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Optics Letters

The quantum Gaussian–Schell model: a link between classical and quantum optics

Riley B. Dawkins, Mingyuan Hong, Chenglong You, Omar S. Magaña‐Loaiza

Published Jul 10, 2024• 9 citations
Publisher

Abstract

The quantum theory of the electromagnetic field uncovered that classical forms of light were indeed produced by distinct superpositions of nonclassical multiphoton wave packets. This situation prevails for partially coherent light, the most common kind of classical light. Here, for the first time, to our knowledge, we demonstrate the extraction of the constituent multiphoton quantum systems of a partially coherent light field. We shift from the realm of classical optics to the domain of quantum optics via a quantum representation of partially coherent light using its complex-Gaussian statistical properties. Our formulation of the quantum Gaussian-Schell model (GSM) unveils the possibility of performing photon-number-resolving (PNR) detection to isolate the constituent quantum multiphoton wave packets of a classical light field. We experimentally verified the coherence properties of isolated vacuum systems and wave packets with up to 16 photons. Our findings not only demonstrate the possibility of observing quantum properties of classical macroscopic objects but also establish a fundamental bridge between the classical and quantum worlds.

DOI
10.1364/ol.520444

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The quantum theory of the electromagnetic field uncovered that classical forms of light were indeed produced by distinct superpositions of nonclassical multiphoton wave packets. This situation prevails for partially coherent light, the most common kind of classical light. Here, for the first time, to our knowledge, we demonstrate the extraction of the constituent multiphoton quantum systems of a partially coherent light field. We shift from the realm of classical optics to the domain of quantum optics via a quantum representation of partially coherent light using its complex-Gaussian statistical properties. Our formulation of the quantum Gaussian-Schell model (GSM) unveils the possibility of performing photon-number-resolving (PNR) detection to isolate the constituent quantum multiphoton wave packets of a classical light field. We experimentally verified the coherence properties of isolated vacuum systems and wave packets with up to 16 photons. Our findings not only demonstrate the possibility of observing quantum properties of classical macroscopic objects but also establish a fundamental bridge between the classical and quantum worlds.
The quantum theory of the electromagnetic field uncovered that classical forms of light were indeed produced by distinct superpositions of nonclassical multiphoton wavepackets. Specifically, partially coherent light represents the most common kind of classical light. Here, for the first time, we demonstrate the extraction of the constituent multiphoton quantum systems of a partially coherent light field. We shift from the realm of classical optics to the domain of quantum optics via a quantum representation of partially coherent light using its complex-Gaussian statistical properties. Our formulation of the quantum Gaussian-Schell model unveils the possibility of performing photon-number-resolving detection to isolate the constituent quantum multiphoton wavepackets of a classical light field. We experimentally verified the coherence properties of isolated vacuum systems and wavepackets with up to sixteen photons. Our findings not only demonstrate the possibility of observing quantum properties of classical macroscopic objects, but also establish a fundamental bridge between the classical and quantum worlds.
The modification of the quantum properties of coherence of photons through their interaction with matter lies at the heart of the quantum theory of light. Indeed, the absorption and emission of photons by atoms can lead to different kinds of light with characteristic quantum statistical properties. As such, different types of light are typically associated with distinct sources. Here, we report on the observation of the modification of quantum coherence of multiphoton systems in free space. This surprising effect is produced by the scattering of thermal multiphoton wavepackets upon propagation. The modification of the excitation mode of a photonic system and its associated quantum fluctuations result in the formation of different light fields with distinct quantum coherence properties. Remarkably, we show that these processes of scattering can lead to multiphoton systems with subshot-noise quantum properties. Our observations are validated through the nonclassical formulation of the emblematic van Cittert–Zernike theorem. We believe that the possibility of producing quantum systems with modified properties of coherence, through linear propagation, can have dramatic implications for diverse quantum technologies.
In semiclassical theory, light is a classical electromagnetic wave and the fundamental source of photodetection noise is the shot effect arising from the discreteness of the electron charge. In quantum theory, light is a quantum-mechanical entity and the fundamental source of photodetection noise comes from measuring the photon-flux operator. The Glauber coherent states are Gaussian quantum states which represent classical electromagnetic radiation. Quantum photodetection of these states yields statistics that are indistinguishable from the corresponding Poisson point-process results of semiclassical photodetection. Optical parametric interactions, however, can be used to produce other Gaussian quantum states, states whose photodetection behavior cannot be characterized semiclassically. A unified analytical framework is presented for Gaussian-state photodetection that includes the full panoply of nonclassical effects that have been produced via parametric interactions.
The theory of partial coherence has a long and storied history in classical statistical optics. The vast majority of this work addresses fields that are statistically stationary in time, hence their complex envelopes only have phase-insensitive correlations. The quantum optics of squeezed-state generation, however, depends on nonlinear interactions producing baseband field operators with phase-insensitive and phase-sensitive correlations. Utilizing quantum light to enhance imaging has been a topic of considerable current interest, much of it involving biphotons, i.e., streams of entangled-photon pairs. Biphotons have been employed for quantum versions of optical coherence tomography, ghost imaging, holography, and lithography. However, their seemingly quantum features have been mimicked with classical-state light, questioning wherein lies the classical-quantum boundary. We have shown, for the case of Gaussian-state light, that this boundary is intimately connected to the theory of phase-sensitive partial coherence. Here we present that theory, contrasting it with the familiar case of phase-insensitive partial coherence, and use it to elucidate the classical-quantum boundary of ghost imaging. We show, both theoretically and experimentally, that classical phase-sensitive light produces ghost images most closely mimicking those obtained with biphotons, and we derive the spatial resolution, image contrast, and signal-to-noise ratio of a standoff-sensing ghost imager, taking into account target-induced speckle.