Traditional imaging relies on three fundamental elements: a light source interacting with the object, detection of scattered light, and a spatially resolved detector. These constraints limit the imaging of sensitive samples due to potential damage from interaction and the limitations of photon-starved detection. This research builds upon previous work in quantum ghost imaging (GI), quantum imaging with undetected photons (QIUP), and interaction-free measurements (IFMs). GI leverages the spatial correlations of entangled photon pairs, requiring two-photon coincidence measurements, while QIUP utilizes induced coherence (IC) and avoids the need for detecting photons interacting with the object. Single-pixel imaging (SPI) techniques offer another avenue, reducing data processing requirements by using spatially resolved masks and a single-pixel detector. The authors aim to develop an imaging protocol that alleviates all three typical imaging requirements by combining IFM, SPI, and IC interferometry. This approach aims to achieve interaction-free quantum imaging with minimal detection needs, opening up possibilities for imaging delicate systems, such as biological tissues and quantum states of atomic ensembles, and wavelengths where spatial single-photon detection is inefficient or unavailable.

The paper reviews existing quantum imaging techniques, including ghost imaging (GI), which uses entangled photon pairs and requires two-photon coincident measurements; and quantum imaging with undetected photons (QIUP), which uses induced coherence and avoids the detection of photons interacting with the object. The limitations of these methods, particularly the need for direct interaction between the object and photons, are discussed. The authors also discuss single-pixel imaging (SPI) techniques, which use spatially resolved masks and a single-pixel detector to reconstruct images. Finally, the authors explore interaction-free measurement (IFM), which allows detection of an object without direct interaction. Existing methods alleviate only one or two of the usual imaging requirements. This work aims to create an imaging protocol that overcomes all three simultaneous limitations.

The experimental setup consists of three main parts: an induced coherence (IC) interferometer, an interaction-free measurement (IFM) interferometer, and a single-pixel imaging (SPI) module. The IC interferometer is a folded Michelson interferometer with a nonlinear crystal (NC) generating signal (810 nm) and idler (1550 nm) photons via spontaneous parametric down-conversion (SPDC). The idler photon is injected into the IFM Michelson interferometer. The presence of an object in the IFM modifies the idler photon's path, affecting the signal photon's interference pattern. The SPI module utilizes a spatial light modulator (SLM) to project Hadamard masks onto the object, with the signal photon counts recorded by a single-pixel detector. For interaction-free quantum sensing, an opaque object is placed in the IFM, and the signal photon's interference visibility is compared with and without the object. For interaction-free quantum imaging, a 3D-printed 'NJU' logo is used as the object, with an intensified CCD (ICCD) camera and the SPI method used to reconstruct the image. The ICCD method uses signal photon counts at two phase settings to highlight the difference in interference between transparent and opaque regions. The SPI method uses Hadamard masks, and signal photon counts at four settings are processed according to equation (1) to generate weighted masks which are summed to reconstruct the image. Mathematical models for the interference images (equations 2-11) are provided.

The experiments demonstrate interaction-free quantum sensing with undetected photons, achieving a confidence level above 99.93% in distinguishing the presence or absence of an opaque object. Interaction-free imaging with undetected photons (IFIUP) is successfully realized using an ICCD camera, imaging a 3D-printed 'NJU' logo. The difference between images captured at different phase settings (θ = 0, φ = π) and (θ = π, φ = 0) clearly highlights the 'NJU' characters due to differences in the interference patterns between the transparent characters and opaque background. Finally, interaction-free, single-pixel quantum imaging with undetected photons is achieved using the SPI module, reconstructing an image of the 'NJU' logo solely from signal photon counts detected by a visible single-photon detector. This conclusively demonstrates that all three requirements of traditional imaging (interaction, detection, and spatially resolved detectors) have been successfully alleviated.

The results demonstrate a significant advancement in quantum imaging, achieving interaction-free imaging with minimal detection requirements. This approach opens up new avenues for imaging sensitive specimens where traditional methods are limited by potential damage from interaction or lack of efficient detection capabilities at specific wavelengths. The combination of IFM, IC, and SPI enables imaging without the object interacting with either the illuminating or detected photon. The use of a visible single-photon detector simplifies the setup and improves efficiency. This technique addresses the challenges of imaging delicate materials and biological samples while offering flexibility in the choice of wavelengths for the detected photons.

This paper successfully demonstrates interaction-free, single-pixel quantum imaging with undetected photons, overcoming the limitations of conventional imaging techniques. The method eliminates the need for object-photon interaction, direct detection, and spatially resolved detectors. Future research could focus on improving IFM efficiency using advanced optical setups and exploring broadband phase matching to expand the spectral range of the technique. The potential of this method extends to diverse fields such as materials science and life sciences, where imaging fragile or sensitive samples is crucial.

While the experiment successfully demonstrates the concept, the IFM efficiency could be improved, potentially through the use of more advanced optical interferometers and low-loss optical switches. The resolution of the single-pixel imaging method is also limited by the number and size of the Hadamard masks and detector size. Furthermore, the 'interaction-free' nature of the measurement is strictly applicable to binary objects; for grey or quantum objects, the study performs quantum interrogation.