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International Conference on Electromagnetics in Advanced Applications (ICEAA)

Quantum noise radar: superresolution with quantum antennas by accessing spatiotemporal correlations

Dmitri S. Mogilevtsev, I. A. Peshko, Ilya Karuseichyk, Alexander B. Mikhalychev, Alexander P. Nizovtsev, Gregory Ya. Slepyan, Amir Boag

Published Sep 1, 2019• 1 citation
Publisher

Abstract

Measuring simultaneous correlations of intensity fluctuations, one can exploit photon correlations of the imaging source and improve resolution in comparison with the intensity detection. However, in this case also information loss unavoidable for intensity detection eventually leads to the phenomenon known as “the Rayleigh catastrophe”. When the details of the imaged object become much smaller than the certain value defined by the wavelength of the imaging field and parameters of the imaging set-up, the information about any individual detail tends to zero making practically unfeasible inferring object parameters from the measured correlation functions.

DOI
10.1109/iceaa.2019.8879404

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Measuring simultaneous correlations of intensity fluctuations, one can exploit photon correlations of the imaging source and improve resolution in comparison with the intensity detection. However, in this case also information loss unavoidable for intensity detection eventually leads to the phenomenon known as “the Rayleigh catastrophe”. When the details of the imaged object become much smaller than the certain value defined by the wavelength of the imaging field and parameters of the imaging set-up, the information about any individual detail tends to zero making practically unfeasible inferring object parameters from the measured correlation functions.
We suggest overcoming the "Rayleigh catastrophe" and reaching superresolution for imaging with both spatially and temporally correlated field of a superradiant quantum antenna. Considering far-field radiation of two interacting spontaneously emitting two-level systems, we show that for the measurement of the temporally delayed second-order correlation function of the scattered field, the Fisher information does not tend to zero with diminishing the distance between a pair of scatterers even for non-sharp time-averaged detection. For position estimation of more scatterers, the measurement of the time-delayed function is able to provide a considerable accuracy gain over the zero-delayed function. We also show that the superresolution with the considered quantum antenna can be achieved for both near-field imaging and for estimating the antenna parameters.
We suggest overcoming the "Rayleigh catastrophe" and reaching superresolution for imaging with both spatially and temporally-correlated field of a superradiant quantum antenna. Considering far-field radiation of two interacting spontaneously emitting two-level systems, we show that for the measurement of the temporally-delayed second-order correlation function of the scattered field, the Fisher information does not tend to zero with diminishing the distance between a pair of scatterers even for non-sharp time-averaged detection. For position estimation of a larger number of scatterers, measurement of the time-delayed function is able to provide a considerable accuracy gain over the zero-delayed function. We show also that the superresolution with the considered quantum antenna can be achieved for both near-field imaging and estimating parameters of the antenna.
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the noise arising from quantum nature of light. Minimizing the effect of this noise requires quantum treatment of optical imaging. By reformulating imaging as a problem of quantum measurement and estimation, it becomes possible to identify optimal detection strategies that recover spatial information previously thought inaccessible. This review summarizes the theoretical framework that underpins this development, from the formulation of quantum Cramer-Rao bounds and Chernoff bounds to the construction of receivers that attain them, such as those based on spatial-mode demultiplexing. We show how these methods can beat conventional imaging in the classification, localization, and imaging of sub-Rayleigh incoherent sources. We then discuss extensions to multiparameter and partially coherent scenarios, and highlight the unifying connections between estimation and discrimination tasks. Finally, we survey recent experimental demonstrations that approach quantum-limited resolution and outline emerging applications in microscopy, astronomy, and optical sensing.
Quantum imaging emerged quite recently as a breakthrough technology of overcoming the diffraction limit in microscopy and enhancement of optical resolution without the necessity to use hard radiation or perform scanning in the near field [1] , [2] . Both, the quantum imaging itself and the more “classical” techniques inspired by it (for example, super-resolution optical fluctuations imaging – SOFI [3] ), rely on detection and analysis of photon (intensity) correlations. Typically, it is believed that the more correlated illuminating light is used and the higher order of the correlations is measured, the larger super-resolution can be achieved. That conclusion is based on efficient narrowing of the point-spread function, which, however, does not necessarily imply better resolution as the ability to reconstruct smaller features of the investigated object successfully.
Imaging is the estimation of the spatial distribution of a physical object by measuring the optical radiation it emits, or by making use of an optical wave that interacts with the object, via reflection or transmission, for example, before being measured by a detector. The resolution of an imaging system is limited by the inability to localize the optical field at points of the object. Under otherwise ideal conditions, resolution is limited by diffraction. The sensitivity of an imaging system is limited by the uncertainty in the measurement. Under ideal conditions, this is determined by photon noise, which depends on the statistical fluctuations of the light. In conventional imaging systems, an extended detector, such as a CCD camera or an array detector, measures the spatial distribution of the optical intensity, which is proportional to the photon flux density. In interferometric systems, the spatial distribution of the optical field is inferred from measurements of the optical intensity. With the emergence of coherence theory, imaging systems based on measurements of the second-order coherence function at pairs of points in the detection plane were developed. An example is the imaging of an incoherent object based on the van Cittert-Zernike theorem. Imaging systems based on measurement of intensity correlation, or the photon coincidence rate, at pairs of points, were developed in the 1960s. A classic example of the photon-correlation imaging of an object emitting thermal light is stellar imaging using a Hanbury-Brown-Twiss intensity-correlation interferometer. More recently, two-photon light, which may be generated via spontaneous parametric downconversion in a second-order nonlinear optical crystal, has been used for imaging. This type of two-photon (or biphoton) imaging, which has come to be called quantum imaging, is also based on the measurement of photon coincidence by the use of photon-counting array detectors or by scanning two photon-counting detectors at pairs of points. To compare the resolution and sensitivity of imaging systems based on the aforementioned types of measurements, it is necessary to derive expressions for the measured quantities in terms of the object distribution. The point-spread functions based on such expressions can be used to assess the resolution. One measure of the sensitivity of the imaging process is the signal-to-noise ratio (SNR) of the measured variables. The statistical nature of the light source must be known in order to determine the SNR. The purpose of this chapter is to compare the resolution and sensitivity of photon-correlation imaging systems that make use of thermal light and two-photon light. We will henceforth refer to these two imaging modalities as classical and quantum photon-correlation imaging, or simply classical and quantum imaging, respectively. Clearly, light in other quantum states can also be used for imaging.