Abstract

In atomic and molecular phase measurements using laser-induced fluorescence detection, optical cycling can enhance the effective photon detection efficiency and hence improve sensitivity. We show that detecting many photons per atom or molecule, while necessary, is not a sufficient condition to approach the quantum projection limit for detection of the phase in a two-level system. In particular, detecting the maximum number of photons from an imperfectly closed optical cycle reduces the signal-to-noise ratio (SNR) by a factor of $\sqrt{2}$, compared to the ideal case in which leakage from the optical cycle is sufficiently small. We derive a general result for the SNR in a system in terms of the photon detection efficiency, probability for leakage out of the optical cycle per scattered photon, and the product of the average photon scattering rate and total scattering time per atom or molecule.