Spin-state estimation using the Stern-Gerlach experiment

TL;DR

This paper introduces a new spin-state estimation method using a modified Stern-Gerlach experiment with a quadrupolar magnetic field and a quadrant detector, providing a statistical framework for error analysis and setup comparison.

Contribution

It presents a linear inversion estimation scheme for spin states in a Stern-Gerlach setup with a quadrupolar magnetic field, including error quantification and comparison metrics.

Findings

The estimator's statistical properties enable error quantification.

The method allows comparison of different Stern-Gerlach configurations.

The approach is applicable to neutral spin-1/2 particles.

Abstract

We propose a state estimation scheme for spins, using a modified setup of the Stern-Gerlach experiment, in which a beam of neutral spin-1/2 point particles interacts with a quadrupolar magnetic field. The proposed linear inversion estimation procedure, based on a quadrant intensity detector, requires a suitable initial spatial state of the beam. The statistical characterization of the estimator of the initial spin state allows us not only to associate an error to the estimated parameters, but also to define a measure for comparing estimation procedures corresponding to different Stern-Gerlach setups.