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Journal of Modern Optics

Experimental demonstration of Klyshko’s advanced-wave picture using a coincidence-count based, camera-enabled imaging system

Reuben S. Aspden, D. S. Tasca, Andrew Forbes, Robert W. Boyd, Miles J. Padgett

Published Mar 18, 2014• 30 citations
Publisher

Abstract

The Klyshko advanced-wave picture is a well-known tool useful in the conceptualisation of parametric down-conversion (SPDC) experiments. Despite being well-known and understood, there have been few experimental demonstrations illustrating its validity. Here, we present an experimental demonstration of this picture using a time-gated camera in an image-based coincidence measurement. We show an excellent agreement between the spatial distributions as predicted by the Klyshko picture and those obtained using the SPDC photon pairs. An interesting speckle feature is present in the Klyshko predictive images due to the spatial coherence of the back-propagated beam in the multi-mode fibre. This effect can be removed by mechanically twisting the fibre, thus degrading the spatial coherence of the beam and time-averaging the speckle pattern, giving an accurate correspondence between the predictive and SPDC images.

DOI
10.1080/09500340.2014.899645

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The Klyshko advanced-wave picture is a well-known tool useful in the conceptualisation of parametric down-conversion (SPDC) experiments. Despite being well-known and understood, there have been few experimental demonstrations illustrating its validity. Here, we present an experimental demonstration of this picture using a time-gated camera in an image-based coincidence measurement. We show an excellent agreement between the spatial distributions as predicted by the Klyshko picture and those obtained using the SPDC photon pairs. An interesting speckle feature is present in the Klyshko predictive images due to the spatial coherence of the back-propagated beam in the multi-mode fibre. This effect can be removed by mechanically twisting the fibre, thus degrading the spatial coherence of the beam and time-averaging the speckle pattern, giving an accurate correspondence between the predictive and SPDC images.
The advanced-wave picture is ``... an intuitive treatment of two-photon correlation with the help of the concept of an effective field acting upon one of the two detectors and formed by parametric conversion of the advanced wave emitted by the second detector ...'' [A. V. Belinskii and D. N. Klyshko, Sov. Phys. JETP 78, 259 (1994)]. This quote from Belinskii and Klyshko nicely describes the concept of the advanced-wave picture: an intuitive tool for designing and predicting results from coincidence-based two-photon experiments. Up to now, the advanced-wave picture has been considered primarily for the case of an ideal plane-wave pump beam and only for design purposes. Here we study the advanced-wave picture for a structured pump beam and in the context of stimulated emission provoked by an auxiliary input laser beam. This suggests stimulated parametric down-conversion as a useful experimental tool for testing the experimental sets designed with the advanced-wave picture. We present experimental results demonstrating the strategy of designing the experiment with advanced-wave picture and testing with stimulated emission.
Stimulated parametric down-conversion (StimPDC) is the seeded version of the process that underlies much of photonic quantum information. Replacing the vacuum at one input port with a coherent seed leaves the interaction Hamiltonian, the phase-matching function and the two-photon amplitude unchanged, while raising the output to levels accessible with ordinary classical detectors. This review treats the transverse spatial physics of that process. We show that a single relation, in which the idler amplitude is the pointwise product of the pump field with the complex conjugate of the seed, organizes results usually presented separately: the image and coherence transfer experiments of the 1990s; phase conjugation and its use for wavefront correction; the conservation and conjugation of orbital angular momentum, together with the generation of radial modes and geometric intensity patterns; and the processing of vector vortex beams carrying spatially varying polarization. We then consider StimPDC as an instrument rather than as an object of study, covering stimulated emission tomography, the experimental realization of Klyshko's advanced-wave picture, and the transfer of partial coherence, including the conservation of the twist phase of twisted Gaussian Schell-model beams. We close with the quantum regime, reached when the seed approaches the single-photon level or the idler is used as a herald, and with an assessment of open problems and prospective applications.
Klyshko's advanced-wave picture (AWP) is mainly interpreted by replacing the nonlinear crystal producing biphotons via spontaneous parametric down-conversion (SPDC) by a mirror in quantum imaging protocols with thin crystals, where the biphotons are perfectly correlated in position at the crystal. To better explain the biphoton spatial states produced by arbitrary crystals and pump beams, we develop a formal theory of AWP with monochromatic lights that the conditional wave function of one photon is calculated by propagation, multiplication, and another propagation. The case of more general photon postselection or no detection and the inclusion of polarization are studied. Then, we explain the form of the biphoton state from SPDC with a bulk crystal and its free-space propagation. By treating the biphoton wave function as an impulse response function of a classical optical setup, we analyze quantum imaging with undetected photons and quantum holography with polarization entanglement, where properties like the spatial resolution can be concisely deduced. This method can be employed to design nonlinear materials or novel quantum imaging techniques. Finally, we discuss Klyshko's original proposal beyond monochromatic lights with the Hong-Ou-Mandel effect as an example.
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
We investigate the fourth-order spatial correlation properties of pseudo-thermal light in the photon counting regime, and apply the Klyshko advanced-wave picture to describe the process of four-photon coincidence counting measurement. We deduce the theory of a proof-of-principle four-photon coincidence counting configuration, and find that if the four randomly radiated photons come from the same radiation area and are indistinguishable in principle, the fourth-order correlation of them is 24 times larger than that when four photons come from different radiation areas. In addition, we also show that the higher-order spatial correlation function can be decomposed into multiple lower-order correlation functions, and the contrast and visibility of low-order correlation peaks are less than those of higher orders, while the resolutions all are identical. This study may be useful for better understanding the four-photon interference and multi-channel correlation imaging.