We present a tutorial on the phenomenon of induced coherence without induced emission, and specifically its application to imaging and metrology. It is based on a striking effect where two nonlinear crystals, by sharing a coherent pump and one or two output beams, can induce coherence between the other two output beams. This can be thought of as a type of quantum-erasure effect, where the “welcher-weg” (which-way), or in this case, “which-source,” information is erased when the shared beams are aligned. With the correct geometry, this effect can allow an object to be imaged using only photons that have never interacted with the object—in other words, the image is formed using undetected photons. Interest in this and related setups has been accelerating in recent years due to a number of desirable properties, mostly centered around the fact that the fields for detection and imaging (since separate) may have different optical properties, entailing significant advantages for various applications. The purpose of this tutorial is to introduce researchers to this area of research, to provide practical tools for setting up experiments as well as understanding the underlying theory, and also to provide a comprehensive overview of the sub-field as a whole.
We present a tutorial on the phenomenon of induced coherence without induced emission, and specifically its application to imaging and metrology. It is based on a striking effect where two nonlinear crystals, by sharing a coherent pump and one or two output beams, can induce coherence between the other two output beams. This can be thought of as a type of quantum-erasure effect, where the “welcher-weg” (which-way), or in this case, “which-source,” information is erased when the shared beams are aligned. With the correct geometry, this effect can allow an object to be imaged using only photons that have never interacted with the object—in other words, the image is formed using undetected photons. Interest in this and related setups has been accelerating in recent years due to a number of desirable properties, mostly centered around the fact that the fields for detection and imaging (since separate) may have different optical properties, entailing significant advantages for various applications. The purpose of this tutorial is to introduce researchers to this area of research, to provide practical tools for setting up experiments as well as understanding the underlying theory, and also to provide a comprehensive overview of the sub-field as a whole.
Since the second quantum revolution, the growing exploitation of quantum states led to many sophisticated and novel applications [Phil. Trans. R. Soc. Lond. A 361, 1655 (2003). Former, mainly academic research is more and more transferred into real-world quantum technology ready to serve practical tasks. Today, the quantum computer is within reach, satellite based quantum communication already started, and the field of sensing and imaging was revolutionized, too. Non-classical states of light promise a phase sensitivity beyond any classical possibility [PRL 112, 103604 (2014)] and super-resolution capability [Nature Commun. 8, 14786 (2017)]. Moreover, based on quantum correlations, which are rooted in the very heart of quantum mechanics, the imaging of samples with photons that have never interacted with the object is feasible. This science fiction like phenomenon was first investigated by Mandel [PRA 44, 4614 (1991)] and later implemented for actual imaging purposes in the Zeilinger group [Nature 512, 409 (2014)]. We are going to present the transfer of this approach into applicable quantum technology within the realm of the Fraunhofer Key Research Initiative Quantum Methods for Advanced Imaging Solutions (QUILT). The method itself is based on induced coherence without induced emission [PRA 44, 4614 (1991)]. We built a novel compact implementation of this scheme based on only one nonlinear crystal. The crystal is coherently pumped by a laser from two sides such that signal and idler photon pairs can be collinearly emitted in either of two opposite directions (to the right or to the left). On the right side the idler beam will be separated by a dichroic mirror (DM) and interacts with an object (directly placed in front of a mirror or reflective object). On the left side the signal beam will be separated by another dichroic mirror and hit the camera, which is either a sCMOS or an EMCCD. Additional lenses provide the particular imaging. Sine the two possibilities for the idler beam – going right and interact with the object or going left from the nonlinear crystal – interfere the object could be observed by idler detection. However, the same interference can be observed for the signal beams although the never interacted with the object. Hence, the object can be imaged by detecting the signal light only. The crucial point here is the lack of wich-path information of the idler beams in this type of Michelson interferometric setup. The following points should be emphasized: (i) the signal channels never interact with the object, (ii) there is no induced emission due to the idler beam that interacted with the object, and (iii) there is no coincidence detection involved in this scheme. The obvious advantage of this technique is that the wavelength of the idler photons can be tailored to match the interesting spectral range for interaction with the object. At the same time, the signal photons, which are actually detected, can stay in the VIS range where, e.g., Si-based detectors are optimized. Besides the application for life science imaging, we are comparing the quantum imaging properties utilizing momentum correlations or spatial correlations, where the ladder is a modus that was never investigated before. As an outlook we work on significantly enhance SPDC sources in scope of quantum performance and wavelength separation. Obviously, pushing the short-wavelength idler photons further into the deep UV or XUV broadens the range of applications, but must be implemented by non-SPDC photon pair sources.
Interference of two beams produced at separate biphoton sources was first observed more than two decades ago. The phenomenon, often called coherence without induced emission, has recently gained attention after its applications to imaging, spectroscopy, and measuring biphoton correlations have been discovered. The sources used in the corresponding experiments are nonlinear crystals pumped by laser light. The use of a laser pump makes the occurrence of induced (stimulated) emission unavoidable and the effect of stimulated emission can be observed in the joint detection rate of the two beams. This fact raises the question whether the stimulated emission also lays a role in inducing the coherence. Here we investigate a case in which the crystals are pumped with a single-photon Fock state. We find that coherence is induced even though the possibility of stimulated emission is now fully ruled out. Furthermore, the joint detection rate of the two beams becomes ideally zero and does no longer change with the pump power. We illustrate our results by numerical simulations and by comparisons with experimental findings. Our results rule out any classical or semi-classical explanation of the phenomenon and also imply that similar experiments can be performed with fermions, for which stimulated emission is strictly forbidden.
Interest in induced coherence [1] has had a resurgence thanks to its demonstration in imaging with undetected photons [2], enabling infrared imaging capability to be achieved without the need for infrared camera technology. More recent implementations of undetected sensing have instead made use of nonlinear interferometers [3], [4], which have allowed simpler experimental designs to achieve similar results. Here we will discuss the differences between the two modes undetected sensing. The primary difference in experimental implementation is that in induced coherence the signals from the two nonlinear processes are mixed on an external beamsplitter, while all fields are instead recombined at the second crystal in a nonlinear interferometer. We have built an experimental setup and accompanying theoretical model, capable of switching between induced coherence and nonlinear inter-ferometry to fully test the fundamental differences in the modalities and the underlying physics. The switch is achieved by altering the distinguishability of the two nonlinear processes both inside and outside of the interferometer. Distinguishability is created and subsequently destroyed through polarisation control of the down-converted signal fields (in a mode akin to a quantum eraser). This allows a simple wave-plate to switch the system between nonlinear interferometer and induced coherence. The mathematical model enables us to fully map out the polarisation space, as well as including the effects of spectral width and coherence lengths. Experimental data shows a very close match to the outcomes predicted by the model, confirming the same underlying principle effect. These tests form the first direct comparison of these interferometric modes; we also further demonstrate the capability to detect both induced coherence and nonlinear interferometry simultaneously - as shown modelled in Fig. 1-opening the pathway to novel imaging modalities as well as further tests of the underlying fundamental physics.
At the heart of recent advances in quantum imaging and spectroscopy with undetected photons is the quantum optical effect known as induced coherence without induced emission. This quantum interference effect has enabled access to challenging wavelength regimes for imaging and spectroscopic applications. However, the potential of undetected photon quantum metrology, particularly the enhanced phase sensitivity offered by Fock or N00N states, has not yet been realized, as prior work focused only on single-photon phenomena. Here, we report the observation of two-photon induced coherence without induced emission. Using a two-photon Fock state, we establish quantum coherence between pairs of two-photon spontaneous emission amplitudes, resulting in a doubling of interferometric phase modulation. Specifically, we show that a phase shift [Formula: see text] applied to undetected 1016-nanometer photons leads to a [Formula: see text] modulation in the detection of 632-nanometer photons. This demonstrates genuine two-photon induced coherence without induced emission and opens possibilities for quantum-enhanced phase measurements using multiphoton coherence without detecting the modulated photons.
Imaging with undetected photons (IUP) enables the possibility of sensing changes in the phase and the transmission of a beam of light that need never be detected. This has led to the possibility of infrared sensing with visible silicon camera technology, for example. Relying on the interference of two identical pairs of photons, IUP was initially achieved using unidirectional paths through two nonlinear crystal pair sources. More recently, folded arrangements using bidirectional paths through a single-crystal have become common for their simplicity. Here, we theoretically model and experimentally implement a novel setup involving three interference paths through a single nonlinear crystal. This establishes two independent IUP sensing modes in addition to a third linear interference mode. We achieve this using a polarization state quantum eraser approach, with excellent agreement between experiment and theory. This system provides a new route to control and optimize IUP interference in a single-crystal folded arrangement by using controllable quantum erasure to balance the interferometer, opening the door to new implementations and applications for IUP.
Interference of two beams produced at separate biphoton sources was first observed more than two decades ago. The phenomenon, often called ``induced coherence without induced emission,'' has recently gained attention after its applications to imaging, spectroscopy, and measuring biphoton correlations have been discovered. The sources used in the corresponding experiments are nonlinear crystals pumped by laser light. The use of a laser pump makes the occurrence of induced (stimulated) emission unavoidable, and the effect of stimulated emission can be observed in the joint detection rate of the two beams. This fact raises the question whether the stimulated emission also plays a role in inducing the coherence. Here we investigate a case in which the crystals are pumped with a single-photon Fock state. We find that coherence is induced even though the possibility of stimulated emission is now fully ruled out. Furthermore, the joint detection rate of the two beams becomes ideally zero. Our results rule out any classical or semiclassical explanation of the phenomenon and also suggest that it is, in principle, possible to perform similar experiments with fermions, for which stimulated emission is strictly forbidden.