We investigate the possibility of using a scattering medium as a highly multimode platform for implementing quantum walks. We demonstrate the manipulation of a single photon propagating through a strongly scattering medium using wavefront-shaping technique. Measurement of the scattering matrix allows the wavefront of the photon to be shaped to compensate the distortions induced by multiple scattering events. The photon can thus be directed coherently to a specific output mode. Using this approach, we show how entanglement of a single photon across different modes can be manipulated despite the enormous wavefront disturbance caused by the scattering medium.
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.
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.
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
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.