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Frontiers in Optics

Entanglement and Propagation: Is there an equivalent of the Van Cittert-Zernike theorem for Quantum Correlations?

Daniel F. V. James

Published Jan 1, 2011• 0 citations
Publisher

Abstract

It has been know for more than a century that spatial coherence of light changes on propagation, a fact quantified by the van Cittert-Zernike theorem. Here we investigate how quantum correlations change on propagation.
DOI
10.1364/fio.2011.fmf1

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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.
Coherence is theorized as the normalized correlation between two superposed optical signals, usually replicated by a two-beam interferometer or by a double-slit system. Prevailing coherence theory is presented as field–field correlation, as it does not go into the technical details of how the measurable transformations are physically generated and registered. Teaching coherence theory using a semiclassical model has been very successful as is evidenced in literature from the extensive reference to the text by M. Born and E. Wolf. This has been further strengthened by the work of Sudarshan, who demonstrated the optical equivalence between Wolf’s classical theory and Glauber’s quantum coherence theories. The discussion about the classical concept of coherence remains incomplete without presenting the van Cittert–Zernike theorem on spatial coherence, because the concept of coherence evolved with historic attempts to understand spatial coherence.
Abstract 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 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 photon statistics modifications. 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 cannot be explained through the classical theory of optical coherence. As such, our work opens new paradigms within the established field of quantum coherence.