E. -K. Tan, John Jeffers, Stephen M. Barnett, David T. Pegg
We use retrodictive quantum theory to analyse two-photon quantum imaging systems. The formalism is particularly suitable for calculating conditional probability distributions.
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Although it has been known for some time that quantum mechanics can be formulated in a way that treats prediction and retrodiction on an equal footing, most attention in engineering quantum states has been devoted to predictive states, that is, states associated with the a preparation event. Retrodictive states, which are associated with a measurement event and propagate backwards in time, are also useful, however. In this paper we show how any retrodictive state of light that can be written to a good approximation as a finite superposition of photon number states can be generated by an optica…
Spontaneous parametric down conversion (PDC), in the perturbative limit, can be considered as a probabilistic splitting of one input photon into two output photons. Conversely, sum-frequency generation (SFG) implements the reverse process of combining two input photons into one. Here we show that a single-photon projective measurement in the temporal-mode basis of the output photon of a two-photon SFG process effects a generalized measurement on the input two-photon state. We describe the positive-operator-valued measure (POVM) associated with such a measurement, and show that its elements are…
Stochastic Mean-field Theory for Conditional Spin Squeezing by Homodyne Probing of Atom-Cavity Photon Dressed States
本文提出一种随机均场理论用于研究强耦合光学腔体中大量三能级原子的条件量子自旋压缩，通过模拟验证其有效性，并拓展至更多量子测量效应研究。
In this article, we propose the two-photon interference imaging based on two-photon interference mechanism with thermal light source. Theoretical and experimental results show that the imaging quality and imaging speed of two-photon interference imaging are comparable to that of classical optical imaging, and much better than that of conventional quantum imaging (ghost imaging). Furthermore, Two-photon interference imaging can effectively overcome the effect of atmospheric turbulence and other harsh optical environments. The physical essence is the inhibition of two-photon interference mechani…
We extend entangled coincidence (ghost) imaging to fluorescent samples. Given the entangled photon correlation, one photon of the pair carries information on where the other photon has been absorbed and has produced fluorescence in a sample. Fluorescent molecules serve as ''detectors breaking'' the entanglement.
We report the first experimental demonstration of two-photon imaging with a pseudo-thermal source. Similarly to the case of entangled states, a two-photon Gaussian thin lens equation is observed, indicating EPR type correlation in position. We introduce the concepts of two-photon coherent and two-photon incoherent imaging. The differences between the entangled and the thermal cases are explained in terms of these concepts.
The use of entangled photons in an imaging system can exhibit effects that cannot be mimicked by any other two-photon source, whatever the strength of the correlations between the two photons. We consider a two-photon imaging system in which one photon is used to probe a remote (transmissive or scattering) object, while the other serves as a reference. We discuss the role of entanglement versus correlation in such a setting, and demonstrate that entanglement is a prerequisite for achieving distributed quantum imaging.
We demonstrate a compressive normalized ghost imaging system with entangled photons employing complementary compressive imaging (CCI) technique. The quantum ghost image reconstruction was achieved at only 19.53% sampling ratio of raster scanning. With the special +1/-1 type sensing matrix and appropriate optimal algorithm, the photon utilization efficiency and robustness of the imaging system is enhanced significantly. Our results reveal the great potential of CCI technique applied in quantum imaging and other quantum optics field such as quantum charactering and quantum state tomography to us…
Quantum imaging with undetected photons relies on the principle of induced coherence without induced emission and uses two sources of photon-pairs with a signal- and an idler photon. Each pair shares strong quantum correlations in both position and momentum, which allows to image an object illuminated with idler photons by just measuring signal photons that never interact with the object. In this work, we theoretically investigate the transverse resolution of this non-local imaging scheme through a general formalism that treats propagating photons beyond the commonly used paraxial approximatio…
We propose a technique capable of imaging a distinct physical object with sub-Rayleigh resolution in an ordinary far-field imaging setup using single-photon sources and linear optical tools only. We exemplify our method for the case of a rectangular aperture and two or four single-photon emitters obtaining a resolution enhanced by a factor of two or four, respectively.
We discuss a correlated two-photon imaging apparatus that is capable of producing images that are free of the effects of odd-order aberration introduced by the optical system. We show that both quantum-entangled and classically correlated light sources are capable of producing the desired spatial-aberration cancelation.
We show that how a recent experiment of quantum imaging with undetected photons can basically be described as a (partial) ancilla-assisted process tomography. We propose a simplified quantum circuit version of this scenario, which also enables to recast quantum imaging in quantum computation language. Our analogy and analysis may help better understand the role of classical and/or quantum correlations in imaging experiments.
A typical imaging scenario requires three basic ingredients: 1. a light source that emits light, which in turn interacts and scatters off the object of interest; 2. detection of the light being scattered from the object and 3. a detector with spatial resolution. These indispensable ingredients in typical imaging scenarios may limit their applicability in the imaging of biological or other sensitive specimens due to unavailable photon-starved detection capabilities and inevitable damage induced by interaction. Here, we propose and experimentally realize a quantum imaging protocol that alleviate…
We report on a delayed-choice quantum eraser experiment based on a two-photon imaging scheme using entangled photon pairs. After the detection of a photon which passed through a double-slit, a random delayed choice is made to erase or not erase the which-path information by the measurement of its distant entangled twin; the particle-like and wave-like behavior of the photon are then recorded simultaneously and respectively by only one set of joint detection devices. The present eraser takes advantage of two-photon imaging. The complete which-path information of a photon is transferred to its d…
We propose a technique to obtain sub-wavelength resolution in quantum imaging with potentially 100% contrast using incoherent light. Our method requires neither path-entangled number states nor multi-photon absorption. The scheme makes use of N photons spontaneously emitted by N atoms and registered by N detectors. It is shown that for coincident detection at particular detector positions a resolution of λ/ N can be achieved.
It has been claimed that ``the use of entangled photons in an imaging system can exhibit effects that cannot be mimicked by any other two-photon source, whatever strength of the correlations between the two photons'' [A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001)]. While we believe that the cited statement is true, we show that the method proposed in that paper, with ``bucket detection'' of one of the photons, will give identical results for entangled states as for appropriately prepared classically correlated states.
A novel quantum imaging technique has recently been demonstrated in an experiment, where the photon used for illuminating an object is not detected; the image is obtained by interfering two beams, none of which ever interacts with the object. Here we present a detailed theoretical analysis of the experiment. We show that the object information is present only in the interference term and not in the individual intensities of the interfering beams. We also theoretically establish that the magnification of the imaging system depends on two wavelengths: the average wavelength of the photon that il…
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 …
We report the first experimental demonstration of two-photon correlated imaging with true thermal light from a hollow cathode lamp. The coherence time of the source is much shorter than that of previous experiments using random scattered light from a laser. A two-pinhole mask was used as object, and the corresponding thin lens equation was well satisfied. Since thermal light sources are easier to obtain and measure than entangled light it is conceivable that they may be used in special imaging applications.
Spatial correlations between two photons are the key resource in realising many quantum imaging schemes. Measurement of the bi-photon correlation map is typically performed using single-point scanning detectors or single-photon cameras based on CCD technology. However, both approaches are limited in speed due to the slow scanning and the low frame-rate of CCD-based cameras, resulting in data acquisition times on the order of many hours. Here we employ a high frame rate, single photon avalanche diode (SPAD) camera, to measure the spatial joint probability distribution of a bi-photon state produ…
Ghost imaging is the remarkable process where an image can be formed from photons that have not "seen" the object. Traditionally this phenomenon has required initially correlated but spatially separated photons, e.g., one to interact with the object and the other to form the image, and has been observed in many physical situations, spanning both the quantum and classical regimes. To date, all instances of ghost imaging record an image with the same contrast as the object, i.e., where the object is bright, the image is also bright, and vice versa. Here we observe ghost imaging in a new system -…
Quantum Imaging and Metrology with Undetected squeezed Photons: Noise Canceling and Noise Based Imaging
提出配备零差检测和 OPO 的未探测压缩光子量子成像方案，建立超越低增益近似的理论，并通过噪声编码信息实现高信噪比、抑噪的非破坏性成像与相位测量。
We discuss advantages of using non-classical states of light for two aspects of optical imaging: creating of miniature images on photosensitive substrates, which constitutes the foundation for optical lithography, and imaging of micro objects. In both cases, the classical resolution limit given by the Rayleigh criterion is approximately a half of the optical wavelength. It has been shown, however, that by using multi-photon quantum states of the light field, and multi-photon sensitive material or detector, this limit can be surpassed. We give a rigorous quantum mechanical treatment of this pro…
Adaptive Optical Imaging with Entangled Photons
针对无标记显微术中传统自适应光学依赖导星和特定优化指标的问题，本文提出利用纠缠光子相关性直接校正PSF的无导星方法，并在生物样品明场成像中证明其对散焦等像差的校正优势。
Non-classical correlations in optical beams offer the unprecedented opportunity of surpassing conventional limits of sensitivity and resolution in optical measurements and imaging, especially but not only, when a low photon flux down to the single photons are measured. We review the principles of quantum imaging and sensing techniques which exploit sub-Poissonian photon statistics and non-classical photon number correlation, presenting some state-of-the-art achievements in the field. These quantum photonics protocols have the potential to trigger major steps in many applications, such as micro…
The production of pairs of entangled photons simply by focusing a laser beam onto a crystal with a non-linear optical response was used to test quantum mechanics and to open new approaches in imaging. The development of the latter was enabled by the emergence of single photon sensitive cameras able to characterize spatial correlations and high-dimensional entanglement. Thereby new techniques emerged such as the ghost imaging of objects - where the quantum correlations between photons reveal the image from photons that have never interacted with the object - or the imaging with undetected photo…
We demonstrate strong coupling of single photons emitted by individual molecules at cryogenic and ambient conditions to individual nanoparticles. We provide images obtained both in transmission and reflection, where an efficiency greater than 55% was achieved in converting incident narrow-band photons to plasmon-polaritons (plasmons) of a silver nanoparticle. Our work paves the way to spectroscopy and microscopy of nano-objects with sub-shot noise beams of light and to triggered generation of single plasmons and electrons in a well-controlled manner.
We present a method to classically enhance noise-robustness of single-pixel imaging in photon counting regime with a pulsed source. By using time-domain cross-correlations between temporal profiles of a pulsed source and received signals, our scheme classically imitates the noise rejection concept of quantum imaging. Under a strong noise environment in which the background noise intensity is up to 120 times higher than the signal one, we compare three different images obtained by conventional, quantum-enhanced, and classically enhanced schemes. The results show that the classically enhanced sc…
We image with cameras entangled photon light transmitted through a random medium. Near-field and far-field spatial quantum correlations show that entangled photon pairs (bi-photons) generated by spontaneous optical parametric down-conversion exhibit speckle pattern. In contrast, no information from the random medium can be extracted using incoherent light issued from one photon of the pair. Although these measurements require several hours to record thousands of image pairs, our method is instantaneous for the recording of one pair of twin images and involve all the photons of the images.
In this review we present the potentialities and the achievements of the use of non-classical photon number correlations in twin beams (TWB) states for many applications, ranging from imaging to metrology. Photon number correlations in the quantum regime are easy to be produced and are rather robust against unavoidable experimental losses, and noise in some cases, if compared to the entanglement, where loosing one photon can completely compromise the state and its exploitable advantage. Here, we will focus on quantum enhanced protocols in which only phase-insensitive intensity measurements (ph…
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 imag…
The relationship between transmission area of an object imaged and the visibility of its image is investigated in a lensless system. We show that the changes of the visibility are quite different when the transmission area is varied by different manners. An increase of the transmission by adding the slit number leads to a decrease of the visibility. While, the change is adverse when the slit width is widened for a given distance between two slits.
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 with mature silicon-based detection technology. All existing implementations of QIUP have so far utilised the momentum correlations within the biphoton state. Here, for the first time, we implement and examine theoretically and numerically the complementary scenario - utilising the tight position correlations formed wit…
Wave-particle duality ellipse and application in quantum imaging with undetected photons
提出量化双路径干涉系统中相干性与波粒二象性相互作用的系统框架，揭示闭式二象性椭圆等式统一相关度量，扩展至未探测光子量子成像建立成像二象性椭圆关联物体透射率，推进基础理解并提供实用工具包。
Large baseline optical imaging assisted by single photons and linear quantum optics
提出融合量子计量与网络技术的单光子线性光学干涉望远镜方案，在高损耗、低光子数条件下仍可将点源定位分辨率提升约 10 μas，且无需光量子存储器。
Biphoton states of signal and idler fields--obtained from spontaneous parametric downconversion (SPDC) in the low-brightness, low-flux regime--have been utilized in several quantum imaging configurations to exceed the resolution performance of conventional imagers that employ coherent-state or thermal light. Recent work--using the full Gaussian-state description of SPDC--has shown that the same resolution performance seen in quantum optical coherence tomography and the same imaging characteristics found in quantum ghost imaging can be realized by classical-state imagers that make use of phase-…
Entangled-photon coincidence imaging is a method to nonlocally image an object by transmitting a pair of entangled photons through the object and a reference optical system, respectively. The image of the object can be extracted from the coincidence rate of these two photons. From a classical perspective, the image is proportional to the fourth-order correlation function of the wave field. Using classical statistical optics, we study a particular aspect of coincidence imaging with incoherent sources. As an application, we give a proposal to realize lensless Fourier-transform imaging, and discu…
It is shown that the use of phase conjugation in one arm of a correlated two-photon imaging apparatus allows undistorted ghost imaging through a region with randomly-varying phase shifts. The images are formed from correlated pairs of photons in such a way that turbulence-induced phase shifts gained by the photons during passage through the medium cancel pairwise.
Quantum imaging exploiting twisted photon pairs
本文提出利用可调空间关联区域的扭曲光子对进行量子成像，通过体密度符合计数和重标度图像信号克服相干面积限制，并揭示反聚束与聚束光子对的相消干涉，为量子全息与显微应用奠定基础。
We use twin photons generated by spontaneous parametric down conversion (SPDC) to perform temporal ghost imaging of a single time signal. The retrieval of a binary signal containing eight bits is performed with an error rate below 1%.
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.
Single-photon-avalanche diode (SPAD) arrays are essential tools in biophotonics, optical ranging and sensing and quantum optics. However, their small number of pixels, low quantum efficiency and small fill factor have so far hindered their use for practical imaging applications. Here, we demonstrate full-field entangled photon pair correlation imaging using a 100-kpixels SPAD camera. By measuring photon coincidences between more than 500 million pairs of positions, we retrieve the full point spread function of the imaging system and subsequently high-resolution images of target objects illumin…
Position Correlation Enabled Quantum Imaging with Undetected Photons
研究通过光子位置关联而非动量关联实现未探测光子量子成像（QIUP）的互补方案，提出通用理论并证明两者所得图像性质显著不同。
The Rayleigh diffraction bound sets the minimum separation for two point objects to be distinguishable in a conventional imaging system. We demonstrate resolution enhancement beyond the Rayleigh bound using random scanning of a highly-focused beam and N-photon photodetection implemented with a single-photon avalanche detector array. Experimental results show resolution improvement by a factor ~sqrt(N) beyond the Rayleigh bound, in good agreement with theory.
Hyper-spectral Imaging with Up-Converted Mid-Infrared Single-Photons
本文提出一种结合腔增强SPDC与频率上转换的单光子高光谱成像平台，利用硅单光子雪崩二极管在室温下实现2.9至3.6微米中红外波段的无标记化学特异性成像，克服了传统MIR成像的光损伤和探测器限制。
Ghost imaging with zero photons
本文提出零光子鬼成像方法，利用无光子时间槽重建图像，揭示了光子数投影测量与热光子统计的协同作用。
Correlated-photon imaging at 10 volumetric images per second
本文提出一种结合混沌光光子数相关性与SPAD超快传感器阵列的单透镜相关全光成像方案，实现了每秒10个体积图像的采集速度，显著提升了相关光子成像的时间性能并证明其实际应用潜力。
We show that a recently discussed apparatus for aberration-cancelled interferometry may be modified to perform correlated-photon imaging in the so-called "ghost" imaging configuration. For objects in the vicinity of a particular plane, the images are free of object-induced phase distortions. This apparatus has the distinctive feature that it may be used to superimpose images of two objects in a manner that could lead to useful effects and applications. We show that the apparatus works using either quantum-entangled or classically correlated light sources.
Indistinguishable quantum states interfere, but the mere possibility of obtaining information that could distinguish between overlapping states inhibits quantum interference. Quantum interference imaging can outperform classical imaging or even have entirely new features. Here, we introduce and experimentally demonstrate a quantum imaging concept that relies on the indistinguishability of the possible sources of a photon that remains undetected. Our experiment uses pair creation in two separate down-conversion crystals. While the photons passing through the object are never detected, we obtain…
Plenoptic imaging is a novel optical technique for three-dimensional imaging in a single shot. It is enabled by the simultaneous measurement of both the location and the propagation direction of light in a given scene. In the standard approach, the maximum spatial and angular resolutions are inversely proportional, and so are the resolution and the maximum achievable depth of focus of the 3D image. We have recently proposed a method to overcome such fundamental limits by combining plenoptic imaging with an intriguing correlation remote-imaging technique: ghost imaging. Here, we theoretically d…
Correlated-photon imaging, popularly known as ghost imaging, is a technique whereby an image is formed from light that has never interacted with the object. In ghost imaging experiments two correlated light fields are produced. One of these fields illuminates the object, and the other field is measured by a spatially resolving detector. In the quantum regime, these correlated light fields are produced by entangled photons created by spontaneous parametric down-conversion. To date, all correlated-photon ghost-imaging experiments have scanned a single-pixel detector through the field of view to …
Resolution limit in quantum imaging with undetected photons using position correlations
本文详细研究了位置相关性使能的未探测光子量子成像（QIUP）的分辨率极限，建立了空间分辨率与SPDC过程中双光子位置相关性及波长的定量关系，并指出该极限无法通过常规光学技术提升。
The concept of correlated two-photon spiral imaging is introduced. We begin by analyzing the joint orbital angular momentum (OAM) spectrum of correlated photon pairs. The mutual information carried by the photon pairs is evaluated, and it is shown that when an object is placed in one of the beam paths the value of the mutual information is strongly dependent on object shape and is closely related to the degree of rotational symmetry present. After analyzing the effect of the object on the OAM correlations, the method of correlated spiral imaging is described. We first present a version using p…
We have built an imaging system that uses a photon's position or time-of-flight information to image an object, while using the photon's polarization for security. This ability allows us to obtain an image which is secure against an attack in which the object being imaged intercepts and resends the imaging photons with modified information. Popularly known as "jamming," this type of attack is commonly directed at active imaging systems such as radar. In order to jam our imaging system, the object must disturb the delicate quantum state of the imaging photons, thus introducing statistical error…
We show a simple yet effective method that can be used to characterize the per pixel quantum efficiency and temporal resolution of a single photon event camera for quantum imaging applications. Utilizing photon pairs generated through spontaneous parametric down-conversion, the detection efficiency of each pixel, and the temporal resolution of the system, are extracted through coincidence measurements. We use this method to evaluate the TPX3CAM, with appended image intensifier, and measure an average efficiency of 7.4% and a temporal resolution of 7.3ns. Furthermore, this technique reveals imp…
Plasmonics and metamaterials have recently been shown to allow the control and interaction with non-classical states of light, a rather counterintuitive finding given the high losses typically encountered in these systems. Here, we demonstrate a range of functionalities that are allowed with correlated and entangled photons that are used to illuminate multiple, overlaid patterns on plasmonic metasurfaces. Correlated photons allow to nonlocally determine the pattern that is imaged or, alternatively to un-scramble an image that is otherwise blurred. Entangled photons allow a more important funct…
We propose a novel quantum diffraction imaging technique whereby one photon of an entangled pair is diffracted off a sample and detected in coincidence with its twin. The image is obtained by scanning the photon that did not interact with matter. We show that when a dynamical quantum system interacts with an external field, the phase information is imprinted in the state of the field in a detectable way. The contribution to the signal from photons that interact with the sample scales as $\propto I_{p}^{1/2}$, where $I_{p}$ is the source intensity, compared to $\propto I_{p}$ of classical diffr…
Metrology of quantum imaging schemes
该研究将基于空间关联光子对的量子成像方案转化为量子多参数估计问题，计算量子费希尔信息矩阵，比较鬼成像、双光子成像和未检测光子成像的性能，确定适合特定任务的成像协议，为量子传感技术设计优化提供指南。
Hyperspectral imaging (HSI) has a wide range of applications from environmental monitoring to biotechnology. Current snapshot HSI techniques all require a trade-off between spatial and spectral resolution and are thus unable to achieve high resolutions in both simultaneously. Additionally, the techniques are resource inefficient with most of the photons lost through spectral filtering. Here, we demonstrate a snapshot HSI technique utilizing the strong spectro-temporal correlations inherent in entangled photons using a modified quantum ghost spectroscopy system, where the target is directly ima…
Ghost Imaging with Free Electron-Photon Pairs
利用透射电子显微镜中产生的电子-阴极发光光子对实现鬼成像，空间分辨率达2微米，为量子增强成像技术从光子量子光学扩展到电子显微镜铺平道路。
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