Monachello, Vincenzo; (2022) The development of a method to observe the weak value of spin in atomic systems. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The development of an experiment to measure the weak value of spin for non-zero mass particles has been outlined. It has been shown how the weak measurement theory allows for a new understanding of quantum mechanical processes through the amplification of small signals and the exploration of phase changes in the wave function. The weak measurement process comprises three stages. In order to measure the weak value of spin, the spin vector of an atomic beam must first be pre-selected into a particular orientation. The atomic beam then travels through two magnets, one with a weak magnetic field gradient imparting a small phase shift, the weak stage, and the other producing a strong magnetic field gradient that splits the spin eigenstates of the system, the strong stage. Both magnets are orientated 90 degrees from one another. This last magnet is referred to as the post-selection stage; this produces a shift (along the weak stage axis) in the probability density from which the weak value can be observed. This thesis describes a full analysis of the weak measurement theory using both the first-order approximation and a case where no approximation is performed. Both scenarios are compared to one another to calculate a unique limit, for which the first-order approximation holds. The experiment utilises a pulsed supersonic beam of spin-1 metastable helium atoms in the 2³S₁ triplet state. A highly collimated atomic beam is produced with an angular divergence of 12 μrad, its spatial half-width can be reduced to 3 μm while maintaining a sufficient signal-to-noise ratio. The spin vector of the atomic beam is set using a hexapole magnet together with a rotatable 50 μm slit attached to its exit. The weak stage is an electromagnet, while the strong stage consists of various grade permanent magnets in order to produce a gradient of ≈50 T/m. Splitting of the spin eigenstates of the system has been observed, along with promising evidence of oscillatory spin transition probabilities. Final results indicate the possibility of obtaining weak measurements for atomic systems, revealing oscillatory changes in the transition amplitude probability density related to the phase changes in the wave function. To the author's knowledge, this is the first-time weak measurements in any form have been applied to atomic systems.

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