The path of light: an investigation about photon trajectories in a double-slit interferometer

Abstract

In classical mechanics, we can define trajectory as the path followed by a body or a particle during its time evolution. If one knows the dynamics of a particle, the knowledge of the position and momentum in a given instant of time is suficient to predict its entire trajectory. However, in quantum mechanics the trajectory of a single particle is an ill defined concept, since, as a consequence of the Heisenberg uncertainty relation, one is not able to simultaneously know its position and momentum. Nevertheless, Wiseman [New Journal of Physics 9, 165 (2007)] proposed an operational way to define the average trajectory of an ensemble of quantum particles using the weak measurement protocol, which is a procedure developed by Aharonov, Albert and Vaidman [Physical Review Letters 60, 1351 (1988)] with the purpose of performing a measurement barely changing the system state. Building on Wiseman's idea, Kocsis et al. [Science 332, 1170 (2011)] have experimentally demonstrated the reconstruction of average trajectories of single photons in a double-slit interferometer. Their strategy consisted in making a weak measurement of the photon momentum followed by a post-selection in a given position. In this way, they were able to map the weak value of momentum as a function of position and, using this information, to reconstruct the average trajectories of a post-selected ensemble of photons. In this dissertation, we present a review of the weak measurement protocol and some of its most recent extensions, applications and interpretations. Within this framework, we reproduced the results obtained by Kocsis et al. and analyse some dierent scenarios through numerical simulations.