A statistical analysis of single photon propagation: how quantum interference modifies the laws of motion

Holger F. Hofmann

doi:10.1117/12.2319573

18 September 2018 A statistical analysis of single photon propagation: how quantum interference modifies the laws of motion

Holger F. Hofmann

Author Affiliations +

Proceedings Volume 10771, Quantum Communications and Quantum Imaging XVI; 1077115 (2018) https://doi.org/10.1117/12.2319573
Event: SPIE Optical Engineering + Applications, 2018, San Diego, California, United States

Abstract

Since the wavefunction of a photon only describes the probability of photon detection in time and space, it is impossible to derive uniquely defined trajectories describing the path taken by the photon between emission and detection. However, it is possible to test whether a particular set of trajectories is consistent with the statistics observed at different times for photons in the same initial state. Recently, I have shown that quantum interference effects between position and momentum can result in a violation of inequalities associated with motion along straight lines. Here, I present a more detailed analysis on the origin of the effect and its relation with other experimentally observable aspects of quantum statistics such as weak measurements and quantum tomography. It is shown that the interference pattern between a quantum state component of well-defined position and a quantum state component of well-defined momentum describes a modified causality relation between the positions detected at different times. The phase of the interference pattern is identified with the classical action of particle motion and the relation between uncertainty and causality is considered. The specific case of single photon wavefunctions is used to explain the possibilities and limitations of control at the ultimate quantum limit.

Conference Presentation

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Holger F. Hofmann "A statistical analysis of single photon propagation: how quantum interference modifies the laws of motion", Proc. SPIE 10771, Quantum Communications and Quantum Imaging XVI, 1077115 (18 September 2018); https://doi.org/10.1117/12.2319573

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