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Journal of Physics Conference Series

Projectile coherence: The Van Cittert - Zernike theorem revisited

Ignacio Fabre, Francisco Navarrete, L. Sarkadi, R O Barrachina

Published Sep 7, 2015• 3 citations
Publisher

Abstract

We study the time evolution of an incoherent mixture of identical particles by solving the Liouville - von Neumann equation for the corresponding density matrix. We demonstrate the quantum mechanical equivalent of van Cittert - Zernike theorem, and apply these results to the quantitative analysis of the coherence of a beam of particles in atomic collisions.

DOI
10.1088/1742-6596/635/4/042003

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We study the time evolution of an incoherent mixture of identical particles by solving the Liouville - von Neumann equation for the corresponding density matrix. We demonstrate the quantum mechanical equivalent of van Cittert - Zernike theorem, and apply these results to the quantitative analysis of the coherence of a beam of particles in atomic collisions.
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Recent advances in quantum optics have highlighted the critical role of spatial propagation in controlling the quantum coherence of light beams. However, the evolution of quantum coherence for light beams undergoing fundamental optical processes at dielectric interfaces remains unexplored. Furthermore, manipulating multiphoton correlations typically requires complex interactions that challenge few-photon level implementation. Here, we introduce a quantum van Cittert-Zernike theorem for light beams, describing how their coherence-polarization properties are influenced by reflection and refraction, as well as how these properties evolve upon subsequent propagation. Our work demonstrates that the quantum statistics of photonic systems can be controllably modified through the inherent polarization coupling arising from reflection and refraction at an interface, without relying on conventional light-matter interactions. Our approach reveals regimes where thermal light can exhibit sub-Poissonian statistics with fluctuations below the shot-noise level through post-selected measurements, and this statistical property can be tuned by the incident angle. Remarkably, this quantum statistical modification is governed by a scaling law linking beam collimation to far-field thermalization. Our work establishes a robust, decoherence-avoiding mechanism for quantum state control, advancing the fundamental understanding of coherence in quantum optics and opening new avenues for applications in quantum information and metrology.
Recent progress on quantum state engineering has enabled the preparation of quantum photonic systems comprising multiple interacting particles. Interestingly, multiphoton quantum systems can host many complex forms of interference and scattering processes that are essential to perform operations that are intractable on classical systems. Unfortunately, the quantum coherence properties of multiphoton systems degrade upon propagation leading to undesired quantum-to-classical transitions. Furthermore, the manipulation of multiphoton quantum systems requires of nonlinear interactions at the few-photon level. Here, we introduce the quantum van Cittert-Zernike theorem to describe the scattering and interference effects of propagating multiphoton systems. This fundamental theorem demonstrates that the quantum statistical fluctuations, which define the nature of diverse light sources, can be modified upon propagation in the absence of light-matter interactions. The generality of our formalism unveils the conditions under which the evolution of multiphoton systems can lead to surprising classical-to-quantum transitions. Specifically, we show that the implementation of conditional measurements may enable the all-optical preparation of multiphoton systems with attenuated quantum statistics below the shot-noise limit. Remarkably, this effect had not been discussed before and cannot be explained through the classical theory of optical coherence. As such, our work opens new paradigms within the established field of quantum coherence.