Fundamental resolution limit of quantum imaging with undetected photons

Abstract

Quantum imaging with undetected photons relies on the principle of induced coherence without induced emission and uses two sources of photon-pairs with a signal-and an idler photon of wavelengths λS and λI, respectively. Each pair shares strong quantum correlations in both position and momentum, which allows to image an object illuminated with idler photons by just measuring signal photons that never interact with the object. In this work, we theoretically investigate the transverse resolution of this non-local imaging scheme through a general formalism that treats propagating photons beyond the commonly used paraxial approximation. We hereby prove that the resolution of quantum imaging with undetected photons is diffraction limited to the longer wavelength of the signal and idler pairs, with a minimum resolvable resolution of max(λS, λI)/2. Moreover, we conclude that this result is also valid for other non-local two-photon imaging schemes.

Subdiffraction Quantum Imaging with Undetected Photons

“…We use the term "far-field" in contrast to "near-field", where nearfield interactions can involve evanescent modes and are usually only effective within wavelength-range distances [13]. Hence, resolution of far-field QIUP will be constrained by the diffraction limit [4,[14][15][16]. For the case where the probing wavelength λ I is larger than the detection wavelength λ S , object's information is transferred by propagating idler fields and consequently the transverse spatial resolution in this information is constrained by the idler diffraction limit [14].…”

“…Hence, resolution of far-field QIUP will be constrained by the diffraction limit [4,[14][15][16]. For the case where the probing wavelength λ I is larger than the detection wavelength λ S , object's information is transferred by propagating idler fields and consequently the transverse spatial resolution in this information is constrained by the idler diffraction limit [14]. Hence, conventional QIUP can provide the object's MIR image by only detecting visible photons, avoiding inefficient and expensive MIR detectors, but no resolution advantage is achieved compared to conventional MIR imaging, since the resolution is restricted by the larger MIR wavelength.…”