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

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.