# Simultaneous tracking of spin angle and amplitude beyond classical limits

## TL;DR

This paper demonstrates a method in atomic interferometry that allows for simultaneous, back-action evading measurement of non-commuting observables, achieving sensitivity beyond classical quantum limits.

## Contribution

It introduces a high-dynamic-range, dynamically-decoupled QND measurement technique for atomic spins that surpasses the standard quantum limit in sensitivity.

## Key findings

- Achieved 2.9 dB sensitivity beyond the standard quantum limit.
- Realized 7.0 dB sensitivity beyond Poisson statistics.
- Enabled steady-state tracking of spin angle and amplitude with negligible back action.

## Abstract

We show how simultaneous, back-action evading tracking of non-commuting observables can be achieved in a widely-used sensing technology, atomic interferometry. Using high-dynamic-range dynamically-decoupled quantum non-demolition (QND) measurements on a precessing atomic spin ensemble, we track the collective spin angle and amplitude with negligible effects from back action, giving steady-state tracking sensitivity 2.9 dB beyond the standard quantum limit and 7.0 dB beyond Poisson statistics.