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arXiv:2310.08007 · New Journal of Physics

Scanning quantum correlation microscopy with few emitters

Jaret J. Vasquez-Lozano, Shuo Li, Andrew D. Greentree

Published Mar 8, 2024• 1 citation
arXivHTMLPDF

Abstract

Abstract Optical superresolution microscopy is an important field, where nonlinear optical processes or prior information is used to defeat the classical diffraction limit of light. Quantum correlation microscopy uses photon arrival statistics from single photon emitters to aid in the determination of properties including the number of emitters and their relative brightness. Here we model quantum correlation microscopy in the few emitter regime, i.e. around four single photon emitters below the diffraction limit. We use the Akaike Information Criterion to determine the number of emitters and we vary the relative contributions of intensity to quantum correlation information to determine contribution that provides optimal imaging. Our results show diffraction unlimited performance and a change in localisation scaling behaviour dependent on emitter closeness.

DOI
10.1088/1367-2630/ad31d5

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Abstract Optical superresolution microscopy is an important field, where nonlinear optical processes or prior information is used to defeat the classical diffraction limit of light. Quantum correlation microscopy uses photon arrival statistics from single photon emitters to aid in the determination of properties including the number of emitters and their relative brightness. Here we model quantum correlation microscopy in the few emitter regime, i.e. around four single photon emitters below the diffraction limit. We use the Akaike Information Criterion to determine the number of emitters and we vary the relative contributions of intensity to quantum correlation information to determine contribution that provides optimal imaging. Our results show diffraction unlimited performance and a change in localisation scaling behaviour dependent on emitter closeness.
Techniques of optical superresolution imaging are vital for uncovering the complex dynamics of biochemistry in cellular environments. However the practical resolution for superresolution imaging is limited by the increased photon budget for superresolution, compared with conventional microscopy. For this reason it is important to determine the optimal methods for analysing all of the incoming information. Most approaches to microscopy use only the wave-like properties of light, but the particle-like nature of light provides extra information that is normally inaccessible and can be used to increase imaging resolution. Here we theoretically study the localisation of quantum emitters using higher-order quantum correlation functions to understand the resolution that is practically achievable for bio-imaging tasks. We show explicit imaging results for varying number of emitters as a function of correlation order to illustrate the necessary tradeoffs between imaging resolution and acquisition time.
The optical diffraction limit imposes a bound on imaging resolution in classical optics. Over the last twenty years, many theoretical schemes have been presented for overcoming the diffraction barrier in optical imaging using quantum properties of light. Here, we demonstrate a quantum superresolution imaging method taking advantage of nonclassical light naturally produced in fluorescence microscopy due to photon antibunching, a fundamentally quantum phenomenon inhibiting simultaneous emission of multiple photons. Using a photon counting digital camera, we detect antibunching-induced second and third order intensity correlations and perform subdiffraction limited quantum imaging in a standard wide-field fluorescence microscope.
Abstract The localisation of fluorophores is an important aspect of determining the biological function of cellular systems. Quantum correlation microscopy (QCM) is a promising technique for providing diffraction unlimited emitter localisation that can be used with either confocal or widefield modalities. However, so far, QCM has not been applied to three dimensional localisation problems. Here we show that QCM provides diffraction-unlimited three-dimensional localisation for two emitters within a single diffraction-limited spot. By introducing a two-stage maximum likelihood estimator, our modelling shows that the localisation precision scales as 1 / t where t is the total detection time. Diffraction unlimited localisation is achieved using both intensity and photon correlation from Hanbury Brown and Twiss measurements at as few as four measurement locations. We also compare the results of (MC) simulations with the Cramér–Rao lower bound.
Quantum correlation microscopy is an emerging technique for improving optical resolution. By taking advantage of the quantum statistics from single-photon fluorophores, more information about the emitters (including number and location) is obtained compared with classical microscopy. Although it is known that the resolution can be improved by increasing detector numbers, as well as using quantum correlation, the quantitative relationship between these two approaches is not immediately clear. Here we explore widefield quantum correlation microscopy using arrays of single-photon detectors. We explicitly compare the use of NNN detectors used in photon counting mode vs N/2N/2N/2 detectors used to measure quantum correlations. i.e., where there are N/2N/2N/2 Hanbury Brown and Twiss systems, using the same NNN detectors, on randomly generated two-emitter systems. We find regimes where N/2N/2N/2 Hanbury Brown and Twiss detectors provide improved localisation compared to NNN photon counting detectors, as a function of emitter position and number of photons sampled.
The fundamental understanding of biological pathways requires minimally invasive nanoscopic optical resolution imaging. Many approaches to high-resolution imaging rely on localization of single emitters, such as fluorescent molecules or quantum dots. Additionally, the exact determination of the number of such emitters in an imaging volume is essential for a number of applications; however, in standard intensity-based microscopy it is not possible to determine the number of individual emitters within a diffraction limited spot without initial knowledge of system parameters. Here we explore how quantum measurements of the emitted photons using photon number resolving detectors can be used to address this challenging task. In the proposed new approach, the problem of counting emitters reduces to the task of determining differences between the emitted photon distribution and the Poisson limit. We show that quantum measurements of the number of photons emitted from an ensemble of emitters enable the determination of both the number of emitters and the probability of emission. This method can be applied for any type of single-photon emitters. The scaling laws of this new approach are presented by the Cramer-Rao Lower Bounds, and this technique has great potential in quantum optical imaging with nanoscopic resolution.