Theory of Quantum Imaging with Undetected Photons

TL;DR

This paper provides a detailed theoretical analysis of a quantum imaging method where the illuminating photons are not detected, revealing how interference encodes object information and how magnification depends on two wavelengths.

Contribution

It offers a comprehensive theoretical framework for understanding quantum imaging with undetected photons, clarifying the role of interference and wavelength dependence.

Findings

Object information resides only in the interference term

Magnification depends on the average wavelengths of illuminating and detected photons

Imaging relies on quantum interference without path information

Abstract

A novel quantum imaging technique has recently been demonstrated in an experiment, where the photon used for illuminating an object is not detected; the image is obtained by interfering two beams, none of which ever interacts with the object. Here we present a detailed theoretical analysis of the experiment. We show that the object information is present only in the interference term and not in the individual intensities of the interfering beams. We also theoretically establish that the magnification of the imaging system depends on two wavelengths: the average wavelength of the photon that illuminates the object and the average wavelength of the photon that is detected. Our analysis affirms that the imaging process is based on the principle that quantum interference occurs when interferometric path information is unavailable.