Measurement of non-commuting spin components using spin-orbit interaction

TL;DR

This paper proposes a method to simulate simultaneous measurement of non-commuting spin components using short-term spin-orbit interaction switching, enabling the evaluation of their time averages with arbitrary accuracy.

Contribution

It introduces a novel approach to measure non-commuting spin components simultaneously by leveraging spin-orbit interaction dynamics in solid-state or cold-atom systems.

Findings

Simultaneous measurement of $\sigma_x$ and $\sigma_y$ is achievable through spin-orbit interaction switching.

The method maps spin dynamics onto coordinate motion to determine time-averaged spin components.

Time averages of spin components can be evaluated with arbitrary precision, unlike instantaneous values.

Abstract

We analyze the physical meaning of a possible experiment aimed at the simultaneous measurement of two non-commuting spin components. We demonstrate that switching of a strong spin-orbit interaction, e.g., in a solid state or a cold-atom system, for a short period of time simulates a simultaneous von Neumann measurement of spin components, $\sigma_x$ and $\sigma_y$. By mapping spin dynamics onto coordinate-space motion, such a measurement determines time averages of $\sigma_x$ and $\sigma_y$ which, unlike their instantaneous values, may be evaluated simultaneously to an arbitrary accuracy.