Continuous Measurement of Spin Systems with Spatially-Distinguishable Particles

TL;DR

This paper demonstrates that dispersive polarimetric detection of collective angular momentum in spatially-distinguishable spin systems does not produce squeezing or anti-squeezing, contrasting with the behavior in indistinguishable particle ensembles.

Contribution

It reveals that spatial distinguishability prevents the generation of squeezing and anti-squeezing in collective spin measurements, challenging previous assumptions.

Findings

Measuring spatially-distinguishable spins reduces uncertainty without squeezing.

Steady state is highly mixed with a well-defined collective angular momentum.

Behavior differs fundamentally from indistinguishable particle ensembles.

Abstract

It is generally believed that dispersive polarimetric detection of collective angular momentum in large atomic spin systems gives rise to: squeezing in the measured observable, anti-squeezing in a conjugate observable, and collective spin eigenstates in the long-time limit (provided that decoherence is suitably controlled). We show that such behavior only holds when the particles in the ensemble cannot be spatially distinguished-- even in principle-- regardless of whether the measurement is only sensitive to collective observables. While measuring a cloud of spatially-distinguishable spin-1/2 particles does reduce the uncertainty in the measured spin component, it generates neither squeezing nor anti-squeezing. The steady state of the measurement is highly mixed, albeit with a well-defined value of the measured collective angular momentum observable.