# Fundamental limits for non-destructive measurement of a single spin by Faraday rotation

## TL;DR

This paper establishes fundamental limits for non-destructive single-spin measurement using Faraday rotation, highlighting the necessity of anisotropic media or optical cavities to avoid spin-flips caused by Raman scattering.

## Contribution

It derives a general relation between Faraday rotation and Raman scattering, setting precise criteria for non-destructive spin detection.

## Key findings

- Non-destructive measurement requires anisotropic media or optical cavities.
- A relation between Faraday rotation and spin-flip Raman scattering is established.
- Ideal conditions still face fundamental limits for non-destructive detection.

## Abstract

Faraday rotation being a dispersive effect, is commonly considered as the method of choice for non-destructive detection of spin states. Nevertheless Faraday rotation is inevitably accompanied by spin-flips induced by Raman scattering, which compromises non-destructive detection. Here, we derive an explicit general relation relating the Faraday rotation and the spin-flip Raman scattering cross-sections, from which precise criteria for non-destructive detection are established. It is shown that, even in ideal conditions, non-destructive measurement of a single spin can be achieved only in anisotropic media, or within an optical cavity.