An entanglement-enhanced microscope

Quantum-Enhanced Weak Absorption Estimation with Correlated Photons

Conventional absorption spectroscopy relies on coherent laser sources, and in turn suffers from the inherent limitation of shot noise, especially in estimating weak absorption. Here, we propose a measurement strategy with correlated photons to determine the weak absorption by distinguishing the output with and without photons, dubbed as the on-off measurement. We demonstrate that absorption spectroscopy that incorporates quantum correlations is capable of estimating weak absorption down to a single-photon level, even in noisy environments, achieving a precision comparable to that obtained through 1000 photons in conventional absorption spectroscopy. Our strategy provides a new method to probe fragile systems with weak absorption, avoiding the occurrence of light-induced damage.

Effects of multi-photon states in the calibration of single-photon detectors based on a portable bi-photon source

Single-photon detectors (SPDs) are ubiquitous in many protocols for quantum imaging, sensing, and communications. Many of these protocols critically depend on the precise knowledge of their detection efficiency. A method for the calibration of SPDs based on sources of quantum-correlated photon pairs uses single-photon detection to generate heralded single photons, which can be used as a standard of radiation at the single-photon level. These heralded photons then allow for precise calibration of SPDs in absolute terms. In this work, we investigate the absolute calibration of avalanche photodiodes based on a portable, commercial bi-photon source, and investigate the effects of multi-photon events from the spontaneous parametric down conversion (SPDC) process in these sources. We show that the multi-photon character of the bi-photon source, together with system losses, has a significant impact on the achievable accuracy for the calibration of SPDs. However, modeling the expected photon counting statistics from the squeezed vacuum in the SPDC process allows for accurate estimation of the efficiency of SPDs, assuming that the system losses are known. This study provides essential information for the design and optimization of portable bi-photon sources for their application in on-site calibration of SPDs with high accuracy, without requiring any other reference standard.

Fiber-integrated quantum microscopy system for cells

Quantum entanglement serves as an essential resource across various fields, including quantum communication, quantum computing, and quantum precision measurement. Quantum microscope, as one of the significant applications in quantum precision measurement, could bring revolutionary advancements in both signal-to-noise ratio (SNR) and spatial resolution of imaging. Here, we present a quantum microscopy system that relies on a fully fiber-integrated high-performance energy-time entangled light source operating within the near-infrared II (NIR-II) window. Complemented by tailored real-time data acquisition and processing software, we successfully demonstrate the quantum imaging of a standard target, achieving a SNR of 131.51 ± 6.74 and a spatial resolution of 4.75 ± 0.27 µm. Furthermore, we showcase quantum imaging of cancer cells, unveiling the potential of quantum entanglement in biomedical applications. Our fiber-integrated quantum microscope, characterized by high imaging SNR, instantaneous image capture, and analysis capabilities, marks an important step toward the practical application in life sciences.

Adaptive optical imaging with entangled photons

Adaptive optics (AO) has revolutionized imaging in fields from astronomy to microscopy by correcting optical aberrations. In label-free microscopes, however, conventional AO faces limitations because of the absence of a guide star and the need to select an optimization metric specific to the sample and imaging process. Here, we propose an AO approach leveraging correlations between entangled photons to directly correct the point spread function. This guide star-free method is independent of the specimen and imaging modality. We demonstrate the imaging of biological samples in the presence of aberrations using a bright-field imaging setup operating with a source of spatially entangled photon pairs. Our approach performs better than conventional AO in correcting specific aberrations, particularly those involving substantial defocus. Our work improves AO for label-free microscopy and could play a major role in the development of quantum microscopes.

Metasurface-Assisted Quantum Nonlocal Weak-Measurement Microscopy

In standard quantum weak measurements, preselection and postselection of quantum states are implemented in the same photon. Here we go beyond this restrictive setting and demonstrate that the preselection and postselection can be performed in two different photons, if the two photons are polarization entangled. The Pancharatnam-Berry phase metasurface is incorporated in the weak measurement system to perform weak coupling between probe wave function and spin observable. By introducing nonlocal weak measurement into the microscopy imaging system, it allows us to remotely switch different microscopy imaging modes of pure-phase objects, including bright-field, differential, and phase reconstruction. Furthermore, we demonstrate that the nonlocal weak-measurement scheme can prevent almost all environmental noise photons from detection and thus achieves a higher image contrast than the standard scheme at a low photon level. Our results provide the possibility to develop a quantum nonlocal weak-measurement microscope for label-free imaging of transparent biological samples.

Realization of photon correlations beyond the linear optics limit

Linear optical transformations of multiple single-photon inputs are fundamental for the development of photonic quantum technologies. Various nonclassical correlations can already be observed directly in states generated using only single-photon inputs and linear optics transformations. However, some quantum correlations require additional operations, and states that exhibit such correlations are classified as non-Fock states. Here, we demonstrate the generation of a two-photon three-mode non-Fock state that exhibits conditional quantum coherences that can only be achieved by non-Fock states. We determine the fidelity of the non-Fock state based on experimentally observed conditional visibilities that characterize the state and compare the result to the fidelity bounds for different classes of Fock and non-Fock states. Our experimental verification of the non-Fock character of the state provides insights into the technological requirements needed to achieve nonclassical correlations in multiphoton quantum optics.

Modeling the space-time correlation of pulsed twin beams

Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications, due their multimodal nature in space and time. However, a satisfactory theoretical description is still lacking. In this work we propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory. The model is used to study the quantum correlation and the coherence in the angle-frequency domain of the parametric emission, and demonstrates a [Formula: see text] growth of their size as the gain g increases, with a corresponding contraction of the space-time distribution. These predictions are systematically compared with the results of stochastic numerical simulations, performed in the Wigner representation, of the full model equations: an excellent agreement is shown even for parameters well outside the expected limit of validity of the model.

Probing exciton dynamics with spectral selectivity through the use of quantum entangled photons

Quantum light is increasingly recognized as a promising resource for developing optical measurement techniques. Particular attention has been paid to enhancing the precision of the measurements beyond classical techniques by using nonclassical correlations between quantum entangled photons. Recent advances in the quantum optics technology have made it possible to manipulate spectral and temporal properties of entangled photons, and photon correlations can facilitate the extraction of matter information with relatively simple optical systems compared to conventional schemes. In these respects, the applications of entangled photons to time-resolved spectroscopy can open new avenues for unambiguously extracting information on dynamical processes in complex molecular and materials systems. Here, we propose time-resolved spectroscopy in which specific signal contributions are selectively enhanced by harnessing nonclassical correlations of entangled photons. The entanglement time characterizes the mutual delay between an entangled twin and determines the spectral distribution of photon correlations. The entanglement time plays a dual role as the knob for controlling the accessible time region of dynamical processes and the degrees of spectral selectivity. In this sense, the role of the entanglement time is substantially equivalent to the temporal width of the classical laser pulse. The results demonstrate that the application of quantum entangled photons to time-resolved spectroscopy leads to monitoring dynamical processes in complex molecular and materials systems by selectively extracting desired signal contributions from congested spectra. We anticipate that more elaborately engineered photon states would broaden the availability of quantum light spectroscopy.

Advantages of one- and two-photon light in inverse scattering

We study an inverse scattering problem in which the far-field spectral cross correlation functions of scattered fields are used to determine the unknown dielectric susceptibility of the scattering object. One-photon states for the incident field can resolve (at 100% visibility) twice as many Fourier components of the susceptibility compared with the (naïve) Rayleigh estimate, provided that the measurement is performed in the back-scattering regime. Coherent states are not capable of reaching this optimal resolution (or do so with negligible visibility). Using two-photon states improves upon the one-photon resolution, but the improvement (at 100% visibility) is smaller than twice, and it demands prior information on the object. This improvement can also be realized via two independent laser fields. The dependence on the prior information can be decreased (but not eliminated completely) upon using entangled states of two photons.

Speed limit of quantum metrology

Quantum metrology employs nonclassical systems to improve the sensitivity of measurements. The ultimate limit of this sensitivity is dictated by the quantum Cramér-Rao bound. On the other hand, the quantum speed limit bounds the speed of dynamics of any quantum process. We show that the speed limit of quantum dynamics sets a fundamental bound on the minimum attainable phase estimation error through the quantum Cramér-Rao bound, relating the precision directly to the underlying dynamics of the system. In particular, various metrologically important states are considered, and their dynamical speeds are analyzed. We find that the bound could, in fact, be related to the nonclassicality of quantum states through the Mandel Q parameter.

Quantum enhanced non-interferometric quantitative phase imaging

Quantum entanglement and squeezing have significantly improved phase estimation and imaging in interferometric settings beyond the classical limits. However, for a wide class of non-interferometric phase imaging/retrieval methods vastly used in the classical domain, e.g., ptychography and diffractive imaging, a demonstration of quantum advantage is still missing. Here, we fill this gap by exploiting entanglement to enhance imaging of a pure phase object in a non-interferometric setting, only measuring the phase effect on the free-propagating field. This method, based on the so-called "transport of intensity equation", is quantitative since it provides the absolute value of the phase without prior knowledge of the object and operates in wide-field mode, so it does not need time-consuming raster scanning. Moreover, it does not require spatial and temporal coherence of the incident light. Besides a general improvement of the image quality at a fixed number of photons irradiated through the object, resulting in better discrimination of small details, we demonstrate a clear reduction of the uncertainty in the quantitative phase estimation. Although we provide an experimental demonstration of a specific scheme in the visible spectrum, this research also paves the way for applications at different wavelengths, e.g., X-ray imaging, where reducing the photon dose is of utmost importance.

Unconditional and Robust Quantum Metrological Advantage beyond N00N States

Quantum metrology employs quantum resources to enhance the measurement sensitivity beyond that can be achieved classically. While multiphoton entangled N00N states can in principle beat the shot-noise limit and reach the Heisenberg limit, high N00N states are difficult to prepare and fragile to photon loss which hinders them from reaching unconditional quantum metrological advantages. Here, we combine the idea of unconventional nonlinear interferometers and stimulated emission of squeezed light, previously developed for the photonic quantum computer Jiuzhang, to propose and realize a new scheme that achieves a scalable, unconditional, and robust quantum metrological advantage. We observe a 5.8(1)-fold enhancement above the shot-noise limit in the Fisher information extracted per photon, without discounting for photon loss and imperfections, which outperforms ideal 5-N00N states. The Heisenberg-limited scaling, the robustness to external photon loss, and the ease-of-use of our method make it applicable in practical quantum metrology at a low photon flux regime.

Fast quantum-enhanced imaging with visible-wavelength entangled photons

Quantum resources can provide supersensitive performance in optical imaging. Detecting entangled photon pairs from spontaneous parametric down conversion (SPDC) with single-photon avalanche diode (SPAD) image sensor arrays (ISAs) enables practical wide-field quantum-enhanced imaging. However, matching the SPDC wavelength to the peak detection efficiency range of complementary metal-oxide-semiconductor (CMOS) compatible mass-producible SPAD-ISAs has remained technologically elusive, resulting in low imaging speeds to date. Here, we show that a recently developed visible-wavelength entangled photon source enables high-speed quantum imaging. By operating at high detection efficiency of a SPAD-ISA, we increase acquisition speed by more than an order of magnitude compared to previous similar quantum imaging demonstrations. Besides being fast, the quantum-enhanced phase imager operating at short wavelengths retrieves nanometer scale height differences, tested by imaging evaporated silica and protein microarray spots on glass samples, with sensitivity improved by a factor of 1.351 ± 0.004 over equivalent ideal classical imaging. This work represents an important stepping stone towards scalable real-world quantum imaging advantage, and may find use in biomedical and industrial applications as well as fundamental research.

Jones-matrix imaging based on two-photon interference

Two-photon interference is an important effect that is tightly related to the quantum nature of light. Recently, it has been shown that the photon bunching from the Hong-Ou-Mandel (HOM) effect can be used for quantum imaging in which sample properties (reflection/transmission amplitude, phase delay, or polarization) can be characterized at the pixel-by-pixel level. In this work, we perform Jones matrix imaging for an unknown object based on two-photon interference. By using a reference metasurface with panels of known polarization responses in pairwise coincidence measurements, the object's polarization responses at each pixel can be retrieved from the dependence of the coincidence visibility as a function of the reference polarization. The post-selection of coincidence images with specific reference polarization in our approach eliminates the need in switching the incident polarization and thus parallelized optical measurements for Jones matrix characterization. The parallelization in preparing input states, prevalent in any quantum algorithms, is an advantage of adopting two-photon interference in Jones matrix imaging. We believe our work points to the usage of metasurfaces in biological and medical imaging in the quantum optical regime.

Probing ultra-fast dephasing via entangled photon pairs

We demonstrate how the Hong-Ou-Mandel (HOM) interference with polarization-entangled photons can be used to probe ultrafast dephasing. We can infer the optical properties like the real and imaginary parts of the complex susceptibility of the medium from changes in the position and the shape of the HOM dip. From the shift of the HOM dip, we are able to measure 22 fs dephasing time using a continuous-wave (CW) laser even with optical loss > 97 %, while the HOM dip visibility is maintained at 92.3 % (which can be as high as 96.7 %). The experimental observations, which are explained in terms of a rigorous theoretical model, demonstrate the utility of HOM interference in probing ultrafast dephasing.

Quantum-enhanced stimulated Raman scattering microscopy in a high-power regime

Quantum-enhanced stimulated Raman scattering (QESRS) microscopy is expected to realize molecular vibrational imaging with sub-shot-noise sensitivity, so that weak signals buried in the laser shot noise can be uncovered. Nevertheless, the sensitivity of previous QESRS did not exceed that of state-of-the-art stimulated Raman scattering (SOA-SRS) microscopes mainly because of the low optical power (3 mW) of amplitude squeezed light [Nature594, 201 (2021)10.1038/s41586-021-03528-w]. Here, we present QESRS based on quantum-enhanced balanced detection (QE-BD). This method allows us to operate QESRS in a high-power regime (>30 mW) that is comparable to SOA-SRS microscopes, at the expense of 3 dB sensitivity drawback due to balanced detection. We demonstrate QESRS imaging with 2.89 dB noise reduction compared with classical balanced detection scheme. The present demonstration confirms that QESRS with QE-BD can work in the high-power regime, and paves the way for breaking the sensitivity of SOA-SRS microscopes.

High-depth-resolution imaging of dispersive samples using quantum optical coherence tomography

Quantum optical coherence tomography (QOCT) is a promising approach to overcome the degradation of the resolution in optical coherence tomography (OCT) due to dispersion. Here, we report on an experimental demonstration of QOCT imaging in the high-resolution regime. We achieved a depth resolution of 2.5 μm, which is the highest value for QOCT imaging, to the best of our knowledge. We show that the QOCT image of a dispersive material remains clear whereas the OCT image is drastically degraded.

Multiclass Classification of Metrologically Resourceful Tripartite Quantum States with Deep Neural Networks

Quantum entanglement is a unique phenomenon of quantum mechanics, which has no classical counterpart and gives quantum systems their advantage in computing, communication, sensing, and metrology. In quantum sensing and metrology, utilizing an entangled probe state enhances the achievable precision more than its classical counterpart. Noise in the probe state preparation step can cause the system to output unentangled states, which might not be resourceful. Hence, an effective method for the detection and classification of tripartite entanglement is required at that step. However, current mathematical methods cannot robustly classify multiclass entanglement in tripartite quantum systems, especially in the case of mixed states. In this paper, we explore the utility of artificial neural networks for classifying the entanglement of tripartite quantum states into fully separable, biseparable, and fully entangled states. We employed Bell's inequality for the dataset of tripartite quantum states and train the deep neural network for multiclass classification. This entanglement classification method is computationally efficient due to using a small number of measurements. At the same time, it also maintains generalization by covering a large Hilbert space of tripartite quantum states.

Pixel super-resolution with spatially entangled photons

Pixelation occurs in many imaging systems and limits the spatial resolution of the acquired images. This effect is notably present in quantum imaging experiments with correlated photons in which the number of pixels used to detect coincidences is often limited by the sensor technology or the acquisition speed. Here, we introduce a pixel super-resolution technique based on measuring the full spatially-resolved joint probability distribution (JPD) of spatially-entangled photons. Without shifting optical elements or using prior information, our technique increases the pixel resolution of the imaging system by a factor two and enables retrieval of spatial information lost due to undersampling. We demonstrate its use in various quantum imaging protocols using photon pairs, including quantum illumination, entanglement-enabled quantum holography, and in a full-field version of N00N-state quantum holography. The JPD pixel super-resolution technique can benefit any full-field imaging system limited by the sensor spatial resolution, including all already established and future photon-correlation-based quantum imaging schemes, bringing these techniques closer to real-world applications.

Pixelation is common in quantum imaging systems and limit the image spatial resolution. Here, the authors introduce a pixel super-resolution approach based on measuring the full spatially-resolved joint probability distribution of spatially-entangled photons, and improve pixel resolution by a factor two.

Intrinsic Optical Spatial Differentiation Enabled Quantum Dark-Field Microscopy

By solving the Maxwell's equations in Fourier space, we find that the cross-polarized component of the dipole scattering field can be written as the second-order spatial differentiation of the copolarized component. This differential operation can be regarded as intrinsic which naturally arises as consequence of the transversality of electromagnetic fields. By introducing the intrinsic spatial differentiation into heralded single-photon microscopy imaging technique, it makes the structure of pure-phase object clearly visible at low photon level, avoiding any biophysical damages to living cells. Based on the polarization entanglement, the switch between dark-field imaging and bright-field imaging is remotely controlled in the heralding arm. This research enriches both fields of optical analog computing and quantum microscopy, opening a promising route toward a nondestructive imaging of living biological systems.

Entangled Photon Spectroscopy

The enhanced interest in quantum-related phenomena has provided new opportunities for chemists to push the limits of detection and analysis of chemical processes. As some have called this the second quantum revolution, a time has come to apply the rules learned from previous research in quantum phenomena toward new methods and technologies important to chemists. While there has been great interest recently in quantum information science (QIS), the quest to understand how nonclassical states of light interact with matter has been ongoing for more than two decades. Our entry into this field started around this time with the use of materials to produce nonclassical states of light. Here, the process of multiphoton absorption led to photon-number squeezed states of light, where the photon statistics are sub-Poissonian. In addition to the great interest in generating squeezed states of light, there was also interest in the formation of entangled states of light. While much of the effort is still in foundational physics, there are numerous new avenues as to how quantum entanglement can be applied to spectroscopy, imaging, and sensing. These opportunities could have a large impact on the chemical community for a broad spectrum of applications.In this Account, we discuss the use of entangled (or quantum) light for spectroscopy as well as applications in microscopy and interferometry. The potential benefits of the use of quantum light are discussed in detail. From the first experiments in porphyrin dendrimer systems by Dr. Dong-Ik Lee in our group to the measurements of the entangled two photon absorption cross sections of biological systems such as flavoproteins, the usefulness of entangled light for spectroscopy has been illustrated. These early measurements led the way to more advanced measurements of the unique characteristics of both entangled light and the entangled photon absorption cross-section, which provides new control knobs for manipulating excited states in molecules.The first reports of fluorescence-induced entangled processes were in organic chromophores where the entangled photon cross-section was measured. These results would later have widespread impact in applications such as entangled two-photon microscopy. From our design, construction and implementation of a quantum entangled photon excited microscope, important imaging capabilities were achieved at an unprecedented low excitation intensity of 10⁷ photons/s, which is 6 orders of magnitude lower than the excitation level for the classical two-photon image. New reports have also illustrated an advantage of nonclassical light in Raman imaging as well.From a standpoint of more precise measurements, the use of entangled photons in quantum interferometry may offer new opportunities for chemistry research. Experiments that combine molecular spectroscopy and quantum interferometry, by utilizing the correlations of entangled photons in a Hong-Ou-Mandel (HOM) interferometer, have been carried out. The initial experiment showed that the HOM signal is sensitive to the presence of a resonant organic sample placed in one arm of the interferometer. In addition, parameters such as the dephasing time have been obtained with the opportunity for even more advanced phenomenology in the future.

Quantum Light-Enhanced Two-Photon Imaging of Breast Cancer Cells

Correct biological interpretation from cell imaging can be achieved only if the observed phenomena proceed with negligible perturbation from the imaging system. Herein, we demonstrate microscopic images of breast cancer cells created by the fluorescence selectively excited in the process of entangled two-photon absorption in a scanning microscope at an excitation intensity orders of magnitude lower than that used for classical two-photon microscopy. Quantum enhanced entangled two-photon microscopy has shown cell imaging capabilities at an unprecedented low excitation intensity of ∼3.6 × 10⁷ photons/s, which is a million times lower than the excitation level for the classical two-photon fluorescence image obtained in the same microscope. The extremely low light probe intensity demonstrated in entangled two-photon microscopy is of critical importance to minimize photobleaching during repetitive imaging and damage to cells in live-cell applications. This technology opens new avenues in cell investigations with light microscopy, such as enhanced selectivity and time-frequency resolution.

Ultra-broadband quadrature squeezing with thin-film lithium niobate nanophotonics

Squeezed light is a key quantum resource that enables quantum advantages for sensing, networking, and computing applications. The scalable generation and manipulation of squeezed light with integrated platforms are highly desired for the development of quantum technology with continuous variables. In this Letter, we demonstrate squeezed light generation with thin-film lithium niobate integrated photonics. Parametric down-conversion is realized with quasi-phase matching using ferroelectric domain engineering. With sub-wavelength mode confinement, efficient nonlinear processes can be observed with single-pass configuration. We measure 0.56 ± 0.09 dB quadrature squeezing (∼2.6 dB inferred on-chip). The single-pass configuration further enables the generation of squeezed light with large spectral bandwidth up to 7 THz. This work represents a significant step towards the on-chip implementation of continuous-variable quantum information processing.

Computing metasurfaces for all-optical image processing: a brief review

Computing metasurfaces are two-dimensional artificial nanostructures capable of performing mathematical operations on the input electromagnetic field, including its amplitude, phase, polarization, and frequency distributions. Rapid progress in the development of computing metasurfaces provide exceptional abilities for all-optical image processing, including the edge-enhanced imaging, which opens a broad range of novel and superior applications for real-time pattern recognition. In this paper, we review recent progress in the emerging field of computing metasurfaces for all-optical image processing, focusing on innovative and promising applications in optical analog operations, image processing, microscopy imaging, and quantum imaging.

Quantum imaging of a polarisation sensitive phase pattern with hyper-entangled photons

A transparent polarisation sensitive phase pattern makes a polarisation dependent transformation of quantum state of photons without absorbing them. Such an invisible pattern can be imaged with quantum entangled photons by making joint quantum measurements on photons. This paper shows a long path experiment to quantum image a transparent polarisation sensitive phase pattern with hyper-entangled photon pairs involving momentum and polarisation degrees of freedom. In the imaging configuration, a single photon interacts with the pattern while the other photon, which has never interacted with the pattern, is measured jointly in a chosen polarisation basis and in a quantum superposition basis of its position which is equivalent to measure its momentum. Individual photons of each hyper-entangled pair cannot provide a complete image information. The image is constructed by measuring the polarisation state and position of the interacting photon corresponding to a measurement outcome of the non-interacting photon. This paper presents a detailed concept, theory and free space long path experiments on quantum imaging of polarisation sensitive phase patterns.

A quantum-enhanced wide-field phase imager

Quantum techniques can be used to enhance the signal-to-noise ratio in optical imaging. Leveraging the latest advances in single-photon avalanche diode array cameras and multiphoton detection techniques, here, we introduce a supersensitive phase imager, which uses space-polarization hyperentanglement to operate over a large field of view without the need of scanning operation. We show quantum-enhanced imaging of birefringent and nonbirefringent phase samples over large areas, with sensitivity improvements over equivalent classical measurements carried out with equal number of photons. The potential applicability is demonstrated by imaging a biomedical protein microarray sample. Our technology is inherently scalable to high-resolution images and represents an essential step toward practical quantum-enhanced imaging.

Nonlinear Optical Microscopy with Ultralow Quantum Light

Nonlinear optical (NLO) microscopy relies on multiple light-matter interactions to provide unique contrast mechanisms and imaging capabilities that are inaccessible to traditional linear optical imaging approaches, making them versatile tools to understand a wide range of complex systems. However, the strong excitation fields that are necessary to drive higher-order optical processes efficiently are often responsible for photobleaching, photodegradation, and interruption in many systems of interest. This is especially true for imaging living biological samples over prolonged periods of time or in accessing intrinsic dynamics of electronic excited-state processes in spatially heterogeneous materials. This perspective outlines some of the key limitations of two NLO imaging modalities implemented in our lab and highlights the unique potential afforded by the quantum properties of light, especially entangled two-photon absorption based NLO spectroscopy and microscopy. We further review some of the recent exciting advances in this emerging filed and highlight some major challenges facing the realization of quantum-light-enabled NLO imaging modalities.

Quantum enhanced multiple-phase estimation with multi-mode N00N states

Quantum metrology can achieve enhanced sensitivity for estimating unknown parameters beyond the standard quantum limit. Recently, multiple-phase estimation exploiting quantum resources has attracted intensive interest for its applications in quantum imaging and sensor networks. For multiple-phase estimation, the amount of enhanced sensitivity is dependent on quantum probe states, and multi-mode N00N states are known to be a key resource for this. However, its experimental demonstration has been missing so far since generating such states is highly challenging. Here, we report generation of multi-mode N00N states and experimental demonstration of quantum enhanced multiple-phase estimation using the multi-mode N00N states. In particular, we show that the quantum Cramer-Rao bound can be saturated using our two-photon four-mode N00N state and measurement scheme using a 4 × 4 multi-mode beam splitter. Our multiple-phase estimation strategy provides a faithful platform to investigate multiple parameter estimation scenarios.

On-Demand Generation of Entangled Photon Pairs in the Telecom C-Band with InAs Quantum Dots

Entangled photons are an integral part in quantum optics experiments and a key resource in quantum imaging, quantum communication, and photonic quantum information processing. Making this resource available on-demand has been an ongoing scientific challenge with enormous progress in recent years. Of particular interest is the potential to transmit quantum information over long distances, making photons the only reliable flying qubit. Entangled photons at the telecom C-band could be directly launched into single-mode optical fibers, enabling worldwide quantum communication via existing telecommunication infrastructure. However, the on-demand generation of entangled photons at this desired wavelength window has been elusive. Here, we show a photon pair generation efficiency of 69.9 ± 3.6% in the telecom C-band by an InAs/GaAs semiconductor quantum dot on a metamorphic buffer layer. Using a robust phonon-assisted two-photon excitation scheme we measure a maximum concurrence of 91.4 ± 3.8% and a peak fidelity to the Φ⁺ state of 95.2 ± 1.1%, verifying on-demand generation of strongly entangled photon pairs and marking an important milestone for interfacing quantum light sources with our classical fiber networks.

Efficient generation of ultra-broadband parametric fluorescence using chirped quasi-phase-matched waveguide devices

We present a highly efficient photon pair source using chirped quasi-phase-matched (QPM) devices with a ridge waveguide structure. We developed QPM waveguide devices with chirp rates of 3% and 6.7%. Spectrum measurements reveal that the generated photons have bandwidths of 229 nm and 325 nm in full width at half maximum (FWHM), alternatively, 418 nm and 428 nm in base-to-base width for the 3% and 6.7% chirped devices, respectively, which are much broader than the bandwidth of 16 nm in FWHM observed with a non-chirp device. We also evaluate the generation efficiency of photon pairs from coincidence measurements using two superconducting single photon detectors (SSPDs). The estimated generation efficiencies of photon pairs were 2.7 × 10⁶ pairs/s·µW and 1.2 × 10⁶ pairs/s·µW for the 3% and 6.7% chirped devices, respectively, which are comparable to the generation efficiency for the non-chirp device of 2.7 × 10⁶ pairs/s·µW. We also measured the frequency correlation of the photon pairs generated from the 6.7% chirped device. The experimental results clearly show the frequency correlation of the generated broadband photon pairs.

Quantum-enhanced nonlinear microscopy

The performance of light microscopes is limited by the stochastic nature of light, which exists in discrete packets of energy known as photons. Randomness in the times that photons are detected introduces shot noise, which fundamentally constrains sensitivity, resolution and speed¹. Although the long-established solution to this problem is to increase the intensity of the illumination light, this is not always possible when investigating living systems, because bright lasers can severely disturb biological processes^2-4. Theory predicts that biological imaging may be improved without increasing light intensity by using quantum photon correlations^1,5. Here we experimentally show that quantum correlations allow a signal-to-noise ratio beyond the photodamage limit of conventional microscopy. Our microscope is a coherent Raman microscope that offers subwavelength resolution and incorporates bright quantum correlated illumination. The correlations allow imaging of molecular bonds within a cell with a 35 per cent improved signal-to-noise ratio compared with conventional microscopy, corresponding to a 14 per cent improvement in concentration sensitivity. This enables the observation of biological structures that would not otherwise be resolved. Coherent Raman microscopes allow highly selective biomolecular fingerprinting in unlabelled specimens^6,7, but photodamage is a major roadblock for many applications^8,9. By showing that the photodamage limit can be overcome, our work will enable order-of-magnitude improvements in the signal-to-noise ratio and the imaging speed.

Entangled photon-pair sources based on three-wave mixing in bulk crystals

Entangled photon pairs are a critical resource in quantum communication protocols ranging from quantum key distribution to teleportation. The current workhorse technique for producing photon pairs is via spontaneous parametric down conversion (SPDC) in bulk nonlinear crystals. The increased prominence of quantum networks has led to a growing interest in deployable high performance entangled photon-pair sources. This manuscript provides a review of the state-of-the-art bulk-optics-based SPDC sources with continuous wave pump and discusses some of the main considerations when building for deployment.

Low-loss microscope optics with an axicon-based beam shaper

We present low-loss microscope optics using an axicon-based beam shaper, which can convert a Gaussian beam to a ring beam to minimize the optical loss from blocking by the back aperture of the objective lens while maintaining spatial resolution. To design the beam shaper, we characterize the position-dependent transmittance of high-transmittance objective lenses and numerically calculate the beam propagation in the beam shaper. We also clarify the effect of misalignments of the beam shaper and wavefront distortion of the input beam. Furthermore, we experimentally demonstrate a low-loss microscope optical system with a high transmittance of 86.6% and high spatial resolution using the full numerical aperture of the objective lenses.

Metasurface enabled quantum edge detection

Metasurfaces consisting of engineered dielectric or metallic structures provide unique solutions to realize exotic phenomena including negative refraction, achromatic focusing, electromagnetic cloaking, and so on. The intersection of metasurface and quantum optics may lead to new opportunities but is much less explored. Here, we propose and experimentally demonstrate that a polarization-entangled photon source can be used to switch ON or OFF the optical edge detection mode in an imaging system based on a high-efficiency dielectric metasurface. This experiment enriches both fields of metasurface and quantum optics, representing a promising direction toward quantum edge detection and image processing with remarkable signal-to-noise ratio.

Leaving the Limits of Linearity for Light Microscopy

Nonlinear microscopy has enabled additional modalities for chemical contrast, deep penetration into biological tissues, and the ability to collect dynamics on ultrafast timescales across heterogenous samples. The additional light fields introduced to a sample offer seemingly endless possibilities for variation to optimize and customize experimentation and the extraction of physical insight. This perspective highlights three areas of growth in this diverse field: the collection of information across multiple timescales, the selective imaging of interfacial chemistry, and the exploitation of quantum behavior for future imaging directions. Future innovations will leverage the work of the studies reviewed here as well as address the current challenges presented.

Real-time shaping of entangled photons by classical control and feedback

Quantum technologies hold great promise for revolutionizing photonic applications such as cryptography. Yet, their implementation in real-world scenarios is challenging, mostly because of sensitivity of quantum correlations to scattering. Recent developments in optimizing the shape of single photons introduce new ways to control entangled photons. Nevertheless, shaping single photons in real time remains a challenge due to the weak associated signals, which are too noisy for optimization processes. Here, we overcome this challenge and control scattering of entangled photons by shaping the classical laser beam that stimulates their creation. We discover that because the classical beam and the entangled photons follow the same path, the strong classical signal can be used for optimizing the weak quantum signal. We show that this approach can increase the length of free-space turbulent quantum links by up to two orders of magnitude, opening the door for using wavefront shaping for quantum communications.

Two-Photon Fluorescence Microscopy at Extremely Low Excitation Intensity: The Power of Quantum Correlations

Quantum entanglement has been shown to imply correlations stronger than those allowed by classical models. The possibility of performing tasks that are classically impossible has made quantum entanglement a powerful resource for the development of novel methods and applications in various fields of research such as quantum computing, quantum cryptography, and quantum metrology. There is a great need for the development of next generation instrumentation and technologies utilizing entangled quantum light. Among the many applications of nonclassical states of light, nonlinear microscopy has the potential to make an impact in broad areas of science from physics to biology. Here, the microscopic image created by the fluorescence selectively excited by the process of the entangled two-photon absorption is reported. Entangled two-photon microscopy offers nonlinear imaging capabilities at an unprecedented low excitation intensity 10⁷, which is 6 orders of magnitude lower than the excitation level for the classical two-photon image. The nonmonotonic dependence of the image on the femtosecond delay between the components of the entangled photon pair is demonstrated. This delay dependence is a result of specific quantum interference effects associated with the entanglement and this is not observable with classical excitation light. In combination with novel spectroscopic capabilities provided by a nonclassical light excitation, this is of critical importance for sensing and biological applications.

Unified integration scheme using an N × N active switch for efficient generation of a multi-photon parallel state

A source to efficiently generate multiple indistinguishable single photons in different spatial modes in parallel (multi-photon parallel state) is indispensable for realizing large-scale photonic quantum circuits. "A naive scheme" may be to use a heralding single photon source with an on-off detector set at each of parallel modes and to select the cases where each mode contains one photon at the same time. However, it is also necessary to suppress the probability of generating more than two photons from a single-photon source. For this requirement, serial-parallel conversion and a multiplexed heralded single photon source (HSPS) have been proposed and demonstrated. In this paper, we propose and demonstrate a novel method to produce a multi-photon parallel state efficiently using multiple HSPSs and an N × N active optical switch. As an advantage over the simple combination of a spatial multiplexed HSPS and a serial-parallel converter, our method, called the "unified integration scheme," can generate a multi-photon parallel state with minimized optical losses in the switch. Using a 2 × 2 active optical switch and a fixed delay, we achieve an enhancement factor of 1.59 ± 0.14, compared with a naive scheme using two HSPSs, and better than the factor of 1.46 using the simple combination scheme. Furthermore, we confirm the reduction of multi-photon events to 62 % of that of the naive scheme.

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.

Discrimination of entangled photon pair from classical photons by de Broglie wavelength

Quantum optics largely relies on the fundamental concept that the diffraction and interference patterns of a multi-partite state are determined by its de Broglie wavelength. In this paper we show that this is still true for a mixed state with one sub-system being in a classical coherent state and one being in entangled state. We demonstrate the quantum-classical light discrimination using de Broglie wavelength for the states with all classical parameters being the same.

Demonstration of a Reconfigurable Entangled Radio-Frequency Photonic Sensor Network

Quantum metrology takes advantage of nonclassical resources such as entanglement to achieve a sensitivity level below the standard quantum limit. To date, almost all quantum-metrology demonstrations are restricted to improving the measurement performance at a single sensor, but a plethora of applications require multiple sensors that work jointly to tackle distributed sensing problems. Here, we propose and experimentally demonstrate a reconfigurable sensor network empowered by continuous-variable (CV) multipartite entanglement. Our experiment establishes a connection between the entanglement structure and the achievable quantum advantage in different distributed sensing problems. The demonstrated entangled sensor network is composed of three sensor nodes each equipped with an electro-optic transducer for the detection of radio-frequency (RF) signals. By properly tailoring the CV multipartite entangled states, the entangled sensor network can be reconfigured to maximize the quantum advantage in distributed RF sensing problems such as measuring the angle of arrival of an RF field. The rich physics of CV multipartite entanglement unveiled by our work would open a new avenue for distributed quantum sensing and would lead to applications in ultrasensitive positioning, navigation, and timing.

Optical beam shift as a vectorial pointer of curved-path geodesics: an evolution-operator perspective

When set to travel along a curved path, e.g., in a bending-waveguide setting, an optical beam tends to re-adjust its position, shifting away from the center of path curvature. This shift is highly sensitive to the spatial profile of the refractive index, providing a vectorial pointer for curved-path geodesics and bending-induced optical tunneling. An evolution-operator analysis of this effect extends an analogy with a time-evolution-operator treatment of quantum dynamics and suggests the routes whereby the ability of an optical beam to sense curved-path geodesics can be understood in terms of the pertinent evolution operators, path integrals, and imaginary-time/path theorems.

Single-photon sources: Approaching the ideal through multiplexing

We review the rapid recent progress in single-photon sources based on multiplexing multiple probabilistic photon-creation events. Such multiplexing allows higher single-photon probabilities and lower contamination from higher-order photon states. We study the requirements for multiplexed sources and compare various approaches to multiplexing using different degrees of freedom.

Experimental demonstration of Einstein-Podolsky-Rosen entanglement in rotating coordinate space

Einstein-Podolsky-Rosen (EPR) entanglement involving a pair of particles entangled in their positions and momenta is of special interest in the field of quantum information. Previously, EPR entanglement has been studied in different physical systems but in fixed coordinate spaces. Here, we demonstrate an experiment of ghost imaging and ghost interference in rotated position-momentum spaces by using position-momentum entangled photons generated from a hot atomic ensemble. By using different image objects, the measured position-momentum correlations exhibit intriguing dynamics, including gradual decrease and axis-independent EPR entanglement. The reported results on manipulating the EPR entanglement in rotating coordinate spaces hold promise in quantum communication and distant quantum image processing.

Imaging through noise with quantum illumination

The contrast of an image can be degraded by the presence of background light and sensor noise. To overcome this degradation, quantum illumination protocols have been theorized that exploit the spatial correlations between photon pairs. Here, we demonstrate the first full-field imaging system using quantum illumination by an enhanced detection protocol. With our current technology, we achieve a rejection of background and stray light of up to 5.8 and also report an image contrast improvement up to a factor of 11, which is resilient to both environmental noise and transmission losses. The quantum illumination protocol differs from usual quantum schemes in that the advantage is maintained even in the presence of noise and loss. Our approach may enable laboratory-based quantum imaging to be applied to real-world applications where the suppression of background light and noise is important, such as imaging under low photon flux and quantum LIDAR.

Adaptive tracking of enzymatic reactions with quantum light

Enzymes are essential to maintain organisms alive. Some of the reactions they catalyze are associated with a change in reagents chirality, hence their activity can be tracked by using optical means. However, illumination affects enzyme activity: the challenge is to operate at low-intensity regime avoiding loss in sensitivity. Here we apply quantum phase estimation to real-time measurement of invertase enzymatic activity. Control of the probe at the quantum level demonstrates the potential for reducing invasiveness with optimized sensitivity at once. This preliminary effort, bringing together methods of quantum physics and biology, constitutes an important step towards full development of quantum sensors for biological systems.

Generation and characterization of position-momentum entangled photon pairs in a hot atomic gas cell

Continuous-variable position-momentum entanglement (or Einstein-Podolsky-Rosen entanglement) of two particles has played important roles in the fundamental study of quantum physics as well as in the progress of quantum information. In this paper, we propose a scheme to generate Einstein-Podolsky-Rosen (EPR) position-momentum entangled photon pairs efficiently via spontaneous four-wave mixing (SFWM) process in a hot rubidium gas cell. The EPR entanglement between the photon pair is measured and characterized by using the ghost interference and the ghost imaging method. Due to the simplicity of the experimental setup and the high photon pair generation rate, our EPR entangled photon source may has potential applications in quantum imaging, hyperentanglement preparation and atomic ensemble based quantum information processing and quantum communication protocols.