Quantum sensing is highly attractive for accessing spectral regions in which the detection of photons is technically challenging: sample information is gained in the spectral region of interest and transferred via biphoton correlations into another spectral range, for which highly sensitive detectors are available. This is especially beneficial for terahertz radiation, where no semiconductor detectors are available and coherent detection schemes or cryogenically cooled bolometers have to be employed. Here, we report on the first demonstration of quantum sensing in the terahertz frequency range in which the terahertz photons interact with a sample in free space and information about the sample thickness is obtained by the detection of visible photons. As a first demonstration, we show layer thickness measurements with terahertz photons based on biphoton interference. As non-destructive layer thickness measurements are of high industrial relevance, our experiments might be seen as a first step towards industrial quantum sensing applications.

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Terahertz spectroscopy allows for identifying different isomers of materials, for drug discrimination as well as for detecting hazardous substances. As many dielectric materials used for packaging are transparent in the terahertz spectral range, substances might even be identified if packaged. Despite these useful applications, terahertz spectroscopy suffers from the still technically demanding detection of terahertz radiation. Thus, either coherent timedomain-spectroscopy schemes employing ultrafast pulsed lasers or continuous-wave detection with photomixers requiring two laser systems are used to circumvent the challenge to detect such low-energetic radiation without using cooled detectors. Here, we report on the first demonstration of terahertz spectroscopy, in which the sample interacts with terahertz idler photons, while only correlated visible signal photons are detected -a concept inspired by quantum optics. To generate these correlated signal-idler photon pairs, a periodically poled lithium niobate crystal and a 660 nm continuous-wave pump source are used. After propagating through a single-crystal nonlinear interferometer, the pump photons are separated from the signal radiation by highly efficient and narrowband volume Bragg gratings. An uncooled scientific CMOS camera detects the frequency-angular spectra of the remaining visible signal and reveals terahertz-spectral information in the Stokes as well as the anti-Stokes part of collinear forward generation. Neither cooled detectors nor expensive pulsed lasers for coherent detection are required. We demonstrate spectroscopy on the well-known absorption features in the terahertz spectral range of -lactose monohydrate and paraaminobenzoic acid by detecting only visible photons.

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 sensing encompasses highly promising techniques with diverse applications including noise-reduced imaging, super-resolution microscopy, as well as imaging and spectroscopy in challenging spectral ranges. These detection schemes use biphoton correlations to surpass classical limits or transfer information to different spectral ranges. Theoretical analysis is mostly confined to idealized conditions. Therefore, theoretical predictions and experimental results for the performance of quantum-sensing systems often diverge. This general simulation method that includes experimental imperfections bridges the gap between theory and experiment. A theoretical approach is developed and the capabilities are demonstrated with the simulation of aligned and misaligned quantum-imaging experiments. The results recreate the characteristics of the experimental data. The simulation results were further used to improve the obtained images in post-processing. As a simulation method for general quantum-sensing systems, this work provides a step toward powerful simulation tools for interactively exploring the design space and optimizing the experiment's characteristics.

Spontaneous parametric down-conversion (SPDC) sources are an important technology for quantum sensing and imaging. We demonstrate a general simulation method, based on modeling from first principles, reproducing the spectrally and spatially resolved absolute counts of a SPDC experiment. By additionally simulating parametric up- and down-conversion processes with thermal photons as well as effects of the optical system we accomplish good agreement with the experimental results. This method is broadly applicable and allows for the separation of contributing processes, virtual characterization of SPDC sources, and enables the simulation of many quantum based applications.

In this erratum, we correct two typing errors from our previously published manuscript [Opt. Express 27, 7458 (2019)10.1364/OE.27.007458]. In the original manuscript, the two errors were limited to the theoretical derivation and did not touch the numerical calculations such that the results and conclusions remain unchanged.