Parity measurement of one- and two-electron double well systems

We outline a scheme to accomplish measurements of a solid state double well system (DWS) with both one and two electrons in non-localised bases. We show that, for a single particle, measuring the local charge distribution at the midpoint of a DWS using an SET as a sensitive electrometer amounts to performing a projective measurement in the parity (symmetric/antisymmetric) eigenbasis. For two-electrons in a DWS, a similar configuration of SET results in close-to-projective measurement in the singlet/triplet basis. We analyse the sensitivity of the scheme to asymmetry in the SET position for some experimentally relevant parameter, and show that it is realisable in experiment.