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arXiv:1804.00135 · Physical Review Letters

Adaptive Quantum Optics with Spatially Entangled Photon Pairs

Hugo Defienne, Matthew C. Reichert, Jason W. Fleischer

Published Dec 4, 2018• 82 citations
arXivHTMLPDF

Abstract

Light shaping facilitates the preparation and detection of optical states and underlies many applications in communications, computing, and imaging. In this Letter, we generalize light shaping to the quantum domain. We show that patterns of phase modulation for classical laser light can also shape higher orders of spatial coherence, allowing deterministic tailoring of high-dimensional quantum entanglement. By modulating spatially entangled photon pairs, we create periodic, topological, and random patterns of quantum illumination, without effect on intensity. We then structure the quantum illumination to simultaneously compensate for entanglement that has been randomized by a scattering medium and to characterize the medium's properties via a quantum measurement of the optical memory effect. The results demonstrate fundamental aspects of spatial coherence and open the field of adaptive quantum optics.

DOI
10.1103/physrevlett.121.233601

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Light shaping facilitates the preparation and detection of optical states and underlies many applications in communications, computing, and imaging. In this Letter, we generalize light shaping to the quantum domain. We show that patterns of phase modulation for classical laser light can also shape higher orders of spatial coherence, allowing deterministic tailoring of high-dimensional quantum entanglement. By modulating spatially entangled photon pairs, we create periodic, topological, and random patterns of quantum illumination, without effect on intensity. We then structure the quantum illumination to simultaneously compensate for entanglement that has been randomized by a scattering medium and to characterize the medium's properties via a quantum measurement of the optical memory effect. The results demonstrate fundamental aspects of spatial coherence and open the field of adaptive quantum optics.
Wavefront shaping enables control of classical light through scattering media. Extending these techniques to spatially entangled photons promises new quantum applications, but their fundamental limits, especially when both photons scatter, remain unclear. Here, we theoretically and numerically investigate the enhancement of two-photon correlations through thick scattering media. We analyze configurations where a spatial light modulator shapes one or both photons, either before or after the medium, and show that the optimal enhancement differs fundamentally from classical expectations. For a system with NNN modes, we show that shaping one photon yields the classical enhancement η≈(π/4)Nη\approx (π/4)Nη≈(π/4)N, while shaping both photons before the medium reduces it to η≈(π/4)2Nη\approx (π/4)^2Nη≈(π/4)2N. However, in some symmetric detection schemes, when both photons are measured at the same mode, perfect correlations are restored with η≈Nη\approx Nη≈N, resembling digital optical phase conjugation. Conversely, shaping both photons after the medium leads to a complex, NP-hard-like optimization problem, yet achieves superior enhancements, up to η≈4.6Nη\approx 4.6Nη≈4.6N. These results reveal unique quantum effects in complex media and identify strategies for quantum imaging and communication through scattering environments.
The ability to engineer the properties of quantum optical states is essential for quantum information processing applications. Here, we demonstrate tunable control of spatial correlations between photon pairs produced by spontaneous parametric down-conversion. By shaping the spatial pump beam profile in a type-I collinear configuration, we tailor the spatial structure of coincidences between photon pairs entangled in high dimensions, without effect on intensity. The results highlight fundamental aspects of spatial coherence and hold potential for the development of quantum technologies based on high-dimensional spatial entanglement.
Wavefront shaping enables control of classical light through scattering media. Extending these techniques to spatially entangled photons promises new quantum applications, but their fundamental limits, especially when both photons scatter, remain unclear. Here, we theoretically and numerically investigate the enhancement of two-photon correlations in two specific output modes through thick scattering media. We analyze three configurations: shaping one photon after the medium, shaping both photons before the medium, and shaping both photons after the medium. We show that each configuration yields fundamentally different enhancements compared to classical expectations. For a system with N modes, we show that shaping one photon yields the classical enhancement η ≈ (π/4)N, while shaping both photons before the medium reduces it to η ≈ (π/4)2N. However, in some symmetric detection schemes, when both photons are measured at the same mode, perfect correlations are restored with η ≈ N, resembling digital optical phase conjugation. Conversely, shaping both photons after the medium leads to a complex, NP-hard-like optimization problem, yet achieves superior enhancements, up to η ≈ 4.6N. These results reveal unique quantum effects in complex media and identify strategies for quantum imaging and communication through scattering environments.
Wavefront shaping is a key technique for mitigating scattering in complex media, enabling advanced imaging and optical communication. Yet existing approaches are inherently local, requiring active correction elements - such as spatial light modulators or deformable mirrors - to lie directly in the optical path of the scattered light, which limits their integration into compact imaging systems. Here, we experimentally demonstrate nonlocal wavefront shaping using spatially entangled photon pairs. By applying a phase correction to a photon that never interacts with the scattering medium, we compensate for the distortions experienced by its entangled partner and restore their initial spatial correlations. Our approach physically decouples the wavefront correction from the scattering medium, paving the way for imaging through complex media in compact and otherwise inaccessible systems.
This study falls within the emerging field of quantum optics in scattering media. By employing wavefront shaping, researchers successfully transmitted spatially entangled photon pairs through scattering media, mitigating optical disturbances by wavefront shaping. They maintained entanglement with a dimensionality of 17 after propagation, opening avenues for applications in quantum microscopy and quantum communication. Interestingly, this work also shows that in certain cases, quantum entanglement can be transmitted through a complex medium, while classical light remains scattered.