Quantum microscopy using photon correlations

Higher-order correlations of the radiation field improve resolution in stellar interferometers, as in the Hanbury-Brown-Twiss effect. It is also possible to improve microscopic resolution beyond the Rayleigh limit by using quantum light fields composed of entangled photons. Focusing on two photons, we distinguish two types of entanglement: frequency entanglement, where the photons in different paths are correlated in frequency, and path entanglement, where the correlation between paths is in photon number. Two paradigms of quantum microscopy are discussed: spectral microscopy, where path- and frequency-entangled photons produced in cascade decay of two atoms make possible sub-natural linewidth resolution of atomic levels, and spatial microscopy, where path-entangled photons emitted by an atomic array produce sub-wavelength diffraction resolution as compared to an equivalent classical grating. These scenarios require two-photon correlation or coincidence measurements. The connection between the two paradigms, and the two types of entanglement, highlights the link between the temporal and spatial aspects of quantum interferometry.