Broadening the scope of weak quantum measurements I: A single particle accurately measured yet left superposed

TL;DR

This paper explores advanced weak measurement techniques using interferometry to measure a single particle’s properties without collapsing its superposition, demonstrating novel applications and practical measurement of the wave-function.

Contribution

It introduces a refined weak measurement method for a single particle that allows simultaneous measurement of position and momentum without disturbing superposition.

Findings

Successfully measured a single photon’s position and momentum simultaneously.

Demonstrated measurement of transmission coefficients while maintaining superposition.

Generalized the method to directly measure the wave-function of a single particle.

Abstract

Weak measurement is unique in enabling measurements of non-commuting operators as well as otherwise-undetectable peculiar phenomena predicted by the Two-State-Vector-Formalism (TSVF). This article, the first in two parts, explores novel applications of weak measurement. We first revisit the basic principles of quantum measurement with the aid of the Michelson interferometer. Weak measurement is then introduced in a simple visualized manner by a specific choice of the reflecting mirror's position and momentum uncertainties. Having introduced the method, we proceed to its refinement for a single particle. We consider a photon going back and forth inside the interferometer, oscillating between a superposed and a localized state, while subjected to alternating strong and weak measurements. This cyclic process enables directly measuring both the photon's position ("which-path") and momentum (interference), without disturbing either. An alternative explanation of this result, not invoking weak values, is thoroughly considered and shown to be at odds with the experimental data. Finally a practical application of this experiment is demonstrated, where a single photon measures the various transmission coefficients of a multiport beam-splitter yet remains superposed. This method is then generalized to measurement of the wave-function itself, performed again on a single particle.