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arXiv:2112.01725 · Physical Review Research

Superresolution of two unbalanced point sources assisted by the entangled partner

Abdelali Sajia, Xiao‐Feng Qian

Published Sep 29, 2022• 9 citations
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Abstract

Sub-diffraction-limit resolution, or superresolution, has been successfully demonstrated in recent theoretical and experimental studies for two equal-brightness and incoherent point sources. However, practical situations of either nonequal brightness (i.e., unbalancedness) or partial coherence are shown to have fatal effects on such superresolution. As a step towards resolving such issues, we consider the effects of both unbalancedness and a form of partial coherence (i.e., quantum state coherence) together by including an entangled degree of freedom of the two point sources. Unexpectedly, it is found that the two negative effects can counteraffect each other, thus permitting credible superresolution, when the measurement is analyzed in the entangled partner's rotated basis. The least resolvable non-zero two-source separation is also identified analytically. Our result represents useful guidance towards the realization of superresolution for practical point sources. The vector-structure analog of quantum and classical light sources also suggests that our analysis applies to both contexts.

DOI
10.1103/physrevresearch.4.033244

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Sub-diffraction-limit resolution, or superresolution, has been successfully demonstrated in recent theoretical and experimental studies for two equal-brightness and incoherent point sources. However, practical situations of either nonequal brightness (i.e., unbalancedness) or partial coherence are shown to have fatal effects on such superresolution. As a step towards resolving such issues, we consider the effects of both unbalancedness and a form of partial coherence (i.e., quantum state coherence) together by including an entangled degree of freedom of the two point sources. Unexpectedly, it is found that the two negative effects can counteraffect each other, thus permitting credible superresolution, when the measurement is analyzed in the entangled partner's rotated basis. The least resolvable non-zero two-source separation is also identified analytically. Our result represents useful guidance towards the realization of superresolution for practical point sources. The vector-structure analog of quantum and classical light sources also suggests that our analysis applies to both contexts.
Fundamental wave features of light play an important role in the realization of superresolution for two spatially separated point sources. It has been shown that (partial) coherence, which is an inevitable feature in practical light propagation, is harmful to measurement precision thus preventing superresolution. Here we study the quantitative effect of another fundamental feature, entanglement, on the quality of superresolution and compare it with that of coherence. Both single- and two-parameter estimations are analyzed in detail. Surprisingly, contrary to coherence, it is found that superresolution measurement precision (in terms of Fisher Information) can be enhanced as the amount of entanglement increases. More importantly, our analysis shows that non-zero entanglement always guarantees the non-vanishing of Fisher Information. Thus, while coherence is unwanted, entanglement is a favorable feature for superresolution.
Analyses based on quantum metrology have shown that the ability to localize the positions of two incoherent point sources can be significantly enhanced over direct imaging through the use of mode sorting. Here we theoretically and experimentally investigate the effect of partial coherence on the sub-diffraction limit localization of two sources based on parity sorting. With the prior information of a negative and real-valued degree of coherence, higher Fisher information is obtained than that for the incoherent case. Our results pave the way to clarifying the role of coherence in quantum-limited metrology.
Resolving the separation between two incoherent optical sources with high precision is of great significance for fluorescence imaging and astronomical observations. In this paper, we focus on a more general scenario where two sources have unequal brightnesses. We give the ultimate precision limit with respect to separation by using the quantum Fisher information. Through the calculation of the classical Fisher information, we analyze and compare several specific measurement schemes including direct measurement, Gaussian mode measurement and zero-photon measurement. The results indicate that Gaussian mode measurement is the nearly optimal for a small separation. On this basis, the effects of relative brightness fluctuation are addressed. Our work provides a positive complement to the aspect of superresolution imaging of incoherent sources.
When two point sources are separated by less than the Abbe-Rayleigh limit, conventional resolution methods fail to distinguish whether there is one source or two. Consequently, it becomes nearly impossible to resolve important relative properties of the two sources, such as mutual coherence, relative phase, and brightness contrast. In this regime, the incoming composite quantum signal must be treated as a single entity described by an overall quantum wave function. In this study, we explore the superresolution of such two-point sources by examining a special wave property, i.e., entanglement between spatial degree of freedom (DoF) and remaining DoFs (both internal and external). Remarkably, we find that increasing this inter-DoF entanglement enhances the precision of superresolution, as quantified by the quantum Fisher information (QFI) in single-parameter estimation. Moreover, we show that this entanglement reliably ensures a nonvanishing QFI in two-parameter estimation, highlighting its role as a valuable resource for quantum superresolution.
Superresolution has been demonstrated to overcome the limitation of Rayleigh's criterion and achieve significant precision improvement in resolving the separation of two incoherent optical point sources. However, in recent years, it was found that, if the photon numbers of two incoherent optical sources are unknown, the precision of superresolution vanishes when the photon numbers are actually different. In this work, we first analyze in detail the estimation precision of the separation for two incoherent optical sources with the same point-spread functions and show that, when the two photon numbers are different but sufficiently close, the superresolution can still be realized but with different precisions. We find the condition on how close the photon numbers need to be to realize the superresolution and derive the precision of superresolution in different regimes of the photon number difference. We further consider the superresolution for two incoherent optical sources with different point-spread functions and show that the competition between the difference of photon numbers, the difference of point-spread functions, and the separation of source locations determines the precision of superresolution. The results exhibit precision limits distinct from that of two identical point-spread functions with equal photon numbers and extend the realizable regimes of quantum superresolution. Finally, the results are illustrated by Gaussian point-spread functions. Published by the American Physical Society 2024
Discriminating two spatially separated sources is one of the most fundamental problems in imaging.Recent research based on quantum parameter estimation theory shows that the resolution limit of two incoherent point sources given by Rayleigh can be broken.However, in realistic optical systems, there often exists coherence in the imaging light field, and there have been efforts to analyze the optical resolution in the presence of partial coherence.Nevertheless, how the degree of coherence between two point sources affects the resolution has not been fully understood.Here, we analyze the quantum-limited resolution of two partially coherent point sources by explicitly relating the state after evolution through the optical systems to the coherence of the sources.In particular, we consider the situation in which coherence varies with the separation.We propose a feasible experiment scheme to realize the nearly optimal measurement, which adaptively chooses the binary spatial-mode demultiplexing measurement and direct imaging.Our results will have wide applications in imaging involving coherence of light.