EAGER: Smart single-pixel quantum statistical imaging beyond the Abbe-Rayleigh criterion

The identification of the photon as a promising information resource has triggered a variety of quantum photonic technologies for multiple purposes that range from information processing to imaging. Recently, the possibility of using the quantum properties of the light field to overcome diffraction has become one of the main goals of quantum imaging.

The interest in quantum optical superresolution resides in its potential for improving the performance of existing schemes for remote imaging and microscopy. Interestingly, seminal work that established the foundations of classical superresolution imaging was awarded with the Nobel Prize of Chemistry in 2014. These fundamental contributions demonstrated the possibility of performing imaging beyond the Abbe-Rayleigh resolution criterion.

Recently, researchers from the quantum optics community have conducted experiments that aim to boost spatial resolution of classical schemes for imaging by projecting target objects onto spatial modes. These conventional protocols rely on a series of spatial projective measurements to pick up phase information that is then used to boost the spatial resolution of optical systems.

Unfortunately, these schemes require a priori information regarding the coherence properties of the light beams, a well as stringent alignment conditions. The purpose of this research program is to demonstrate that the limited spatial resolution of optical instruments can be overcome through measurements of the quantum statistical properties of photons, which are insensitive to diffraction.

The identification of the quantum properties of light will be performed using artificial neural networks. The successful completion of the program will enable transformative technology for remote imaging and superresolving microscopy. The educational objectives of this project are to contribute to the inclusive and fair diffusion of science by engaging students to perform research on superresolving imaging, and by developing a series of lectures and demonstrations for general audiences in the Ascension Parish Library from Louisiana.

This program includes a series of theoretical and experimental milestones. The theoretical component of this research program aims to develop new formalisms to model the evolution of the properties of quantum coherence of multiparticle systems. These physical systems lead to computationally hard problems scaling on the order of O(2nn!), where n represents the number of photons in the imaging system.

The experimental part of the program will be carried out in table-top optical setups. The investigators will prepare multiple light sources with tunable coherence properties and degrees of indistinguishability, these beams will be characterized through photon-number-resolving detection. These capabilities will enable the team to 1) develop a general theory of quantum coherence to describe the photon statistics produced by the combination of an arbitrary number of light sources, 2) design artificial neural networks to demonstrate single-pixel cameras with photon-number resolution, and 3) experimentally demonstrate single-pixel superresolution imaging of an arbitrary number of photon emitters and scatterers.

The completion of these milestones will lead to the first family of superresolving single-pixel cameras that exploit the self-learning features of artificial intelligence to identify the statistical fluctuations of truly unknown mixtures of light sources. The potential of these novel photonic devices will be explored in the context of remote imaging and microscopy.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.