A method for measuring the real part of the weak value of spin using non-zero rest mass particles

TL;DR

This paper proposes a method to measure the real part of the weak value of spin in metastable helium using a modified Stern-Gerlach setup, supported by simulations predicting measurable beam displacements.

Contribution

It introduces a novel experimental approach for weak value measurement with metastable helium and provides simulation results predicting measurable beam shifts.

Findings

Predicted beam displacement of 17-33 μm.

Simulation indicates potential to observe the imaginary part of the weak value.

Discusses methods to enhance measurement sensitivity.

Abstract

A method for measuring the real part of the weak (local) value of spin is presented using a variant on the original Stern-Gerlach apparatus. The experiment utilises metastable helium in the $\rm 2^{3}S_{1}$ state. A full simulation using the impulsive approximation has been carried out and it predicts a displacement of the beam by $\rm \Delta_{w} = 17 - 33\,\mu m$. This is on the limit of our detector resolution and we will discuss ways of increasing $\rm \Delta_{w}$. The simulation also indicates how we might observe the imaginary part of the weak value.