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.
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.
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.
Coherence can be induced or stimulated in parametric down-conversion using two or three crystals when, for example, the idler modes of the crystals are aligned. Previous experiments with induced coherence [Phys. Rev. Lett. 114, 053601 (2015)] focused on which-path information and the role of vacuum fields in realizing complementarity via reduced visibility in single-photon interference. Here we describe experiments comparing induced and stimulated coherence. Different single-photon interference experiments were performed by blocking one of the pump beams in a three-crystal setup. Each counted photon is emitted from one of two crystals and which-way information may or not be available, depending on the setup. Distinctly different results are obtained in the induced and stimulated cases, especially when a variable transmission filter is inserted between the crystals. A simplified theoretical model accounts for all the experimental results and is also used to address the question of whether the phases of the signal and idler fields in parametric down-conversion are correlated.
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.
There is renewed interest on the concept of induced coherence between beams generated by separate biphoton sources, that has led to the demonstration of new schemes for imaging, spectroscopy, microscopy and optical coherence tomography (OCT). These schemes make use of continuous wave pumping in the low parametric gain regime, which reflects the frequency entanglement between the down-converted photons. However, is entanglement a requisite to observe induced coherence? Contrary to some claims, we will show that it is not. This might be an advantage for OCT applications. High axial resolution requires a large bandwidth and for continuous wave pumping this requires the use of short nonlinear crystals. This is detrimental since short crystals generate small photon fluxes. We show that the use of ultrashort pump pulses increases axial resolution even with long crystals.
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.
There is renewed interest in using the coherence between beams generated in separate down-converter sources for new applications in imaging, spectroscopy, microscopy, and optical coherence tomography (OCT). These schemes make use of continuous-wave (cw) pumping in the low parametric gain regime, which produces frequency correlations and frequency entanglement between signal-idler pairs generated in each single source. But can induced coherence still be observed if there is no frequency correlation, so the biphoton wave function is factorable? We will show that this is the case and might be an advantage for OCT applications. High axial resolution requires a large bandwidth. For cw pumping, this requires the use of short nonlinear crystals. This is detrimental since short crystals generate small photon fluxes. We show that the use of ultrashort pump pulses allows one to improve the axial resolution even for a long crystal that produces higher photon fluxes.