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arXiv:1604.06928 · Optics Letters

Beyond the diffraction limit via optical amplification

Aglaé N. Kellerer, Erez N. Ribak

Published Jul 5, 2016• 22 citations
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Abstract

In a previous article [Astron. Astrophys.561, A118 (2014)], we suggested a method to overcome the diffraction limit behind a telescope. We discuss and extend recent numerical simulations and test whether it is indeed possible to use photon amplification to enhance the angular resolution of a telescope or a microscope beyond the diffraction limit. An essential addition is the proposal to select events with an above-average ratio of stimulated to spontaneous photons. The analysis shows that the diffraction limit of a telescope is surpassed by a factor of 10 for an amplifier gain of 200, if the analysis is restricted to a tenth of the incoming astronomical photons. A gain of 70 is sufficient with a hundredth of the photons. More simulations must be performed to account for the bunching of spontaneous photons.

DOI
10.1364/ol.41.003181

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In a previous article [Astron. Astrophys.561, A118 (2014)], we suggested a method to overcome the diffraction limit behind a telescope. We discuss and extend recent numerical simulations and test whether it is indeed possible to use photon amplification to enhance the angular resolution of a telescope or a microscope beyond the diffraction limit. An essential addition is the proposal to select events with an above-average ratio of stimulated to spontaneous photons. The analysis shows that the diffraction limit of a telescope is surpassed by a factor of 10 for an amplifier gain of 200, if the analysis is restricted to a tenth of the incoming astronomical photons. A gain of 70 is sufficient with a hundredth of the photons. More simulations must be performed to account for the bunching of spontaneous photons.
The use of probabilistic amplification for astronomical imaging is discussed. Probabilistic single photon amplification has been theoretically proven and practically demonstrated in quantum optical laboratories. In astronomy it should allow to increase the angular resolution beyond the diffraction limit at the expense of throughput: not every amplification event is successful - unsuccessful events contain a large fraction of noise and need to be discarded. This article indicates the fundamental limit in the trade-off between gain in angular resolution and loss in throughput. The practical implementation of probabilistic amplification for astronomical imaging remains an open issue.
Heisenberg's uncertainty principle tells us that it’s impossible to determine simultaneously the position of a photon crossing a telescope's aperture as well as the angle of its momentum. A new technique suggests to overcome the diffraction limit via optical amplification. A number of entangled photons, created by amplification of a single photon, behaves as a single quantum system with respect to the uncertainty principle. Unfortunately, spontaneous emission contributes noise and negates the possible gain from this stimulated emission. The spontaneous photons guarantee the uncertainty principle. Thus the problem of low resolution is replaced by the problem of low SNR. The detection of spontaneous photons follows the same Poisson statistics in time and space. However, the stimulated photons are spatially and temporally coherent with the incoming photons. A pixel with additional hidden thermal signal will slightly modify the Poisson statistics, and only within the diffraction pattern of the photon packets. We characterise the average number of spontaneous photons in all pixels, and subtract it from the stimulated photons. This algorithm is applied on simulated detection events of an amplified signal. The reconstructed image is resolved beyond the limit of the same optical system in the absence of amplification. We produced a number of samples of a wide-band solid-state dye (DCM within PMMA), because the expected number of (stellar) photons is small, and a solid-state dye is easier to handle compared to a dye solution. Initial results with a white light source and a laser pump depict the parameters of the method.
Classically, the angular resolution of a telescope is limited by its diffraction limit: the ratio of its observing wavelength to its diameter. Developments in quantum information theory over the past decade have uncovered quantum-optimal measurement methods that enable super-resolution imaging beyond the diffraction limit, and many laboratory-scale demonstrations of these methods have been performed over the past decade, culminating in the recent first on-sky demonstration of quantum-enhanced astronomical imaging. In this Review, we detail the current progress and achievements of these theoretical and experimental results, discuss the astronomical science cases motivating the development of higher resolution telescopes, summarise the technological challenges facing the practical application of quantum imaging technologies to astronomy, and present a vision for the realization of \emph{quantum telescopes} with imaging resolutions orders of magnitude better than current observatories.
Heisenberg’s uncertainty principle tells us that it is impossible to determine simultaneously the position of a photon crossing a telescope’s aperture and its momentum. Super-resolution imaging techniques rely on modification of the observed sample or on entangling photons. In astronomy, we have no access to the object, but resolution may be improved by optical amplification. Unfortunately, spontaneous emission contributes noise and negates the possible gain from stimulated emissions. We show that it is possible to increase the weight of the stimulated photons by considering photon statistics and observe an improvement in resolution. Most importantly, we demonstrate a method that can apply for all imaging purposes.
High-angular-resolution imaging is crucial for many applications in modern astronomy and astrophysics. The fundamental diffraction limit constrains the resolving power of both ground-based and spaceborne telescopes. The recent idea of a quantum telescope based on the optical parametric amplification (OPA) of light aims to bypass this limit for the imaging of extended sources by an order of magnitude or more. We present an updated scheme of an OPA-based device and a more accurate model of the signal amplification by such a device. The semiclassical model that we present predicts that the noise in such a system will form so-called light speckles as a result of light interference in the optical path. Based on this model, we analysed the efficiency of OPA in increasing the angular resolution of the imaging of extended targets and the precise localization of a distant point source. According to our new model, OPA offers a gain in resolved imaging in comparison to classical optics. For a given time-span, we found that OPA can be more efficient in localizing a single distant point source than classical telescopes.