A Method for Measuring the Real Part of the Weak Value of Spin for Metastable Atoms

A method for measuring the real part of the weak value of spin for non-zero rest mass atoms is presented using a variant on the original Stern-Gerlach apparatus. The experiment utilises helium in the metastable 23S1 state. A full simulation for observing the real part of the weak value using the impulsive approximation has been carried out and it predicts a displacement of the beam, Δw, that is within the resolution of our detector. It also indicates how this shift might be increased. The full analysis also indicated that there is a limit, L, to the applicability of the weak value approximation and has been evaluated for our apparatus. This experiment has the possibility to be expanded to utilise other nobal gas species such as neon and argon in the 3P2 metastable state, but we shall restrict this paper to metastable helium only.