Collective Uncertainty in Partially-Polarized and Partially-Decohered Spin-1/2 Systems

TL;DR

This paper examines how symmetric state assumptions in large spin ensembles are often invalidated by typical decoherence, impacting the interpretation of experiments on spin-squeezing and collective phenomena.

Contribution

It challenges the common modeling approach that restricts large spin ensembles to symmetric states, showing that decoherence rapidly degrades these states and affects experimental interpretations.

Findings

Symmetric states are not well-preserved under typical decoherence.

Decoherence acts locally, degrading symmetric states quickly.

Implications for interpreting spin-squeezing experiments.

Abstract

It has become common practice to model large spin ensembles as an effective pseudospin with total angular momentum J = N x j, where j is the spin per particle. Such approaches (at least implicitly) restrict the quantum state of the ensemble to the so-called symmetric Hilbert space. Here, we argue that symmetric states are not generally well-preserved under the type of decoherence typical of experiments involving large clouds of atoms or ions. In particular, symmetric states are rapidly degraded under models of decoherence that act identically but locally on the different members of the ensemble. Using an approach [Phys. Rev. A 78, 052101 (2008)] that is not limited to the symmetric Hilbert space, we explore potential pitfalls in the design and interpretation of experiments on spin-squeezing and collective atomic phenomena when the properties of the symmetric states are extended to systems where they do not apply.