Lu-Ming Duan, Guang-Can Guo
A simple scheme is proposed for observing the ghost interference and diffraction. The signal and the idler beams are produced by a beam splitter with the incident light being in a thermal state. A slit is inserted into the signal beam. We derive rigorously that interference-diffraction patterns can be observed in the first-order correlation by scanning the probe in the idler beam.
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High-resolution ghost image and ghost diffraction experiments are performed by using a single source of thermal-like speckle light divided by a beam splitter. Passing from the image to the diffraction result solely relies on changing the optical setup in the reference arm, while leaving untouched the object arm. The product of spatial resolutions of the ghost image and ghost diffraction experiments is shown to overcome a limit which was formerly thought to be achievable only with entangled photons.
Diffraction of slow neutrons by nanoparticle-polymer composite gratings has been observed. By carefully choosing grating parameters such as grating thickness and spacing, a three-port beam splitter operation for cold neutrons - splitting the incident neutron intensity equally into the plus-minus first and zeroth diffraction orders - was realized. As a possible application, a Zernike three-path interferometer is briefly discussed.
We use trajectory calculations to successfully explain two-photon "ghost" diffraction, a phenomenon previously explained via quantum mechanical entanglement. The diffraction patterns are accumulated one photon pair at a time. The calculations are based on initial correlation of the trajectories in the crystal source and a trajectory-wave ordering interaction with a variant generator inherent in its structure. Details are presented in comparison with ordinary diffraction calculated with the same trajectory model.
Within the second-quantization framework, we develop a formalism for describing a spatially multimode optical field diffracted through a spatial mask and show that this process can be described as an effective interaction between various spatial modes. We demonstrate a method to calculate the quantum state in the diffracted optical field for any given quantum state in the incident field. Using numerical simulations, we also show that with single-mode squeezed-vacuum state input, the prediction of our theory is in qualitative agreement with our experimental data. We also give several additional…
We show that single-slit two-photon ghost diffraction can be explained very simply by using a wave-packet evolution of a generalised EPR state. Diffraction of a wave travelling in the x-direction can be described in terms of the spreading in time of the transverse (z-direction) wave-packet, within the Fresnel approximation. The slit is assumed to truncate the transverse part of the wavefunction of the photon to within the width of the slit. The analysis reproduces all features of the two-photon single-slit ghost diffraction.
We cast diffraction-based interferometry in the framework of post-selected unitary description towards enabling it as a platform for quantum information processing. We express slit-diffraction as an infinite-dimensional transformation and truncate it to a finite-dimensional transfer matrix by post-selecting modes. Using such a framework with classical fields, a customized double-slit setup is effectively a lossy beam splitter in a post-selected sense. Diffraction optics provides a robust alternative to conventional multi-beam interferometry with scope for miniaturization, and also has applicat…
For conventional imaging, shaking of the imaging system or the target leads to the degradation of imaging resolution. In this work, the influence of the target's shaking to fourier-transform ghost diffraction (FGD) is investigated. The analytical results, which are backed up by numerical simulation and experiments, demonstrate that the quiver of target has no effect on the resolution of FGD, thus the target's imaging with high spatial resolution can be always achieved by phase-retrieval method from the FGD patterns. This approach can be applied in high-precision imaging systems, to overcome th…
A test on quantum mechanics proposed long ago by Karl Popper is reconsidered with further detail and new insight. An ambiguity in the proposal, which turns out to be essential in order to make the test conclusive, is identified and taken into account for the first time. Its implications for recently performed photon experiments [such as in D. V. Strekalov \textit{et al.}, Phys. Rev.\ Lett. {\bf 74}, 3600 (1995)] are briefly analyzed.
The X-ray free electron lasers (XFEL) can enable diffractive structural determination of protein crystals or single molecules that are too radiation-sensitive for conventional X-ray analysis. However the electronic form factor could have been modified during the ultrashort X-ray pulse due to photoionization and electron cascade caused by the intense X-ray pulse. For general X-ray imaging techniques, to minimize radiation damage effect is of major concern to ensure faithful reconstruction of the structure. Here we show that a radiation-damage-free diffraction can be achieved with an atomic spat…
We investigate experimentally fundamental properties of coherent ghost imaging using spatially incoherent beams generated from a pseudo-thermal source. A complementarity between the coherence of the beams and the correlation between them is demonstrated by showing a complementarity between ghost diffraction and ordinary diffraction patterns. In order for the ghost imaging scheme to work it is therefore crucial to have incoherent beams. The visibility of the information is shown for the ghost image to become better as the object size relative to the speckle size is decreased, and therefore a re…
Quantum formalism of Fraunhofer diffraction is obtained. The state of the diffraction optical field is connected with the state of the incident optical field by a diffraction factor. Based on this formalism, correlations of the diffraction modes are calculated with different kinds of incident optical fields. Influence of correlations of the incident modes on the diffraction pattern is analyzed and an explanation of the ''ghost'' diffraction is proposed.
The Fourier-Transform ghost imaging of both amplitude-only and pure-phase objects was experimentally observed with classical incoherent light at Fresnel distance by a new lensless scheme. The experimental results are in good agreement with the standard Fourier-transform of the corresponding objects. This scheme provides a new route towards aberration-free diffraction-limited 3D images with classically incoherent thermal light, which have no resolution and depth-of-field limitations of lens-based tomographic systems.
We have built and operated an atom interferometer of the Mach-Zehnder type. The atomic wave is a supersonic beam of lithium seeded in argon and the mirrors and beam-splitters for the atomic wave are based on elastic Bragg diffraction on laser standing waves at 671 nm. We give here a detailed description of our experimental setup and of the procedures used to align its components. We then present experimental signals, exhibiting atomic interference effects with a very high visibility, up to 84.5 %. We describe a series of experiments testing the sensitivity of the fringe visibility to the main …
We demonstrate Bragg diffraction of the antibiotic ciprofloxacin and the dye molecule phthalocyanine at a thick optical grating. The observed patterns show a single dominant diffraction order with the expected dependence on the incidence angle as well as oscillating population transfer between the undiffracted and diffracted beams. We achieve an equal-amplitude splitting of $14 \hbar k$ (photon momenta) and maximum momentum transfer of $18 \hbar k$. This paves the way for efficient, large-momentum beam splitters and mirrors for hot and complex molecules.
A special algorithm for the Fourier-transform Ghost Imaging (GI) scheme is discussed based on the Compressive Sampling (CS) theory. Though developed mostly in real space, CS algorithm could also be used for the Fourier spectrum reconstruction of pure phase object by setting a proper sensing matrix. This could find its application in diffraction imaging of X-ray, neutron and electron with higher efficiency and resolution. Simulation and experiment results are also presented to prove the feasibility.
In an effort to challenge the Copenhagen interpretation of quantum mechanics, Karl Popper proposed an experiment involving spatially separated entangled particles. In this experiment, one of the particles passes through a very narrow slit, and thereby its position becomes well-defined. This particle therefore diffracts into a large divergence angle; this effect can be understood as a consequence of the Heisenberg uncertainty principle. Popper further argued that its entangled partner would become comparably localized in position, and that, according to his understanding of the Copenhagen inter…
We investigate the specific form that the collapsed quantum state of a signal photon can take when its entangled idler is measured in an entangled ghost imaging configuration using a type II collinear phase matched spontaneous parametric downconversion (SPDC) interaction. Calculation of the correlated counting rate distributions in the ghost image plane and diffraction plane show that agreement between collapse and non-collapse models is obtained if the signal is assumed to collapse into a specific mixed state. However, if the signal is assumed to collapse into a pure state, significant differ…
In ghost imaging schemes information about an object is extracted by measuring the correlation between a beam that passed the object and a reference beam. We present a spatial averaging technique that substantially improves the imaging bandwidth of such schemes, which implies that information about high-frequency Fourier components can be observed in the reconstructed diffraction pattern. In the many-photon regime the averaging can be done in parallel and we show that this leads to a much faster convergence of the correlations. We also consider the reconstruction of the object image, and discu…
Time-reversed Young's experiment: Deterministic, diffractionless second-order interference effect
本文提出时间反演的杨氏双缝实验配置，能产生无衍射和第一阶效应的确定性二阶“鬼”干涉图样，无需量子纠缠或非经典关联，为超分辨光学成像与传感技术提供了新途径。
In the Kapitza-Dirac effect, atoms, molecules, or swift electrons are diffracted off a standing wave grating of the light intensity created by two counter-propagating laser fields. In ultrafast electron optics, such a coherent beam splitter offers interesting perspectives for ultrafast beam shaping. Here, we study, both analytically and numerically, the effect of the inclination angle between two laser fields on the diffraction of pulsed, low-energy electron beams. For sufficiently high light intensities, we observe a rich variety of complex diffraction patterns. These do not only reflect inte…
Estimation with ultimate quantum precision of the transverse displacement between two photons via two-photon interference sampling measurements
本文提出基于横向动量采样测量的双光子干涉方案，可在估计两光子横向位移时实现终极量子精度，且不受波包重叠影响，为超分辨纳米成像开辟新范式。
Ultrasensitive Transverse Deflection Measurement with Two-photon Interference
本研究提出并实验演示了一种空间 HOM 干涉技术，通过横向动量采样测量光束横向偏转，利用 Fisher 信息分析确定最佳工作点，规避了衍射极限下的直接成像分辨率要求，实现了高精度空间传感。
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-…
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