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Hybrid second-order coherence in a time-reversed Young's experiment

Jianming Wen

Published Feb 2, 2026• 3 citations
Publisher

Abstract

We develop a quantum-optical theory of the operational second-order correlation function underlying the time-reversed Young's experiment with a scanned point emitter and a fixed single-pixel detector. By embedding the source coordinate in an auxiliary Hilbert space with a position projector, we show that the empirical correlator can be written as a genuine Glauber-type $G^{(2)}$ that correlates a one-channel field intensity with a position projector, with projector idempotence ensuring that it remains second order. Evaluated in the time-reversed Young geometry, this hybrid field-plus-label correlator reproduces deterministic diffraction-free fringes and captures ghost imaging, imaging with undetected photons, and related schemes.

DOI
10.1364/opticaopen.31198534

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We develop a quantum-optical theory of the operational second-order correlation function underlying the time-reversed Young's experiment with a scanned point emitter and a fixed single-pixel detector. By embedding the source coordinate in an auxiliary Hilbert space with a position projector, we show that the empirical correlator can be written as a genuine Glauber-type G(2)G^{(2)}G(2) that correlates a one-channel field intensity with a position projector, with projector idempotence ensuring that it remains second order. Evaluated in the time-reversed Young geometry, this hybrid field-plus-label correlator reproduces deterministic diffraction-free fringes and captures ghost imaging, imaging with undetected photons, and related schemes.
We develop a quantum-optical theory of the operational second-order correlation function underlying the time-reversed Young's experiment with a scanned point emitter and a fixed single-pixel detector. By embedding the source coordinate in an auxiliary Hilbert space with a position projector, we show that the empirical correlator can be written as a genuine Glauber-type G(2)G^{(2)}G(2) that correlates a one-channel field intensity with a position projector, with projector idempotence ensuring that it remains second order. Evaluated in the time-reversed Young geometry, this hybrid field-plus-label correlator reproduces deterministic diffraction-free fringes and captures ghost imaging, imaging with undetected photons, and related schemes.
Correlated-photon imaging, popularly known as ghost imaging, is a technique whereby an image is formed from light that has never interacted with the object. In ghost imaging experiments two correlated light fields are produced. One of these fields illuminates the object, and the other field is measured by a spatially resolving detector. In the quantum regime, these correlated light fields are produced by entangled photons created by spontaneous parametric down-conversion. To date, all correlated-photon ghost-imaging experiments have scanned a single-pixel detector through the field of view to obtain the spatial information. However, scanning leads to a poor sampling efficiency, which scales inversely with the number of pixels, N, in the image. In this work we overcome this limitation by using a time-gated camera to record the single-photon events across the full scene. We obtain high-contrast images, 90%, in either the image plane or the far-field of the photon pair source, taking advantage of the EPR-like correlations in position and momentum of the photon pairs. Our images contain a large number of modes, >500, creating opportunities in low-light-level imaging and in quantum information processing.
Temporal ghost diffraction (TGD) is observed by taking two-photon cross-correlation in the configuration of reciprocal two-slit diffraction where interference fringes develop on the light source side as opposed to the detector side. To this end, a narrow-band chaotic light source and a gated detector are used in the frequency-time domain, which emulate a randomly pointing incoherent light source and a stationary pinhole detector in the momentum-space domain, respectively. Spectral fringes with a signed visibility that closely follows a sinc function of the spectral bandwidth are clear evidence that legitimate TGD fringes due to two-photon interference have developed. This compares with the previous attempt [M. Bellini et al., Phys. Rev. Lett. 90, 043602 (2003)] that is essentially ``ghost imaging of spectral fringes'' to be distinguished from TGD, which implies that the putative GD reports in the literature might demand a revision in terms of their physical insights.
Single-pixel quantum ghost imaging involves the exploitation of non-local photon spatial correlations to image objects with light that has not interacted with them and, using intelligent spatial scanning with projective masks, reduces detection to a single pixel. Despite many applications, extension to complex amplitude objects remains challenging. Here, we reveal that the necessary interference for phase retrieval is naturally embedded in the correlation measurements formed from traditional projective masks in bi-photon quantum ghost imaging. Using this, we develop a simple approach to obtain the full phase and amplitude information of complex objects. We demonstrate straightforward reconstruction without ambiguity using objects exhibiting spatially varying structures from phase steps to gradients as well as complex amplitudes. This technique could be an important step toward imaging the phase of light-sensitive structures in biological matter.
We outline and experimentally demonstrate a method to image pure phase objects using traditional quantum ghost imaging with single pixel detectors. We provide a theoretical description of the process, showing how phase information is embedded in the correlation measurements of spatially entangled photon pairs in which only one of the pair interacts with the object. Using pairs of digital projective masks, one amplitude-only and one phase-only, we reconstruct two partial phase images of the object. Using both these images, we can retrieve the full detailed phase profile of the object without ambiguity, which we demonstrate on objects exhibiting phase steps and gradients.
Two-photon correlation phenomena, including the historical experiment of Hanbury Brown and Twiss, may have to be described quantum mechanically, regardless of whether the source of radiation is classical or quantum. Supporting this point, we present a ghost imaging type of second-order spatial correlation experiment of chaotic light to show that the classical understanding based on the concept of statistical intensity fluctuations does not give a correct interpretation for the observation. From a practical point of view, this experiment demonstrates the possibility of having high contrast lensless two-photon imaging with chaotic light, suggesting imaging applications for radiations for which no effective lens is available.