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Physical Review A

Coherent reconstruction of pump beams through recombination of entangled photon pairs

G. Daniel Jimenez, Veneranda G. Garces, Kevin A. O’Donnell

Published Feb 26, 2019• 3 citations
Publisher

Abstract

In theoretical and experimental work, we consider the process in which an entangled photon pair recombines into a single photon in a nonlinear crystal, with particular interest in the amplitude distribution and coherence properties of the up-converted light. It is found that the up-converted state has perfect mutual coherence with the pump that originally produced the photon pair in another nonlinear crystal and that the amplitude has the spatiotemporal structure of the original pump mode, filtered by a linear transfer function. These conclusions are drawn from leading-order calculations performed in the interaction picture, with the multimodal nature of all fields being fully accounted for. In our experimental results, we observe the spatial similarity between the up-converted light and the original pump mode; their mutual coherence is demonstrated through observation of fringes with near-unit visibility. The effects studied here have potential applications in quantum information processing and also confirm that the principle of path indistinguishability holds even under unusually extreme conditions.

DOI
10.1103/physreva.99.023853

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In theoretical and experimental work, we consider the process in which an entangled photon pair recombines into a single photon in a nonlinear crystal, with particular interest in the amplitude distribution and coherence properties of the up-converted light. It is found that the up-converted state has perfect mutual coherence with the pump that originally produced the photon pair in another nonlinear crystal and that the amplitude has the spatiotemporal structure of the original pump mode, filtered by a linear transfer function. These conclusions are drawn from leading-order calculations performed in the interaction picture, with the multimodal nature of all fields being fully accounted for. In our experimental results, we observe the spatial similarity between the up-converted light and the original pump mode; their mutual coherence is demonstrated through observation of fringes with near-unit visibility. The effects studied here have potential applications in quantum information processing and also confirm that the principle of path indistinguishability holds even under unusually extreme conditions.
We investigate the amplitude and intensity spatiotemporal coherence and the photon coincidence rates of far-field down-converted light resulting from the interaction of a pump wave of finite spectral width with a nonlinear crystal of finite spatial width. We examine the interplay between energy and phase mismatches and their effects on the intrabeam and interbeam spatial and temporal coherence of the down-converted beams. We show that the down-converted light is spatially incoherent in the second order, and that the signal-idler fourth-order coherence extends over finite entanglement angles. We also study the effect of the apertures through which the down-converted light is collected, when they are centered at phase-matched or misaligned directions.
Entangled photons produced by spontaneous parametric down-conversion have been of paramount importance for our current understanding of quantum mechanics and advances in quantum information. In this process, the quantum correlations of the down-converted photons are governed by the optical properties of the pump beam illuminating the nonlinear crystal. Extensively, the pump beam has been modeled by either coherent beams or by the well-known Gaussian-Schell model, which leads to the natural conclusion that a high degree of optical coherence is required for the generation of highly entangled states. Here, we show that when a novel class of partially coherent Gaussian pump beams is considered, a distinct type of quantum state can be generated for which the amount of entanglement increases inversely with the degree of coherence of the pump beam. This leads to highly incoherent yet highly entangled multiphoton states, which should have interesting consequences for photonic quantum information science.
Here we investigate the all-optical control of spectral correlations in spontaneous parametric down-conversion. We show that when photon pairs are projected onto high-order spatial modes, the spatial structure of the pump field defines the phase-matching function of the nonlinear interaction. Thus, by structuring the pump field in both space and spectrum, the biphoton spectral correlations are fully controlled. Considering a standard periodically-poled crystal as the nonlinear medium, we show that the Gouy phase matching method proposed here can generate both spectrally uncorrelated and high-dimensional spectrally entangled photon pairs, similarly to what is achieved with aperiodically-poled crystals. Furthermore, we show that our method can generate a wider class of quantum states if the pump field is a spatiotemporal wavepacket, that is, if its spatial and spectral structures are correlated.
In the process of spontaneous parametric down-conversion, photons from a pump field are converted to signal and idler photon pairs in a nonlinear crystal. The reversed process, or up-conversion of these pairs back to single photons in a second crystal, is also possible. Here, we present experimental measurements of the up-conversion rate with a controlled time delay introduced between the signal and idler photons. As a function of delay, this rate presents a full width at half maximum of 27.9 fs under our experimental conditions, and we further demonstrate that group delay dispersion of the photon pairs broadens this width. These observations are in close agreement with our calculations, thus demonstrating an ultrafast, nonclassical correlation between the signal and idler waves.
Partially coherent optical beams present phenomena that may not appear in perfectly coherent beams. In this regard, spontaneous parametric downconversion is an intriguing physical process, since the optical properties of the pump laser beam are transferred to the quantum properties of the down-converted photon pairs. Here, the authors study the transfer of twist phase, a novel property of the so-called twisted Gaussian Schell model beams, from a pump beam to down-converted photons. The authors show that a non-zero twist phase can lead to highly entangled yet highly mixed states. The correlations that appear in near/far-field intensity measurements, in the two-photon covariance matrix as well as in orbital angular momentum modes, are explored. The authors derive expressions for the purity of the two-photon state and relate it to the transverse spatial coherence of the pump beam. Their main results utilize a Wigner function formalism that can be applied to a number of scenarios involving partially coherent downconversion sources and contribute to the recent interest in spatially correlated photon pairs produced in mixed states, with possible applications in quantum communication and imaging.
We demonstrate experimental generation of spatially entangled photon pairs by spontaneous parametric down-conversion (SPDC) using a partial spatially coherent pump beam. By varying the spatial coherence of the pump, we show its influence on the down-converted photon's spatial correlations and on its degree of entanglement, in excellent agreement with theory. We then exploit this property to produce pairs of photons with a specific degree of entanglement by tailoring of the pump coherence length. This work thus unravels the fundamental transfer of coherence occurring in SPDC processes, and provides a simple experimental scheme to generate photon pairs with a well-defined degree of spatial entanglement, which may be useful for quantum communication and information processing.