W. Görlich, I. Hoffmann, T. Schürmann
Monochromatic light is prepared by a single slit of spatial width Δx. The diffraction pattern is considered to obtain the corresponding probability density of the momentum. Let P be the probability weight to measure a momentum in a finite window of width Δp. For small Δp the asymptotic law P ~ ΔxΔp/h is verified, while h is Planck's constant of action.
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In this paper, we apply the full new method of quantum theory to study the double-slit diffraction of ${C_{60}}$ molecules. We calculate the double-slit wave functions of ${C_{60}}$ molecules by Schrödinger equation, and calculate the diffraction wave function behind the slits with the Feynman path integral quantum theory, and then give the relation between the diffraction intensity of double-slit and diffraction pattern position. We compare the calculation results with two different double-slit diffraction experiments. When the decoherence effects are considered, the calculation results are i…
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.
Double-slit diffraction is a corner stone of quantum mechanics. It illustrates key features of quantum mechanics: interference and the particle-wave duality of matter. In 1965, Richard Feynman presented a thought experiment to show these features. Here we demonstrate the full realization of his famous thought experiment. By placing a movable mask in front of a double-slit to control the transmission through the individual slits, probability distributions for single- and double-slit arrangements were observed. Also, by recording single electron detection events diffracting through a double-slit…
In this paper, we study the light double-slit diffraction experiment with quantum theory approach. Firstly, we calculate the light wave function in slits by quantum theory of photon. Secondly, we calculate the diffraction wave function with Kirchhoff's law. Thirdly, we give the diffraction intensity of light double-slit diffraction, which is proportional to the square of diffraction wave function. Finally, we compare calculation result of quantum theory and classical electromagnetic theory with the experimental data. We find the quantum calculate result is accordance with the experiment data, …
The phenomena of electron, neutron, atomic and molecular diffraction have been studied by many experiments, and these experiments are explained by some theoretical works. In this paper, we study electronic double-slit diffraction with quantum mechanical approach. We can obtain the results: (1) When the slit width $a$ is in the range of $3λ\sim 50λ$ we can obtain the obvious diffraction patterns. (2) when the ratio of $\frac{d+a}{a}=n (n=1, 2, 3,\cdot\cdot\cdot)$, order $2n, 3n, 4n,\cdot\cdot\cdot$ are missing in diffraction pattern. (3)When the ratio of $\frac{d+a}{a}\neq n (n=1, 2, 3,\cdot\cd…
We provide a quantum approach description of neutron single and double-slit diffraction, with specific attention to the cold neutron diffraction ($λ\approx 20$Å) carried out by Zeilinger et al. in 1988. We find the theoretical results are good agreement with experimental data.
It was recently proposed that the fringe visibility in the interference pattern of a double-slit diffraction experiment with a HeNe laser beam was reduced as a consequence of the focused attention of participants on the double-slit that initiated the collapse of the photon wavefunction. A thorough examination of the reported apparatus and diffraction pattern data is presented here revealing a number of inconsistencies in the experimental setup. The hypothesis for wavefunction collapse under the proposed experimental conditions is found problematic as the use of single photon sources is demande…
A setup is proposed to play a quantum version of the famous bimatrix game of Prisoners' Dilemma. Multi-slit electron diffraction with each player's pure strategy consisting of opening one of the two slits at his/her disposal are essential features of the setup. Instead of entanglement the association of waves with travelling material objects is suggested as another resource to play quantum games.
In diffraction experiments with particle beams, several effects lead to a fringe visibility reduction of the interference pattern. We theoretically describe the intensity one can measure in a double-slit setup and compare the results with the experimental data obtained with cold neutrons. Our conclusion is that for cold neutrons the fringe visibility reduction is due not to decoherence, but to initial incoherence.
At present, the theory of light diffraction only has the simple wave-optical approach. In this paper, we study light diffraction with the approach of relativistic quantum theory. We find that the slit length, slit width, slit thickness and wave-length of light have affected to the diffraction intensity and form of diffraction pattern. However, the effect of slit thickness on the diffraction pattern can not be explained by wave-optical approach, and it can be explained in quantum theory. We compare the theoretical results with single and multiple slits experiment data, and find the theoretical …
Double Slit Experiment in the Heisenberg Picture of Quantum Mechanics
本文在量子力学海森堡图像中重新审视双缝实验，指出无需讨论非局域性即可解释干涉条纹，并强调位置和动量算符应同时依赖空间和时间。
We study the quantum slit diffraction problem in three dimensions. In the treatment of diffraction of particles by a slit, it is usually assumed that the motion perpendicular to the slit is classical. Here we take into account the effect of the quantum nature of the motion perpendicular to the slit using the Green function approach [18]. We treat the diffraction of a Gaussian wave packet for general boundary conditions on the shutter. The difference between the standard and our three-dimensional slit diffraction models is analogous to the diffraction in time phenomenon introduced in [16]. We d…
Heisenberg's position-measurement--momentum-disturbance relation is derivable from the uncertainty relation $σ(q)σ(p) \geq \hbar/2$ only for the case when the particle is initially in a momentum eigenstate. Here I derive a new measurement--disturbance relation which applies when the particle is prepared in a twin-slit superposition and the measurement can determine at which slit the particle is present. The relation is $d \times Δp \geq 2\hbar/π$, where $d$ is the slit separation and $Δp=D_{M}(P_{f},P_{i})$ is the Monge distance between the initial $P_{i}(p)$ and final $P_{f}(p)$ momentum dist…
We provide support for the claim that momentum is conserved for individual events in the electron double slit experiment. The natural consequence is that a physical mechanism is responsible for this momentum exchange, but that even if the fundamental mechanism is known for electron crystal diffraction and the Kapitza-Dirac effect, it is unknown for electron diffraction from nano-fabricated double slits. Work towards a proposed explanation in terms of particle trajectories affected by a vacuum field is discussed. The contentious use of trajectories is discussed within the context of oil droplet…
We employ the broken-link model to create a barrier with slits in a two-dimensional lattice. The diffraction and interference patterns of the probability distribution of quantum walkers passing through the slits are analyzed. Simulations were performed using the main types of coins, and display diffraction and interference patterns that depend on the choice of coins.
Even 100 years after its introduction by Louis de Broglie, the wave-nature of matter is often regarded as a mind-boggling phenomenon. To give an intuitive introduction to this field, we here discuss the diffraction of massive molecules through a single, double, and triple slit, as well as a nanomechanical grating. While the experiments are in good agreement with undergraduate textbook predictions, we also observe pronounced differences resulting from the molecules' mass and internal complexity. The molecules' polarizability causes an attractive van der Waals interaction with the slit walls, wh…
A double cavity with a quantum mechanical and a classical field is located immediately behind of a double-slit in order to analyse the wave-particle duality. Both fields have common nodes and antinodes through which a three-level atom passes after crossing the double-slit. The atom-field interaction is maximum when the atom crosses a common antinode and path-information can be recorded on the phase of the quantum field. On other hand, if the atom crosses a common node, the interaction is null and no path-information is stored. A quadrature measurement on the quantum field can reveal the path f…
The effects of incoherence and decoherence in the double--slit experiment are studied using both optical and quantum--phenomenological models. The results are compared with experimental data obtained with cold neutrons.
By probability theory the probability space to underlie the set of statistical data described by the squared modulus of a coherent superposition of microscopically distinct (sub)states (CSMDS) is non-Kolmogorovian and, thus, such data are mutually incompatible. For us this fact means that the squared modulus of a CSMDS cannot be unambiguously interpreted as the probability density and quantum mechanics itself, with its current approach to CSMDSs, does not allow a correct statistical interpretation. By the example of a 1D completed scattering and double slit diffraction we develop a new quantum…
We present a new approach to the quantum-classical problem, which treats it as the problem of modelling the quantum phenomenon described by a coherent superposition of microscopically distinct substates (CSMDS) as a compound one consisting of alternative subprocesses creating unremovable contexts for each other, or as that of reducing a non-Kolmogorovian quantum probability space to underlie a CSMDS to the sum of Kolmogorovian ones. We develop such models for a 1D completed scattering and double slit diffraction. The quantum-classical problem disappears when, in quantum theory with its integra…
Coherence spectroscopy by the Nth power of the measured signal in an interferometer overcoming the diffraction limit
本研究提出对N缝干涉仪的测量信号强度取K次方的方法，在满足散粒噪声极限下突破N缝干涉仪分辨率极限，可应用于现有光谱设备，还能突破量子计量学中的超分辨率极限。
A study of the effects of Gaussian distribution of coherence length of source on the diffraction of partial temporal coherence beam from multi slits: Theory and simulation
本文将单缝时间相干光衍射推广至任意n缝，研究退相干参数对衍射图样的影响，并进一步引入高斯分布的光源相干长度进行数值模拟，以更贴近实际地分析远场衍射效应。
It is generally accepted that the disturbance interpretation cannot explain Heisenberg's uncertainty relation DxDp=h. In this paper a clear distinction will be made between the notions of state preparation and measurement, noting that the disturbance that is referred to in Heisenberg's disturbance interpretation is usually caused by the measurement. The main goal of this paper is to examine and discuss to what extent disturbance during the state preparation plays a role in the interpretation of Heisenberg's uncertainty relation. This examination will be done in the context of a single-slit exp…
Diffraction phenomena of large molecules have been studied in many experiments, and these experiments are described by many theoretical works. In this paper, we study $C_{60}$ molecules single and double-slit diffraction with quantum theory approach, and we pay close attention to the $C_{60}$ diffraction experiment carried out by A.Zeilinger et.at in 1999. In double-slit diffraction, we consider the decoherence effect, and find the theoretical results are good agreement with experimental data.
We generalize the notion of the Franhoufer diffraction from a single slit and a circular aperture to the case of partially temporal coherent and quasimonochromatic light. The problem is studied analytically and the effect of coherence length on the diffraction pattern is investigated. In this case the far-field distribution of the irradiance depends on the newly introduced parameter(decoherence parameter) which governs the deviation of the diffraction pattern from the usual one. The corrections due to temporal decoherency on the irradiance distribution in the far field is obtained. Numerical s…
Diffraction on the slit can be interpreted in accordance with the Heisenberg uncertainty principle. This elementary example hints at the importance of the information theory for the quantum physics. The role played by one particularly interesting measure of information -- the Fisher information -- in quantum measurements is further discussed in the context of quantum interferometry.
The scattering of wave packets from a single slit and a double slit with the Schrödinger equation, is studied numerically and theoretically. The phenomenon of diffraction of wave packets in space and time in the backward region, previously found for barriers and wells, is encountered here also. A new phenomenon of forward diffraction that occurs only for packets thiner than the slit, or slits, is calculated numerically as well as, in a theoretical approximation to the problem. This diffraction occurs at the opposite end of the usual diffraction phenomena with monochromatic waves.
Matter-wave interferometry has been largely studied in the last few years. Usually, the main problem in the analysis of the diffraction experiments is to establish the causes for the loss of coherence observed in the interference pattern. In this work, we use different type of environmental couplings to model a two slit diffraction experiment with massive particles. For each model, we study the effects of decoherence on the interference pattern and define a visibility function that measures the loss of contrast of the interference fringes on a distant screen. Finally, we apply our results to t…
We study the diffraction of atoms and weakly-bound three-atomic molecules from a transmission grating at non-normal incidence. Due to the thickness of the grating bars the slits are partially shadowed. Therefore, the projected slit width decreases more strongly with the angle of incidence than the projected period, increasing, in principle, the experimental resolution. The shadowing, however, requires a revision of the theory of atom diffraction. We derive an expression in the style of the Kirchhoff integral of optics and show that the diffraction pattern exhibits a characteristic asymmetry wh…
In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we exhibit various approximations of the electron distribution which facilitate the interpretation of the results. Our derivation is based on the Feynman path integral formula and this work could therefore also serve as an interesting pedagogical introduction to Feynman's formulation of quantum mechanics for university students dealing with the foundations of qua…
The double slit problem is idealized by simplifying each slit by a point source. A composite reduced action for the two correlated point sources is developed. Contours of the reduced action, trajectories and loci of transit times are developed in the region near the two point sources. The trajectory through any point in Euclidian 3-space also passes simultaneously through both point sources.
We introduce diffraction-based interaction-free measurements. In contrast with previous work where a set of discrete paths is engaged, good quality interaction-free measurements can be realized with a continuous set of paths, as is typical of optical propagation. If a bomb is present in a given spatial region -- so sensitive that a single photon will set it off -- its presence can still be detected without exploding it. This is possible because, by not absorbing the photon, the bomb causes the single photon to diffract around it. The resulting diffraction pattern can then be statistically dist…
Atomic diffraction through double slits and transmission gratings is well described in terms of the associated de Broglie waves and classical wave optics. However, for weakly bound and relatively large systems, such as the He_2 dimer, this might no longer hold true due to the possibility of break-up processes and finite-size effects. We therefore study the diffraction of weakly bound two-particle systems. If the bar and slit widths of the grating are much larger than the diameter of the two-particle system we recover the usual optics results. For smaller widths, however, deviations therefrom o…
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…
We analyze Niels Bohr's proposed two-slit interference experiment with highly charged particles that argues that the consistency of elementary quantum mechanics requires that the electromagnetic field must be quantized. In the experiment a particle's path through the slits is determined by measuring the Coulomb field that it produces at large distances; under these conditions the interference pattern must be suppressed. The key is that as the particle's trajectory is bent in diffraction by the slits it must radiate and the radiation must carry away phase information. Thus the radiation field m…
General diffraction properties of aperiodic slit arrays
本文研究了非周期性缝隙阵列的夫琅和费衍射特性，提供了观测干涉极大值峰值的实验条件，并通过实验验证了理论分析。
Interference and diffraction of two-identical-particles are considered in the context of open quantum systems. This theoretical study is carried out within two approaches, the effective time-dependent Hamiltonian due to Caldirola-Kanai (CK) and the Caldeira-Leggett (CL) one where a master equation for the reduced density matrix is used under the presence of dissipation and temperature of the environment. Two simple but very illustrative examples are considered, diffraction by a single and two Gaussian slits by analyzing the mean square separation between particles, single-particle probability …
We address the problem of interference using the Heisenberg picture and highlight some new aspects through the use of pre-selection, post-selection, weak measurements, and modular variables, We present a physical explanation for the different behaviors of a single particle when the distant slit is open or closed: instead of having a quantum wave that passes through all slits, we have a localized particle with non-local interactions with the other slit(s). We introduce a Gedankenexperiment to measure this non-local exchange. While the Heisenberg picture and the Schrodinger pictures are equivale…
Double-slit interference with charged particles. Density matrices and decoherence from time-dependent quantum Monte Carlo
本文利用含时量子蒙特卡洛方法研究带电粒子双缝干涉中的退相干，并展示可直接由单粒子波函数构建含时密度矩阵，无需迹掉环境粒子，从而为理解多体量子动力学提供新途径。
Quantum Origin of Diffraction from Bright and Dark States
基于亮态和暗态框架的连续模式扩展，通过构建单缝衍射的完整探测器基，将衍射图案归因于光子态到单个亮模的投影，并揭示高阶关联中的量子特征。
The Heisenberg uncertainty principle for material objects is an essential corner stone of quantum mechanics and clearly visualizes the wave nature of matter. Here we report a demonstration of the Heisenberg uncertainty principle for the most massive, complex and hottest single object so far, the fullerene molecule C70 at a temperature of 900 K. We find a good quantitative agreement with the theoretical expectation: dx * dp = h, where dx is the width of the restricting slit, dp is the momentum transfer required to deflect the fullerene to the first interference minimum and h is Planck's quantum…
The momentum changes caused by position measurements are a central feature of wave-particle duality. Here we investigate two cases - localization by a single slit, and which-way detection in the double-slit interference experiment - and examine in detail the associated momentum changes. Particular attention is given to the transfer of momentum between particle and detector, and the recoil of the measuring device. We find that single-slit diffraction relies on a form of `interaction-free' scattering, and that an ideal which-way measurement can be made without any back-reaction on the detector.
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。
Single-particle Fraunhofer diffraction in a classical pilot-wave model
针对经典导波模型能否呈现单粒子夫琅禾费衍射的争议，本文采用 Darrow–Bush 拉格朗日模型复现单缝与双缝图样，并揭示两项关键动力学机制。
A which-way measurement in Young's double-slit will destroy the interference pattern. Bohr claimed this complementarity between wave- and particle behaviour is enforced by Heisenberg's uncertainty principle: distinguishing two positions a distance s apart transfers a random momentum q \sim \hbar/s to the particle. This claim has been subject to debate: Scully et al. asserted that in some situations interference can be destroyed with no momentum transfer, while Storey et al. asserted that Bohr's stance is always valid. We address this issue using the experimental technique of weak measurement. …
Time-Varying Strong Coupling and Its Induced Time Diffraction of Magnon Modes
本文通过构建两个磁子模式间的时间变化强耦合，利用频率梳光谱技术表征频率转换，并首次演示磁子模式的双缝时间衍射，为全磁混频器和片上GHz源开辟新途径。
Diffraction in time manifests itself as the appearance of probability-density fringes when a matter wave passes through an opaque screen with abrupt temporal variations of transmission properties. Here we analytically describe the phase-space structure of diffraction-in-time fringes for a class of smooth time gratings. More precisely, we obtain an analytic expression for the Husimi distribution representing the state of the system in the case of time gratings comprising a succession of Lorentzian-like slits. In particular, for a double-slit scenario, we derive a simple and intuitive expression…
In a recent, modified double-pinhole diffraction experiment the existence of an interference pattern was established indirectly along with a near-perfect imaging of the double pinhole. Our theoretical analysis shows that the experiment constitutes a preparation of a quantum state that is, to a good approximation, a joint eigenstate of commuting functions of position and momentum. Gaining information about the momentum distribution by means of the particular experimental setup is thus possible with negligible impact on the position distribution. Furthermore, we construct explicitly a class of s…
As normally used, no commercially available camera has a low-enough dark noise to directly produce video recordings of double-slit interference at the photon-by-photon level, because readout noise significantly contaminates or overwhelms the signal. In this work, noise levels are significantly reduced by turning on the camera only when the presence of a photon has been heralded by the arrival, at an independent detector, of a time-correlated photon produced via parametric down-conversion. This triggering scheme provides the improvement required for direct video imaging of Young's double-slit e…
We explore the hydrodynamic analogues of quantum wave-particle duality in the context of a bouncing droplet system which we model in such a way as to promote comparisons to the de Broglie-Bohm interpretation of quantum mechanics. Through numerical means we obtain single-slit diffraction and double-slit interference patterns that strongly resemble those reported in experiment and that reflect a striking resemblance to quantum diffraction and interference on a phenomenological level. We, however, identify evident differences from quantum mechanics which arise from the governing equations at the …
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…
Tunable Einstein-Bohr recoiling-slit gedankenexperiment at the quantum limit
本文利用光镊中三维冷却至运动基态的单原子，忠实实现了爱因斯坦-玻尔可移动缝隙干涉仪，通过动态调谐原子动量波函数证明了其量子本质，并揭示了由原子加热和进动导致的量子到经典转变。
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