Induced coherence without induced emission

Quantum Interferometric Pathway Selectivity in Difference-Frequency-Generation Spectroscopy

Even-order spectroscopies such as sum-frequency generation (SFG) and difference-frequency generation (DFG) can serve as direct probes of molecular chirality. Such signals are usually given by the sum of several interaction pathways that carry different information about matter. Here we focus on DFG, involving impulsive optical-optical-IR interactions, where the last IR pulse probes vibrational transitions in the ground or excited electronic state manifolds, depending on the interaction pathway. Spectroscopy with classical light can use phase matching to select the two pathways. In this theoretical study, we propose a novel quantum interferometric protocol that uses entangled photons to isolate individual pathways. This additional selectivity originates from engineering the state of light using a Zou-Wang-Mandel interferometer combined with coincidence detection.

Quantum Induced Coherence Light Detection and Ranging

Quantum illumination has been proposed and demonstrated to improve the signal-to-noise ratio (SNR) in light detection and ranging (LiDAR). When relying on coincidence detection alone, such a quantum LiDAR is limited by the timing jitter of the detector and suffers from jamming noise. Inspired by the Zou-Wang-Mandel experiment, we design, construct, and validate a quantum induced coherence (QuIC) LiDAR which is inherently immune to ambient and jamming noises. In traditional LiDAR the direct detection of the reflected probe photons suffers from deteriorating SNR for increasing background noise. In QuIC LiDAR we circumvent this obstacle by only detecting the entangled reference photons, whose single-photon interference fringes are used to obtain the distance of the object, while the reflected probe photons are used to erase path information of the reference photons. In consequence, the noise accompanying the reflected probe light has no effect on the detected signal. We demonstrate such noise resilience with both LED and laser light to mimic the background and jamming noise. The proposed method paves a new way of battling noise in precise quantum electromagnetic sensing and ranging.

Multiphoton non-local quantum interference controlled by an undetected photon

The interference of quanta lies at the heart of quantum physics. The multipartite generalization of single-quanta interference creates entanglement, the coherent superposition of states shared by several quanta. Entanglement allows non-local correlations between many quanta and hence is a key resource for quantum information technology. Entanglement is typically considered to be essential for creating non-local quantum interference. Here, we show that this is not the case and demonstrate multiphoton non-local quantum interference that does not require entanglement of any intrinsic properties of the photons. We harness the superposition of the physical origin of a four-photon product state, which leads to constructive and destructive interference with the photons' mere existence. With the intrinsic indistinguishability in the generation process of photons, we realize four-photon frustrated quantum interference. This allows us to observe the following noteworthy difference to quantum entanglement: We control the non-local multipartite quantum interference with a photon that we never detect, which does not require quantum entanglement. These non-local properties pave the way for the studies of foundations of quantum physics and potential applications in quantum technologies.

One-Photon Measurement of Two-Photon Entanglement

Measuring entanglement is an essential step in a wide range of applied and foundational quantum experiments. When a two-particle quantum state is not pure, standard methods to measure the entanglement require detection of both particles. We realize a conceptually new method for verifying and measuring entanglement in a class of two-part (bipartite) mixed states. Contrary to the approaches known to date, in our experiment we verify and measure entanglement in mixed quantum bipartite states by detecting only one subsystem, the other remains undetected. Only one copy of the mixed or pure state is used but that state is in a superposition of having been created in two identical sources. We show that information shared in entangled systems can be accessed through single-particle interference patterns. Our experiment enables entanglement characterization even when one of the subsystems cannot be detected, for example, when suitable detectors are not available.

Crystal superlattices for versatile and sensitive quantum spectroscopy

Nonlinear interferometers with quantum correlated photons have been demonstrated to improve optical characterization and metrology. These interferometers can be used in gas spectroscopy, which is of particular interest for monitoring greenhouse gas emissions, breath analysis and industrial applications. Here, we show that gas spectroscopy can be further enhanced via the deployment of crystal superlattices. This is a cascaded arrangement of nonlinear crystals forming interferometers, allowing the sensitivity to scale with the number of nonlinear elements. In particular, the enhanced sensitivity is observed via the maximum intensity of interference fringes that scales with low concentration of infrared absorbers, while for high concentration the sensitivity is better in interferometric visibility measurements. Thus, a superlattice acts as a versatile gas sensor since it can operate by measuring different observables, which are relevant to practical applications. We believe that our approach offers a compelling path towards further enhancements for quantum metrology and imaging using nonlinear interferometers with correlated photons.

Phase-quadrature quantum imaging with undetected 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.

Phase Sensitivity Improvement in Correlation-Enhanced Nonlinear Interferometers

Interferometers are widely used as sensors in precision measurement. Compared with a conventional Mach–Zehnder interferometer, the sensitivity of a correlation-enhanced nonlinear interferometer can break the standard quantum limit. Phase sensitivity plays a significant role in the enhanced performance. In this paper, we review improvement in phase estimation technologies in correlation-enhanced nonlinear interferometers, including SU(1,1) interferometer and SU(1,1)-SU(2) hybrid interferometer, and so on, and the applications in quantum metrology and quantum sensing networks.

Coherence and Anticoherence Induced by Thermal Fields

Interesting coherence and correlations appear between superpositions of two bosonic modes when the modes are parametrically coupled to a third intermediate mode and are also coupled to external modes which are in thermal states of unequal mean photon numbers. Under such conditions, it is found that one of linear superpositions of the modes, which is effectively decoupled from the other modes, can be perfectly coherent with the other orthogonal superposition of the modes and can simultaneously exhibit anticoherence with the intermediate mode, which can give rise to entanglement between the modes. It is shown that the coherence effects have a substantial effect on the population distribution between the modes, which may result in lowering the population of the intermediate mode. This shows that the system can be employed to cool modes to lower temperatures. Furthermore, for appropriate thermal photon numbers and coupling strengths between the modes, it is found that entanglement between the directly coupled superposition and the intermediate modes may occur in a less restricted range of the number of the thermal photons such that the modes could be strongly entangled, even at large numbers of the thermal photons.

Subdiffraction Quantum Imaging with Undetected Photons

We propose a nonlinear imaging scheme with undetected photons that overcomes the diffraction limit by transferring near-field information at one wavelength to far-field information of a correlated photon with a different wavelength generated through spontaneous photon-pair generation. At the same time, this scheme allows for retrieval of high-contrast images with zero background, making it a highly sensitive scheme for imaging of small objects at challenging spectral ranges with subdiffraction resolutions.

Mid-infrared microscopy via position correlations of undetected photons

Quantum imaging with undetected photons (QIUP) has recently emerged as a new powerful imaging tool. Exploiting the spatial entanglement of photon pairs, it allows decoupling of the sensing and detection wavelengths, facilitating imaging in otherwise challenging spectral regions by leveraging mature silicon-based detection technology. All existing implementations of QIUP have so far utilised the momentum correlations within the biphoton states produced by spontaneous parametric downconversion. Here, for the first time, we implement and examine theoretically and numerically the complementary scenario - utilising the tight position correlations formed within photon pairs at birth. This image plane arrangement facilitates high resolution imaging with comparative experimental ease, and we experimentally show resolutions below 10 μm at a sensing wavelength of 3.7 μm. Moreover, we present a quantitative numerical model predicting the imaging capabilities of QIUP for a wide range of parameters. Finally, by imaging mouse heart tissue at the mid-IR to reveal morphological features on the cellular level, we further demonstrate the viability of this technique for the life sciences. These results offer new perspectives on the capabilities of QIUP for label-free widefield mid-IR microscopy, enabling real-world biomedical as well as industrial imaging applications.

Quantum holography with undetected light

Holography exploits the interference of a light field reflected/transmitted from an object with a reference beam to obtain a reconstruction of the spatial shape of the object. Classical holography techniques have been very successful in diverse areas such as microscopy, manufacturing technology, and basic science. However, detection constraints for wavelengths outside the visible range restrict the applications for imaging and sensing in general. For overcoming these detection limitations, we implement phase-shifting holography with nonclassical states of light, where we exploit quantum interference between two-photon probability amplitudes in a nonlinear interferometer. We demonstrate that it allows retrieving the spatial shape (amplitude and phase) of the photons transmitted/reflected from the object and thus obtaining an image of the object despite those photons are never detected. Moreover, there is no need to use a well-characterized reference beam, since the two-photon scheme already makes use of one of the photons as reference for holography.

Resolution limit in quantum imaging with undetected photons using position correlations

Quantum imaging with undetected photons (QIUP) is a unique method of image acquisition where the photons illuminating the object are not detected. This method relies on quantum interference and spatial correlations between the twin photons to form an image. Here we present a detailed study of the resolution limits of position correlation enabled QIUP. We establish a quantitative relation between the spatial resolution and the twin-photon position correlation. Furthermore, we also quantitatively establish the roles that the wavelength of the undetected illumination field and the wavelength of the detected field play in the resolution. Like ghost imaging and unlike conventional imaging, the resolution limit imposed by the spatial correlation between the twin photons in QIUP cannot be further improved by conventional optical techniques.

Interference fringes in a nonlinear Michelson interferometer based on spontaneous parametric down-conversion

Quantum nonlinear interferometers (QNIs) can measure the infrared physical quantities of a sample by detecting visible photons. A QNI with Michelson geometry based on the spontaneous parametric down-conversion in a second-order nonlinear crystal is studied systematically. A simplified theoretical model of the QNI is presented. The interference visibility, coherence length, equal-inclination interference, and equal-thickness interference for the QNI are demonstrated theoretically and experimentally. As an application example of the QNI, the refractive index and the angle between two surfaces of a BBO crystal are measured using equal-inclination interference and equal-thickness interference.

Quantitative complementarity of wave-particle duality

To test the principle of complementarity and wave-particle duality quantitatively, we need a quantum composite system that can be controlled by experimental parameters. Here, we demonstrate that a double-path interferometer consisting of two parametric downconversion crystals seeded by coherent idler fields, where the generated coherent signal photons are used for quantum interference and the conjugate idler fields are used for which-path detectors with controllable fidelity, is useful for elucidating the quantitative complementarity. We show that the quanton source purity μ _s is tightly bounded by the entanglement E between the quantons and the remaining degrees of freedom by the relation [Formula: see text], which is experimentally confirmed. We further prove that the experimental scheme using two stimulated parametric downconversion processes is an ideal tool for investigating and understanding wave-particle duality and Bohr's complementarity quantitatively.

Path identity as a source of high-dimensional entanglement

Quantum entanglement amounts to an extremely strong link between two distant particles, a link so strong that it eludes any classical description and so unsettling that Albert Einstein described it as “spooky action at a distance.” Today, entanglement is not only a subject of fundamental research, but also a workhorse of emerging quantum technologies. In our current work we experimentally demonstrate a completely different method of entanglement generation. Unlike many traditional methods, where entanglement arises due to conservation of a physical quantity, such as momentum, in our method it is rather a consequence of indistinguishability of several particle-generating processes. This approach, where each process effectively adds one dimension to the entangled state, allows for a high degree of customizability.

We present an experimental demonstration of a general entanglement-generation framework, where the form of the entangled state is independent of the physical process used to produce the particles. It is the indistinguishability of multiple generation processes and the geometry of the setup that give rise to the entanglement. Such a framework, termed entanglement by path identity, exhibits a high degree of customizability. We employ one class of such geometries to build a modular source of photon pairs that are high-dimensionally entangled in their orbital angular momentum. We demonstrate the creation of three-dimensionally entangled states and show how to incrementally increase the dimensionality of entanglement. The generated states retain their quality even in higher dimensions. In addition, the design of our source allows for its generalization to various degrees of freedom and even for the implementation in integrated compact devices. The concept of entanglement by path identity itself is a general scheme and allows for construction of sources producing also customized states of multiple photons. We therefore expect that future quantum technologies and fundamental tests of nature in higher dimensions will benefit from this approach.

Microscopy with undetected photons in the mid-infrared

Owing to its capacity for unique (bio)-chemical specificity, microscopy with mid-infrared (IR) illumination holds tremendous promise for a wide range of biomedical and industrial applications. The primary limitation, however, remains detection, with current mid-IR detection technology often marrying inferior technical capabilities with prohibitive costs. Here, we experimentally show how nonlinear interferometry with entangled light can provide a powerful tool for mid-IR microscopy while only requiring near-IR detection with a silicon-based camera. In this proof-of-principle implementation, we demonstrate widefield imaging over a broad wavelength range covering 3.4 to 4.3 μm and demonstrate a spatial resolution of 35 μm for images containing 650 resolved elements. Moreover, we demonstrate that our technique is suitable for acquiring microscopic images of biological tissue samples in the mid-IR. These results form a fresh perspective for potential relevance of quantum imaging techniques in the life sciences.

Hyperspectral infrared microscopy with visible light

Hyperspectral microscopy is an imaging technique that provides spectroscopic information with high spatial resolution. When applied in the relevant wavelength region, such as in the infrared (IR), it can reveal a rich spectral fingerprint across different regions of a sample. Challenges associated with low efficiency and high cost of IR light sources and detector arrays have limited its broad adoption. Here, we introduce a new approach to IR hyperspectral microscopy, where the IR spectral map is obtained with off-the-shelf components built for visible light. The method is based on the nonlinear interference of correlated photons generated via parametric down-conversion. In this proof-of-concept we demonstrate the chemical mapping of a patterned sample, where different areas have distinctive IR spectroscopic fingerprints. The method provides a wide field of view, fast readout, and negligible heat delivered to the sample, which opens prospects for its further development for applications in material and biological studies.

Nonlinear interference in crystal superlattices

Nonlinear interferometers with correlated photons hold promise to advance optical characterization and metrology techniques by improving their performance and affordability. These interferometers offer subshot noise phase sensitivity and enable measurements in detection-challenging regions using inexpensive and efficient components. The sensitivity of nonlinear interferometers, defined by the ability to measure small shifts of interference fringes, can be significantly enhanced by using multiple nonlinear elements, or crystal superlattices. However, to date, experiments with more than two nonlinear elements have not been realized, thus hindering the potential of nonlinear interferometers. Here, we build a nonlinear interferometer with up to five nonlinear elements, referred to as superlattices, in a highly stable and versatile configuration. We study the modification of the interference pattern for different configurations of the superlattices and perform a proof-of-concept gas sensing experiment with enhanced sensitivity. Our approach offers a viable path towards broader adoption of nonlinear interferometers with correlated photons for imaging, interferometry, and spectroscopy.

Terahertz quantum sensing

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 used. 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 nondestructive layer thickness measurements are of high industrial relevance, our experiments might be seen as a first step toward industrial quantum sensing applications.

Pancharatnam-Berry geometric phase memory based on spontaneous parametric down-conversion

Phase memory is an effect in which the interaction between a coherent pump beam and a nonlinear crystal generates photon pairs via the spontaneous parametric down-conversion process, then the down-converted photons (signal and idler) can carry the phase information of the pump beam. There has been much research on the memory of the dynamic phase so far; however, there is no report on the memory of non-dynamic phase, to the best of our knowledge. Here we acquire a Pancharatnam-Berry (PB) geometric phase in a physical system when light travels along a trajectory in polarization-state space. Induced coherence occurs in a cascaded scheme composed of two nonlinear crystals, when the idler photons in both crystals are aligned to be indistinguishable. A NOON ($N\; = \;{2}$N=2) state is established when blocking the two idler photons. We explore the PB geometric phase memory of the NOON state and induced coherence. We find that the first-order interference of the two-photon state or signal photons can be controlled by introducing the PB geometric phase to the pump light. This may facilitate precise control of the phase of the down-converted photons.

Interferometric quantum spectroscopy with undetected photons via distinguishability modulation

Quantum spectroscopy with undetected photons (QSUP) utilizing the quantum entanglement of parametrically down-converted photons has emerged as a new spectroscopic platform. Here, we demonstrate a high-resolution and remote-measurement QSUP, where light-matter interactions and photon detections are performed in spectrally and spatially different regions. A dual-stimulated parametric down-conversion scheme with an optical frequency-comb pump and ultra-narrow coherent seed beam in an idler mode is used to generate path-entangled pairs of the undetected idler and measured frequency-comb signal photons. To demonstrate the frequency resolution of this scheme, a Fabry-Pérot cavity with a narrow bandwidth is used as a sample that modulates the distinguishability of one-photon-added coherent idler beams, which directly affects the interference fringe visibility of the entangled signal photons. We thus anticipate that the remote QSUP whose frequency resolution is determined by the linewidth of the coherent seed laser will enable the development of quantum spectroscopy featuring high resolution.

Quantum experiments and graphs II: Quantum interference, computation, and state generation

We present an approach to describe state-of-the-art photonic quantum experiments using graph theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that introducing complex weights in graphs naturally leads to quantum interference. This viewpoint immediately leads to many interesting results, some of which we present here. First, we identify an experimental unexplored multiphoton interference phenomenon. Second, we find that computing the results of such experiments is #P-hard, which means it is a classically intractable problem dealing with the computation of a matrix function Permanent and its generalization Hafnian. Third, we explain how a recent no-go result applies generally to linear optical quantum experiments, thus revealing important insights into quantum state generation with current photonic technology. Fourth, we show how to describe quantum protocols such as entanglement swapping in a graphical way. The uncovered bridge between quantum experiments and graph theory offers another perspective on a widely used technology and immediately raises many follow-up questions.

Periodic revival of frustrated two-photon creation via interference

It has been known that suitably placed external mirrors can enhance and suppress emission of entangled photon pairs in spontaneous parametric down-conversion (SPDC), known as frustrated two-photon creation via interference. In this work, we report periodic revival of frustrated two-photon creation via interference with SPDC pumped by a continuous-wave (cw) multi-mode laser. As the mirrors are translated relative to the position of the SPDC source, the effect of frustrated two-photon creation via interference gradually dies off. However, as the mirrors are translated even further, the effect of frustrated two-photon creation via interference re-appears periodically. Our theoretical and numerical analyses show that this revival phenomenon is due to the nature of cw multi-mode pump laser. This work clearly demonstrates how the properties of the pump laser, in addition to suitably placed external mirrors, can be used to modify the process of spontaneous two-photon emission.

Polarization effects in nonlinear interference of down-converted photons

We study polarization effects in the nonlinear interference of photons generated via frequency nondegenerate spontaneous parametric-down conversion. Signal and idler photons, which are generated in the visible and infrared (IR) range, respectively, are split into different arms of a nonlinear Michelson interferometer, and the interference pattern for signal photons is detected. Due to the effect of induced coherence, the interference pattern for the signal photons depends on the polarization rotation of idler photons, which are introduced by a birefringent sample. Based on this concept, we realize two new methods of measuring sample retardation in the IR range by using well-developed and inexpensive components for visible light. The methods' accuracy reaches specifications that are reported for industrial-grade optical elements. The developed IR polarimetry technique is relevant to material research, optical inspection, and quality control.

Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings

We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and graph theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the #P-complete complexity class, thus it cannot be done efficiently. To strengthen the link further, theorems from graph theory-such as Hall's marriage problem-are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows one to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and how to potentially simulate properties of graphs and networks with quantum experiments (such as critical exponents and phase transitions).

Entanglement by Path Identity

Quantum entanglement is one of the most prominent features of quantum mechanics and forms the basis of quantum information technologies. Here we present a novel method for the creation of quantum entanglement in multipartite and high-dimensional systems. The two ingredients are (i) superposition of photon pairs with different origins and (ii) aligning photons such that their paths are identical. We explain the experimentally feasible creation of various classes of multiphoton entanglement encoded in polarization as well as in high-dimensional Hilbert spaces-starting only from nonentangled photon pairs. For two photons, arbitrary high-dimensional entanglement can be created. The idea of generating entanglement by path identity could also apply to quantum entities other than photons. We discovered the technique by analyzing the output of a computer algorithm. This shows that computer designed quantum experiments can be inspirations for new techniques.

Nonlinear infrared spectroscopy free from spectral selection

Infrared (IR) spectroscopy is an indispensable tool for many practical applications including material analysis and sensing. Existing IR spectroscopy techniques face challenges related to the inferior performance and the high cost of IR-grade components. Here, we develop a new method, which allows studying properties of materials in the IR range using only visible light optics and detectors. It is based on the nonlinear interference of entangled photons, generated via Spontaneous Parametric Down Conversion (SPDC). In our interferometer, the phase of the signal photon in the visible range depends on the phase of an entangled IR photon. When the IR photon is traveling through the media, its properties can be found from observations of the visible photon. We directly acquire the SPDC signal with a visible range CCD camera and use a numerical algorithm to infer the absorption coefficient and the refraction index of the sample in the IR range. Our method does not require the use of a spectrometer and a slit, thus it allows achieving higher signal-to-noise ratio than the earlier developed method.

Quantifying the momentum correlation between two light beams by detecting one

We report a measurement of the transverse momentum correlation between two photons by detecting only one of them. Our method uses two identical sources in an arrangement in which the phenomenon of induced coherence without induced emission is observed. In this way, we produce an interference pattern in the superposition of one beam from each source. We quantify the transverse momentum correlation by analyzing the visibility of this pattern. Our approach might be useful for the characterization of correlated photon pair sources and may lead to an experimental measure of continuous variable entanglement, which relies on the detection of only one of two entangled particles.

Induced coherence, vacuum fields, and complementarity in biphoton generation

It is well established that spontaneous parametric down-conversion with induced coherence across two coupled interferometers results in high-visibility single-photon interference. We describe experiments in which additional photon channels are introduced such that "which-path" information is made possible and the fringe visibility in single-photon interference is reduced in accordance with basic notions of complementarity. However, these additional pathways result in nearly perfect visibility when photons are counted in coincidence. A simplified theoretical model accounts for these observations and attributes them directly to the vacuum fields at the different crystals.

Measurements of the probability distribution of the phase difference between two quantum fields

We have measured the probability distribution of the phase difference Phi(2) - Phi(1) between two signal fields produced by parametric downconversion from two cascaded nonlinear crystals for several different values of the degree of mutual coherence. The experimental results are compared with theory, based on our operational approach to phase operators for quantum fields, and good agreement is obtained. These results are of interest because they constitute what we believe is the first experimental test of our phase theory for nonclassical states of light.