# Simultaneous Readout of Noncommuting Collective Spin Observables beyond the Standard Quantum Limit

## TL;DR

This paper introduces a method to simultaneously measure multiple noncommuting spin observables in a Bose-Einstein condensate, surpassing the standard quantum limit by coupling to auxiliary states and enabling direct access to quantum correlations.

## Contribution

The authors develop a novel measurement scheme that allows for the concurrent readout of multiple spin components beyond the standard quantum limit in a spinor BEC.

## Key findings

- Simultaneous measurement of three orthogonal spin directions in a $^{87}$Rb condensate.
- Detection of spin nematic squeezing without full state tomography.
- Enhanced information extraction from a single absorption image.

## Abstract

We augment the information extractable from a single absorption image of a spinor Bose-Einstein condensate by coupling to initially empty auxiliary hyperfine states. Performing unitary transformations in both, the original and auxiliary hyperfine manifold, enables the simultaneous measurement of multiple spin-1 observables. We apply this scheme to an elongated atomic cloud of $ ^{87} $Rb to simultaneously read out three orthogonal spin directions and with that directly access the spatial spin structure. The readout even allows the extraction of quantum correlations which we demonstrate by detecting spin nematic squeezing without state tomography.