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APL Photonics

Quantum phase imaging via diffraction of correlated bi-photon states

Nazanin Dehghan, Alessio D’Errico, Yingwen Zhang, Benjamin Sussman, Ebrahim Karimi

Published Jun 1, 2026• 1 citation
Publisher

Abstract

Two-photon states generated through degenerate spontaneous parametric downconversion (SPDC) can exhibit sharp correlations in the transverse spatial coordinates. This property leads to unique free-space propagation features. Here, we show that a phase object placed in the image plane of the source affects the free space propagation of the SPDC in a way that is mathematically analogous to the Fresnel diffraction of a first-order coherent source. This effect can be observed via the extraction of correlation images. We demonstrate this prediction with an experiment where the diffraction of correlated bi-photons is detected using an event-based camera. The results allow us to reconstruct the phase structure of the sample via non-interferometric phase retrieval methods. We verify that the retrieved phase patterns exhibit a factor of two contrast enhancement due to the probe’s two-photon nature. Our findings offer a proof of principle application for quantitative phase imaging, particularly in regimes where low light conditions are required to prevent photo-damage and, at the same time, is desirable to preserve high resolution, contrast, and low noise.

DOI
10.1063/5.0313716

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Two-photon states generated through degenerate spontaneous parametric downconversion (SPDC) can exhibit sharp correlations in the transverse spatial coordinates. This property leads to unique free-space propagation features. Here, we show that a phase object placed in the image plane of the source affects the free space propagation of the SPDC in a way that is mathematically analogous to the Fresnel diffraction of a first-order coherent source. This effect can be observed via the extraction of correlation images. We demonstrate this prediction with an experiment where the diffraction of correlated bi-photons is detected using an event-based camera. The results allow us to reconstruct the phase structure of the sample via non-interferometric phase retrieval methods. We verify that the retrieved phase patterns exhibit a factor of two contrast enhancement due to the probe’s two-photon nature. Our findings offer a proof of principle application for quantitative phase imaging, particularly in regimes where low light conditions are required to prevent photo-damage and, at the same time, is desirable to preserve high resolution, contrast, and low noise.
Two-photon states generated through degenerate spontaneous parametric down-conversion (SPDC) can exhibit sharp correlations in the transverse spatial coordinates. This property leads to unique free-space propagation features. Here, we show that a phase object placed in the image plane of the source affects the free space propagation of the SPDC in a way that is mathematically analogous to the Fresnel diffraction of a first-order coherent source. This effect can be observed via the extraction of correlation images. We demonstrate this prediction with an experiment where the diffraction of correlated bi-photons is detected using an event-based camera. The results allow us to reconstruct the phase structure of the sample via non-interferometric phase retrieval methods. We verify that the retrieved phase patterns exhibit an enhanced contrast due to the probe two-photon nature. Our findings offer applications for non-interferometric, quantum-enhanced phase imaging.
The complete measurement of the quantum state of two correlated photons requires reconstructing the amplitude and phase of the biphoton wavefunction. We show how, by means of spatially resolved single photon detection, one can infer the spatial structure of biphotons generated by spontaneous parametric down conversion. In particular, a spatially resolved analysis of the second-order correlations allows us to isolate the moduli of the pump and phase-matching contributions to the two-photon states. When carrying this analysis on different propagation planes, the free-space propagation of pump and phase-matching is observed. This result allows us, in principle, to gain enough information to also reconstruct the phase of the pump and the phase-matching and thus the full biphoton wavefunction. We show this in different examples where the pump is shaped as a superposition of orbital angular momentum modes or as a smooth amplitude with a phase structure with no singularities. The corresponding phase structure is retrieved employing maximum likelihood or genetic algorithms. These findings have potential applications in fast, efficient quantum state characterization that does not require phase locking of the unknown source with a reference biphoton.
Quantum imaging leverages nonclassical correlations to reveal features that may vanish in conventional event integration [ 1, 2]. While single-photon detectors are well-established, quantum imaging demands complex data acquisition across many thousands of detectors, each generating rich metadata including triggering time, duration, and other properties. Consequently, effective data management, data wrangling, and correlation extraction become critical challenges. In this work, we investigate optimal handling of spatial correlations from a quantum-photonic source (spontaneous parametric down-conversion, SPDC) using an emerging single-photon event-based camera, the TPX3CAM (256×256 array, supported by an intensifier). Utilizing a femtosecond photon-pair source, we comprehensively analyse noise characteristics, including temporal dynamics and spatial distribution, to develop advanced spatio-temporal noise suppression strategies tailored to camera performance. Our primary objectives include real-time isolation and preprocessing of correlative data. Our analysis demonstrates the potential of these real-time correlation detection and noise reduction algorithms to expand quantum imaging capabilities across diverse scientific domains. Potential applications include high-resolution spectroscopy in biology, materials science, and advanced electron microscopy, where these techniques could enable identification of cascaded two-photon processes with atomic-scale precision. Figure 1 shows an excellent example of such a detection in real-space. The ring feature corresponds to the location of the correlated photon-pairs produced from the SPDC process. This is also apparent in figure 2, where we see a strong anti-correlation between the coordinates of the detected photons – corresponding to photon-pairs. <!-- named anchor --> Figure 1: Distribution of SPDC photons on TPX3CAM <!-- named anchor --> Figure 2: Spatial anti-correlation of x-coordinates
Quantitative phase imaging provides a way to image transparent objects, such as biological cells, and measure their thickness. We report on a phase-imaging method that achieves twice the phase shift and approximately 1.7 times the spatial resolution of an equivalent spatially and temporally coherent classical quantitative phase-imaging system by using quantum interference between successive spontaneous parametric downconversion events in a nonlinear crystal. Furthermore, our method is approximately 1000 times faster than imaging the parametric downconversion photons in coincidence, which requires measurement times on the order of tens of hours. Our method may be useful for imaging sensitive transparent objects that require low illumination intensities at near-infrared and longer illumination wavelengths, such as photosensitive biological samples.
High-dimensional entanglement in the form of transverse spatial correlation between a pair of photons generated via spontaneous parametric downconversion is not only a valuable resource in many academic and real-life applications but also provides access to several intriguing quantum phenomena. One such non-intuitive phenomenon is phase entanglement, in which the biphoton state is correlated in the complex phase of its wavefunction. This state, which emerges during the propagation of the biphoton wavefunction, exhibits neither position nor momentum correlation, yet retains full entanglement. In this work, we experimentally explore this state in two distinct ways. The first is by tracking the vanishing spatial photon number correlation over propagation distances lying in [0,∞)\left[0,\infty\right)[0,∞), folded into a finite range using single-lens imaging. These observations show excellent agreement with our theoretical predictions based on the Double Gaussian (DG) approximation of the biphoton state. The second approach involves performing a two-photon interference experiment using a double slit and this state, which reveals the correlated phase front. We show, both theoretically and experimentally, that the observed two-photon interference structure is markedly different from that produced by position-correlated photons, as confirmed by computing the joint probability distribution of photons (JPD) and related metrics. Such interference using phase-entangled light has not been attempted before and opens avenues for advanced experiments and applications in the field of spatial entanglement.
Classical light sources emit a randomly-timed stream of individual photons, the spatial distribution of which can be detected with a camera to form an image. Quantum light sources, based on parametric down conversion, emit photons as correlated photon-pairs. The spatial correlations between the photons enables imaging systems where the preferential selection of photon-pairs allows for enhancements in the noise performance over what is possible using classical light sources. However, until now the technical challenge of measuring, and correlating both photons has led to system complexity. Here we show that a camera capable of resolving the number of individual photons in each pixel of the detector array can be used to record an image formed from these photon-pair events and hence achieve a greater contrast than possible using a classical light source. We achieve an enhancement in the ratio of two-photon events compared to one-photon events using spatially correlated SPDC light compared to uncorrelated illumination by a LED. These results indicate the potential advantages of using photon counting cameras in quantum imaging schemes and these advantages will further increase as the technology is developed. Operating in photon sparse regimes such systems have potential applications in low-light microscopy and covert imaging.