Spin squeezing of high-spin, spatially extended quantum fields

TL;DR

This paper demonstrates that high-spin, spatially extended quantum fields can achieve extensive spin squeezing across multiple spatial modes, surpassing previous limitations, with potential reductions in quantum noise by up to 20 dB.

Contribution

It introduces a theoretical framework showing enhanced spin squeezing in high-spin, spatially extended ensembles, including multiple spatial modes and observables like magnetization and nematicity.

Findings

Achieves sub-quantum-limited fluctuations in multiple spin observables.

Predicts 20 dB reduction in quantum noise for magnetization and nematicity.

Demonstrates spin squeezing in multiple spatial modes of a quantum field.

Abstract

Investigations of spin squeezing in ensembles of quantum particles have been limited primarily to a subspace of spin fluctuations and a single spatial mode in high-spin and spatially extended ensembles. Here, we show that a wider range of spin-squeezing is attainable in ensembles of high-spin atoms, characterized by sub-quantum-limited fluctuations in several independent planes of spin-fluctuation observables. Further, considering the quantum dynamics of an $f=1$ ferromagnetic spinor Bose-Einstein condensate, we demonstrate theoretically that a high degree of spin squeezing is attained in multiple spatial modes of a spatially extended quantum field, and that such squeezing can be extracted from spatially resolved measurements of magnetization and nematicity, i.e.\ the vector and quadrupole magnetic moments, of the quantum gas. Taking into account several experimental limitations, we predict that the variance of the atomic magnetization and nematicity may be reduced as far as 20 dB below the standard quantum limits.