Quantum correlations of observables for two particle states have demonstrated the nonlocal character of the quantum mechanics. However nonlocality can be exhibited even for noncommuting observables of a single particle system. In this paper we show nonlocality of position-momentum correlations of a single particle in the double-slit experiment modeled by an initially correlated Gaussian wavepacket. The positivity or negativity of the Wigner function for the state of the particle at the detection screen is related with the $σ_{xp}$ covariances. A Bell's inequality is constructed from the Wigner…
In this somewhat pedagogical paper we revisit complementarity relations in bipartite quantum systems. Focusing on continuous variable systems, we examine the influential class of EPR-like states through a generalization to Gaussian states and present some new quantitative relations between entanglement and local interference within symmetric and asymmetric double-double-slit scenarios. This approach is then related to ancilla-based quantum measurements, and weak measurements in particular. Finally, we tie up the notions of distinguishability, predictability, coherence and visibility while draw…
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…
The interference pattern produced by a quantum particle in Young's double-slit setup is attributed to the particle's wavefunction having gone through both slits. In the path integral formulation, this interference involves a superposition of paths, going through either slit, linking the source to the detection point. We show how these paths superpositions can in principle be observed by implementing a series of minimally-perturbing weak measurements between the slits and the detection plane. We further propose a simplified protocol in order to observe these "weak trajectories" with single phot…
基于量子力学高斯色散(Groessing et al. 2010)以及两个高斯干涉(Groessing et al. 2012)的经典解释的重新表述,我们提出了一种新的更实用的模拟方法。量子力学的“波包的衰减“可以用反常的亚量子扩散来描述,由于粒子的热环境变化,特定的扩散率随时间变化。在对不同缝宽的双缝实验的模拟中,这种新方法的相位可以作为一个局部量来实现。我们描述了扩散率的条件,并通过连接到波动力学,我们计算精确的量子力学强度分布,以及相应的轨迹分布根据两个高斯波包从双缝中出现的速度场。我们还计算了概率密度电流分布,包括移相器影响单个狭缝电流的情况,并提供了计算机模拟。
In the the double-slit experiment, nonclassical paths are Feynman paths that go through both slits. Prior work with atom cavities as which-way detectors in the double-slit experiment has shown these paths to be experimentally inaccessible. In this paper, we show how such a setup can indeed detect nonclassical paths with 1% probability if one considers a different type of nonclassical path than previously investigated. We also show how this setup can be used to erase and restore the coherence of the nonclassical paths. Finally, we also show how atom cavities may be used to implement a exact mea…
In which-way double-slit experiments with perfect detectors, it is assumed that having a second detector at the slits is redundant, as it will not change the interference pattern. We however show that if higher-order or non-classical paths are accounted for, the presence of the second detector will have an effect on the interference pattern. Accounting for these non-classical paths also means that the Sorkin parameter in triple-slit experiments is only an approximate measure of Born rule violation. Using the difference between single and double which-way detectors, we give an alternative param…
In classical optics, Young's double-slit experiment with colored coherent light gives rise to individual interference fringes for each light frequency, referring to single-photon interference. However, two-photon double-slit interference has been widely studied only for wavelength-degenerate biphoton, known as subwavelength quantum lithography. In this work, we report double-slit interference experiments with two-color biphoton. Different from the degenerate case, the experimental results depend on the measurement methods. From a two-axis coincidence measurement pattern we can extract complete…
We show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. The key concept of the theory is decoherence, which appears as an inherent characteristic of quantum mechanics and results from the uncertainty relation. In contrast to environment-induced decoherence, this decoherence exists prior to a measurement being made. To clarify our idea, we examine three elemental experiments: a Stern-Gerlach-like experiment, the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment, and the double-slit experiment. By consid…
Event-by-event simulation of double-slit experiments with single photons
我们提出了一个计算机模拟模型,再现,事件的事件,双缝和双光束干涉实验的波动力学结果。相同的模型还模拟了使用菲涅耳双棱镜的单光子干涉实验的一对一副本(Jacques V. EUR. J. D,35(2005)561)。该模型满足爱因斯坦的局部因果关系标准,并且完全基于实验事实,包括实验中使用的设备和对单个探测器点击的观察。我们的结果证明了对单光子双缝实验进行粒子描述是可能的。
The double slit experiment provides a classic example of both interference and the effect of observation in quantum physics. When particles are sent individually through a pair of slits, a wave-like interference pattern develops, but no such interference is found when one observes which "path" the particles take. We present a model of interference, dephasing, and measurement-induced decoherence in a one-dimensional version of the double-slit experiment. Using this model, we demonstrate how the loss of interference in the system is correlated with the information gain by the measuring apparatus…
The determination of the density matrix of an ensemble of identically prepared quantum systems by performing a series of measurements, known as quantum tomography, is minimal when the number of outcomes is minimal. The most accurate minimal quantum tomography of qubits, sometimes called a tetrahedron measurement, corresponds to projections over four states which can be represented on the Bloch sphere as the vertices of a regular tetrahedron. We investigate whether it is possible to implement the tetrahedron measurement of double slit qubits of light, using measurements performed on a single pl…
A double-slit experiment with entangled photons is theoretically analyzed. It is shown that, under suitable conditions, two entangled photons of wavelength $λ$ can behave like a \emph{biphoton} of wavelength $λ/2$. The interference of these biphotons, passing through a double-slit can be obtained by detecting both photons of the pair at the same position. This is in agreement with the results of an earlier experiment. More interestingly, we show that even if the two entangled photons are separated by a polarizing beam splitter, they can still behave like a biphoton of wavelength $λ/2$. In this…
We study the observation of exotic looped trajectories in double-slit experiments with matter waves. We consider the relative intensity at $x=0$ as a function of the time-of-flight from the double-slit to the screen inside the interferometer. This allows us to define a fringe visibility associated to the contribution to the interference pattern given by exotic lopped trajectories. We demonstrate that the Sorkin parameter is given in terms of this visibility and of the axial phases which include the Gouy phase. We verify how this parameter can be obtained by measuring the relative intensity at …
We present a fully local treatment of the double slit experiment in the formalism of quantum field theory. Our exposition is predominantly pedagogical in nature and exemplifies the fact that there is an entirely local description of the quantum double slit interference that does not suffer from any supposed paradoxes usually related to the wave-particle duality. The wave-particle duality indeed vanishes in favour of the field picture in which particles should not be regarded as the primary elements of reality and only represent excitations of some specific field configurations. Our treatment i…
In this study, we solve analytically the Schrodinger equation for a macroscopic quantum oscillator as a central system coupled to two environmental micro-oscillating particles. Then, the double-slit interference patterns are investigated in two limiting cases, considering the limits of uncertainty in the position probability distribution. Moreover, we analyze the interference patterns based on a recent proposal called stochastic electrodynamics with spin. Our results show that when the quantum character of the macro-system is decreased, the diffraction pattern becomes more similar to a classic…
We discuss a parameter estimation problem using quantum decoherece in the double-slit interferometer. We consider a particle coupled to a massive scalar field after the particle passing through the double slit and solve the dynamics non-perturbatively for the coupling by the WKB approximation. This allows us to analyze the estimation problem which cannot be treated by master equation used in the research of quantum probe. In this model, the scalar field reduces the interference fringes of the particle and the fringe pattern depends on the field mass and coupling. To evaluate the contrast and t…
We provide a semiclassical description of the double-slit experiment based on momentous quantum mechanics, where the implementation of canonical variables facilitate the derivation of the equations of motion for the system. We show the evolution of individual particles and their semiclassical trajectories, collectively reproduce the well-known quantum interference pattern. It is found that the non-crossing rule for trajectories, present in Bohmian mechanics, is not required under our treatment. We are able to follow classical configuration variables from this semiclassical scheme, and discuss …
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…
Negative probabilities and Counterfactual Reasoning on the double-slit Experiment
本文试图从基本原理出发,建立负(准)几率分布理论,并将其应用于量子力学双缝实验的研究。我们这样做的方式保留了主要概念问题的完整性,但通过用马赫-曾德干涉仪来表示双缝实验,可以进行更清晰的分析,并表明与双缝相关的量子系统的主要特征也存在于马赫-曾德干涉仪中。这将问题从连续随机变量表示转换为离散随机变量表示。然后,我们表明,马赫-曾德尔干涉仪,不存在负概率是一致的干扰和哪些路径的信息,相反,费曼认为。然而,与Scully et al.的实验,如果我们减少有关系统的实验信息量,并依靠反事实推理,可以为Mach-Zehnder实验构造一个联合负概率分布。
Shahriar S. Afshar claimed that his 2007 modified version of the double-slit experiment violates complementarity [1]. He makes two modifications to the standard double-slit experiment. First, he adds a wire grid that is placed in between the slits and the screen at locations of interference minima. The second modification is to place a converging lens just after the wire grid. The idea is that the wire grid implies the existence of interference minima(wave-like behavior), while the lens can simultaneously obtain which-way information (particle-like behavior). More recently, John G. Cramer [2] …
As per Einstein's design, particles are introduced into the double-slit experiment through a small hole in a plate which can either move up and down (and its momentum can be measured) or be stopped (and its position can be measured). Suppose one measures the position of the plate and this act verifies the statement that the interference pattern is observed in the experiment. However, if it is possible to think about the outcome that one would have obtained if one had measured plate's momentum instead of its position, then it is possible to consider, together with the aforesaid statement, anoth…