Quantum-inspired distance sensing using thermal light second-order interference Francesco V. Pepe, 1, 2 Gabriele Chilleri, 3 Giovanni Scala, 1, 2 Danilo Triggiani, 3 Yoon-Ho Kim, 4 and Vincenzo Tamma 3, 5, * 1 Dipartimento Interateneo di Fisica, Universit` a degli Studi di Bari, I-70126 Bari, Italy 2 INFN, Sezione di Bari, I-70125 Bari, Italy 3 School of Mathematics and Physics, University of Portsmouth, Portsmouth PO1 3QL, UK 4 Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea 5 Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK We introduce and describe a technique for distance sensing, based on second-order interferometry of thermal light. The method is based on measuring correlation between intensity fluctuations on two detectors, and provides estimates of the distances separating a remote mask from the source and the detector, even when such information cannot be retrieved by first-order intensity measurements. We show how the sensitivity to such distances is intimately connected to the degree of correlation of the measured interference pattern in different experimental scenarios and independently of the spectral properties of light. Remarkably, this protocol can be also used to measure the distance of remote reflective objects in the presence of turbulence. We demonstrate the emergence of new critical parameters which benchmark the degree of second order correlation, describing the counterintuitive emergence of spatial second-order interference not only in the absence of (first-order) coherence at both detectors but also when first order interference is observed at one of the two detectors. Since the discovery of the Hanbury-Brown and Twiss (HBT) effect in the 1950s [1, 2], the measurement of cor- relations of light intensities, leading to counterintuitive higher-order interference effects in absence of field co- herence [3, 4], has triggered the development of quan- tum optics [5]. In particular, the correlation measure- ment at the heart of HBT effect has been the working tool of all entanglement-based protocols, from studies of quantum foundations [6–11] to quantum-enhanced tech- nologies such as quantum imaging and lithography [12– 18], information [19–24], and teleportation [25]. Inter- estingly, starting from the early 2000s, many of these ef- fects have been replicated by exploiting the correlations of chaotic light [26–35]. Recently, novel schemes where second-order interference occurs effectively between light propagating through two pairs of paths that are mutually incoherent at first order have been proposed [36–38] and experimentally realized [39–42] in both the temporal and spatial domain. In this letter, we shed new light on the physics of sec- ond order interference with thermal light and show its sensitivity to distances in different experimental scenar- ios where spatial coherence is absent at either one or both the detectors and turbulence may occur. Remarkably, we demonstrate the emergence of second order coherence from two new critical physical parameters. In particular, we show how a newly defined thermal light second-order correlation length determines the degree of second order correlations depending on the interplay between trans- verse first-order coherence lengths at two locations arbi- trarily distant from each other. This not only provides a deep understanding of second order correlation of ther- mal light beyond (first-order) spatial coherence, but also enables us to be sensitive to arbitrary distances between an incoherent source and an object and between an ob- ject and a detector. This is the case even when first-order interference cannot provide information on such param- eters. Our results also lay the foundations of novel proto- cols for distance sensing, where no frequency informa- tion about the employed thermal light is required. This can integrate and improve state-of-the-art applications, such as those based on pulsed light (e.g., time-of-flight cameras [43]) or first-order interference (e.g., coherent LIDAR [44]), tasks in metrology and information pro- cessing [21, 26, 29, 45–47], as well as optical algorithms [48–52]. Interestingly, we show the ranging sensitivity of our second-order interference technique by employ- ing simple double slit masks. In the more general ex- perimental scenario, pictured in Fig. 1(a), after beam splitting a thermal beam as in a standard HBT experi- ment, light propagates at the two output ports through two double-slit masks (usually a remote “target” mask T and a “controlled” reference mask C in the laboratory) before measurements of spatial correlation in the inten- sity fluctuations are performed at the two detectors. We demonstrate that the measured effective second order in- terference between the two pairs of paths through the upper and lower slits depends in a non trivial way on both the distances (z C ,z T ) from the source to the two masks and to the distances (f C ,f T ) from each mask to the corresponding detector. By properly tuning the de- gree of second-order correlations through the values of the slit separations and the distances z C and f C , related to controlled mask, one can enhance the sensitivity of correlation measurements to the distances z T and f T of the remote target mask, even when first order interfer- ence provides no information on one of those distances or both. We also show that when z T = z C = z [Fig. 1(b)], the arXiv:2011.05224v1 [quant-ph] 10 Nov 2020