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arXiv:quant-ph/0311147 · Physical Review Letters

Entangled-Photon Imaging of a Pure Phase Object

Ayman F. Abouraddy, Patrick R. Stone, Alexander V. Sergienko, Bahaa E. A. Saleh, Malvin Carl Teich

Published Nov 17, 2004• 109 citations
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Abstract

We demonstrate experimentally and theoretically that a coherent image of a pure phase object [implemented by a microelectromechanical system (MEMS) micromirror array] may be obtained by use of a spatially incoherent illumination beam. This is accomplished by employing a two-beam source of entangled photons generated by spontaneous parametric down-conversion. One of the beams probes the phase object while the other is scanned. Though each of the beams is, in and of itself, spatially incoherent, the pair of beams exhibits higher-order interbeam coherence.

DOI
10.1103/physrevlett.93.213903

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We demonstrate experimentally and theoretically that a coherent image of a pure phase object [implemented by a microelectromechanical system (MEMS) micromirror array] may be obtained by use of a spatially incoherent illumination beam. This is accomplished by employing a two-beam source of entangled photons generated by spontaneous parametric down-conversion. One of the beams probes the phase object while the other is scanned. Though each of the beams is, in and of itself, spatially incoherent, the pair of beams exhibits higher-order interbeam coherence.
Entangled-photon beams, generated for example by spontaneous parametric down-conversion from a nonlinear crystal, may be used to implement holography based on quantum interferometry. One beam is split into a probe component that illuminates the object and another serving as a reference, and is detected with no spatial resolution. The other beam is measured with full spatial resolution. The rate of two-photon coincidence contains full holographic information on the object. Since the beams are not monochromatic, this is a form of higher-order white light holography.
We report the experimental observation of quantum holographic imaging of one-dimensional object with entangled photon pairs, generated in a spontaneous parametric down-conversion process. The signal photons play both roles of “object wave” and “reference wave” in holography but are recorded by a point detector providing only encoding information, while the idler photons travel freely and are locally manipulated with spatial resolution. The holographic image is formed by the two-photon correlation measurement, although both the signal and idler beams are incoherent. Three types of quantum holography schemes are analyzed according to the detection regime of the signal photons.
In this work, pairs of entangled photons are aimed at two spatially separated detectors: the path to one detector contains a physical object, while the path to the second detector does not. Yet, the second detector can be used to create an image of the object, even though none of the photons arriving at that detector have ever interacted with the object! This “ghost” imaging takes advantage of information that is shared between entangled photon pairs. This work aims to explore the underlying principles in a ghost imaging system that utilizes spontaneous parametric down-conversion (SPDC) as the source of entangled photons, with the larger goal of understanding the principles and operation of key parts of the system.
Biphoton systems exhibiting entanglement in position-momentum variables, known as spatial entanglement, are among the most intriguing and well-studied phenomena in quantum optics. A notable subset of these are phase entangled states, where entanglement manifests purely through correlations in the spatial phase of the wavefunction. While the generation of such states from biphotons via spontaneous parametric down-conversion has been explored, their physical implications and applications remain under-investigated. In this work, we theoretically and experimentally examine a unique form of phase entanglement known as `pure' phase entanglement. This state exhibits the unusual feature that the position of one photon is correlated with the momentum of the other. Unlike typical spatially entangled states, it shows no direct correlation in position or momentum between the two photons, underscoring that all correlations arise purely from the spatial phase of the wavefunction. We delve deeper into the theory of this state and experimentally construct it from known phase-entangled states. To certify its properties, we propose a setup that performs a "one-particle momentum measurement" and explore the various tunable parameters. We also highlight potential applications of this state in quantum optics and imaging experiments.
Entangled photons have the remarkable ability to be more sensitive to signal and less sensitive to noise than classical light. Joint photons can sample an object collectively, resulting in faster phase accumulation and higher spatial resolution, while common components of noise can be subtracted. Even more, they can accomplish this while physically separate, due to the nonlocal properties of quantum mechanics. Indeed, nearly all quantum optics experiments rely on this separation, using individual point detectors that are scanned to measure coincidence counts and correlations. Scanning, however, is tedious, time consuming, and ill-suited for imaging. Moreover, the separation of beam paths adds complexity to the system while reducing the number of photons available for sampling, and the multiplicity of detectors does not scale well for greater numbers of photons and higher orders of entanglement. We bypass all of these problems here by directly imaging collinear photon pairs with an electron-multiplying CCD camera. We show explicitly the benefits of quantum nonlocality by engineering the spatial entanglement of the illuminating photons and introduce a new method of correlation measurement by converting time-domain coincidence counting into spatial-domain detection of selected pixels. We show that classical transport-of-intensity methods are applicable in the quantum domain and experimentally demonstrate nearly optimal (Heisenberg-limited) phase measurement for the given quantum illumination. The methods show the power of direct imaging and hold much potential for more general types of quantum information processing and control.