Sensing with undetected photons allows access to spectral regions with simultaneous detection of photons of another region and is based on nonlinear interferometry. To obtain the full information of a sample, the corresponding interferogram has to be analyzed in terms of amplitude and phase, which has been realized so far by multiple measurements followed by phase variation. Here, we present a polarization-optics-based phase-quadrature implementation in a nonlinear interferometer for imaging with undetected photons in the infrared region. This allows us to obtain phase and visibility with a single image acquisition without the need of varying optical paths or phases, thus enabling the detection of dynamic processes. We demonstrate the usefulness of our method on a static phase mask opaque to the detected photons as well as on dynamic measurement tasks as the drying of an isopropanol film and the stretching of an adhesive tape.

Optical nonlinear conversion processes are ubiquitously applied to scientific as well as industrial tasks. In particular, nonlinear processes are employed to generate radiation in many frequency ranges. In plenty of these nonlinear processes, the generation of paired photons occurs -the so-called signal and idler photons. Although this type of generation has undergone a tremendous development over the last decades, either the generated signal or the idler radiation has been used experimentally. In contrast, novel quantum-based measurement principles enable the usage of both partners of the generated photon pairs based on their correlation. These measurement approaches have an enormous potential for future applications, as they allow to transfer information from one spectral range to another. In particular, spectral ranges where photon generation and detection is particularly challenging can benefit from this principle. Above all, these include the extreme frequency ranges, such as on the low-frequency side the mid to far infrared or even the terahertz spectral range, but also on the high-frequency side the ultraviolet or X-ray spectral range. In this review article, theoretical and experimental developments based on correlated biphotons are described specifically for the extreme spectral regions.

Quantum-inspired terahertz sensing using nonlinear interferometers enables detection of terahertz spectral properties while only measuring visible light, which never interacted with the sample. Applications in spectroscopy and thickness determination are presented.