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.
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.
The two-slit interference experiment has been modelled a number of times using Gaussian wave-packets and the Bohm-de Broglie causal interpretation. Here we consider the experiment with pinholes instead of slits and model the experiment in terms of two-dimensional Gaussian wave-packets and the Bohm-de Broglie causal interpretation.
The double slit experiment provides a standard way of demonstrating how quantum mechanics works. We consider modifying the standard arrangement so that a photon beam incident upon the double slit encounters a polarizer in front of either one or both of the slits.
Based on a re-formulation of the classical explanation of quantum mechanical Gaussian dispersion (Groessing et al. 2010) as well as interference of two Gaussians (Groessing et al. 2012), we present a new and more practical way of their simulation. The quantum mechanical "decay of the wave packet" can be described by anomalous sub-quantum diffusion with a specific diffusivity varying in time due to a particle's changing thermal environment. In a simulation of the double-slit experiment with different slit widths, the phase with this new approach can be implemented as a local quantity. We descri…
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…
We perform a nonlocal double-slit interference experiment with pseudothermal light. The experimental result exhibits a typical double-slit interference fringe in the intensity correlation measurement, in agreement with the theoretical analysis by means of the property of the second-order spatial correlation of field.
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…
Recent work using spontaneous parametric down-conversion (SPDC) has made possible investigations of the Einstein-Podolsky-Rosen paradox in its original (position-momentum) form. We propose an experiment that uses SPDC photon pairs to measure through which slit a photon passes while simultaneously observing double-slit interference.
Young's double slit experiment is formulated in the framework of canonical quantum field theory in view of the modern quantum optics. We adopt quantum scalar fields instead of quantum electromagnetic fields ignoring the vector freedom in gauge theory. The double slit state is introduced in Fock space corresponding to experimental setup. As observables, expectation values of energy density and positive frequency part of current with respect to the double slit state are calculated which give the interference term. Classical wave states are realized by coherent double slit states in Fock space wh…
Double-slit experiment very well lends itself in describing the problem of measuring simultaneously incompatible properties. In such a context, we theoretically design an ideal experiment for spin-7/2 particles, able to produce the entanglement which makes possible the detection.
In this paper we present a double slit experiment where two undistinguishable photons produced by type I PDC are sent each to a well defined slit. Data about the diffraction and interference patterns for coincidences are presented and discussed. An analysis of these data allows a first test of standard quantum mechanics against de Broglie-Bohm theory.
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.
A new scheme for a double-slit experiment in the time domain is presented. Phase-stabilized few-cycle laser pulses open one to two windows (``slits'') of attosecond duration for photoionization. Fringes in the angle-resolved energy spectrum of varying visibility depending on the degree of which-way information are observed. A situation in which one and the same electron encounters a single and a double slit at the same time is discussed. The investigation of the fringes makes possible interferometry on the attosecond time scale. The number of visible fringes, for example, indicates that the sl…
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…
Based on a proposed classical explanation, the quantum mechanical "decay of the wave packet" is shown to simply result from sub-quantum diffusion with a specific diffusivity varying in time due to a particle's changing thermal environment. The exact quantum mechanical intensity distribution, as well as the corresponding trajectory distribution and the velocity field of a Gaussian wave packet are therewith computed. We utilize no quantum mechanics, but only familiar simulation techniques for diffusion, e.g., finite differences or coupled map lattices (CML).
We exploit the notion of which-slit detector introduced by Englert, Scully and Walther (ESW), to show that two incompatible properties can be detected together for each particle hitting the screen, without disturbing the center-of-mass motion of the particle.
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.
The paradoxes of the double-slit and the EPR experiments with particles are shown to originate in the implicit assumption that the particles are always located in the classical space. It is demonstrated that there exists a natural substitute for this assumption that provides a method of resolving the paradoxes.
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…
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…
A modified double slit experiment of light was implemented. In the experiment, a spatial shape filter is used to manipulate the shape of cross section of laser beam. When this modified laser beam was shined on the double slit, the intensity distribution of laser beam on double slit is asymmetrical. In this way, the laser light was directed to pass through only one or two slits of double slit in different sections. So the which-way information is predetermined before the photons pass through the slits. At the same time, the visible interference pattern can be observed on a monitor screen after …
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…
We present a numerical simulation of the double slit interference experiment realized by F. Shimizu, K. Shimizu and H. Takuma with ultracold atoms. We show how the Feynman path integral method enables the calculation of the time-dependent wave function. Because the evolution of the probability density of the wave packet just after it exits the slits raises the issue of the interpreting the wave/particle dualism, we also simulate trajectories in the de Broglie-Bohm interpretation.
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…
The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The experiment is described by a system of contextually labeled binary random variables each of which answers the question: has the particle hit the detector, having passed through a given slit (left or right) in a given state (open or closed)? This system of random variables is a cyclic system of rank 4, formally the same as the system describing the EPR/Bell paradigm with signaling. Unlike the latter, however, the system describing the double-slit experiment is always noncont…
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.
The Fraunhofer diffraction intensity distribution of Laguerre-Gaussian beam is studied in an angular-double-slit interferometer. We demonstrate that the spiral phase structure of vortex light can be clearly revealed in this interference geometry, and it gives us an efficient way to distinguish different order of Laguerre-Gaussian beams. This angular-double-slit interference gives us a better understanding to the nature of orbital angular momentum and the interpretation of vortex beams interference phenomenon.
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.
Time double-slit interference experiments have been achieved and presented as complementary to spatial double-slit interference experiments, providing a further confirmation of the wave-particle duality. Numerical solutions of the free particle time dependent Schrödinger equation were presented as explanation of the experimental results, but have been objected to on the basis that the standard non relativistic quantum theory does not have the property of coherence in time. In this note the theoretical and experimental results are derived in a schematic but analytic solution of the TDSE with ap…
The double-slit experiment strikingly demonstrates the wave-particle duality of quantum objects. In this famous experiment, particles pass one-by-one through a pair of slits and are detected on a distant screen. A distinct wave-like pattern emerges after many discrete particle impacts as if each particle is passing through both slits and interfering with itself. While the direct event-by-event buildup of this interference pattern has been observed for massive particles such as electrons, neutrons, atoms and molecules, it has not yet been measured for massless particles like photons. Here we pr…
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, …
We present a computer simulation model that reproduces, event-by-event, the wave mechanical results of double-slit and two-beam interference experiments. The same model also simulates a one-to-one copy of a single-photon interference experiment with a Fresnel biprism (Jacques V. et al., Eur. Phys. J. D, 35 (2005) 561). The model satisfies Einstein's criterion of local causality and is solely based on experimental facts, comprising the apparatuses used in the experiment and the observation of individual detector clicks. Our results prove that it is possible to give a particle-only description o…
We report a quantum eraser experiment which actually uses a Young double-slit to create interference. The experiment can be considered an optical analogy of an experiment proposed by Scully, Englert and Walther. One photon of an entangled pair is incident on a Young double-slit of appropriate dimensions to create an interference pattern in a distant detection region. Quarter-wave plates, oriented so that their fast axes are orthogonal, are placed in front of each slit to serve as which-path markers. The quarter-wave plates mark the polarization of the interfering photon and thus destroy the in…
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 present a treatment of the double-slit interference of matter-waves represented by Gaussian wavepackets. The interference pattern is modelled with Green's function propagator which emphasizes the coordinate correlations and phases. We explore the connection between phases and position-momentum correlations in the intensity, visibility and predictability of the wavepackets interference. This formulation will indicate some aspects that can be useful for theoretical and experimental treatment of particles, atoms or molecules interferometry.
We study and experimentally implement a double-slit quantum eraser in the presence of a controlled decoherence mechanism. A two-photon state, produced in a spontaneous parametric down conversion process, is prepared in a maximally entangled polarization state. A birefringent double-slit is illuminated by one of the down-converted photons, and it acts as a single-photon two-qubits controlled not gate that couples the polarization with the transversal momentum of these photons. The other photon, that acts as a which-path marker, is sent through a Mach-Zehnder-like interferometer. When the interf…
Permutations of particle labels are usually used to illustrate the relationship between classical and quantum statistics. We use permutations of attributes/properties of particles to express properties of waves. We express events of the well-known two-double-slit experiment (in regimes that are appropriate to quantum interference and classical interference) in terms of symmetries of permutations of particle labels and attributes. We also obtain a new system called residual interference, and suggest an experiment to detect it.
Double-slits provide incoming photons with a choice. Those that survive the passage have chosen from two possible paths which interfere to distribute them in a wave-like manner. Such wave-particle duality continues to be challenged and investigated in a broad range of disciplines with electrons, neutrons, helium atoms, C60 fullerenes, Bose-Einstein condensates and biological molecules. All variants have hitherto involved material constituents. We present a matterless double-slit scenario in which photons generated from virtual electron-positron pair annihilation in head-on collisions of a prob…
We formulate the Schrödinger equation as the equation of motion of a small external influence which serves as the initial boundary condition of a physical system in classical laboratory space. The Hilbert space of possible external influences for a given physical system is then equivalent to the Hilbert space of a quantum system without spin. We discuss the double-slit experiment in the context of this approach and show that wave-particle dualism reduces to the choice of a basis in the geometrical construction of the Hilbert space of small external influences.
As is well known, the double slit experiment contains every key concepts of quantum mechanics such as phase effect, probability wave, quantum interference, quantum superposition. In this article, I will clarify the meaning of quantum superposition in terms of phase effect between states. After applying standard quantum theory, it leads to serious questions about the unitary process of an isolated system. It implies that non collapsing interpretations including many worlds may not be justified. This also could explain that there is no such boundary between classical and quantum domains.
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 …
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…
When both slits of the double slit experiment are open, closing one paradoxically increases the detection rate at some points on the detection screen. Feynman famously warned that temptation to "understand" such a puzzling feature only draws us into blind alleys. Nevertheless, we gain insight into this feature by drawing an analogy between the double slit experiment and a time reversed fire alarm. Much as closing the slit increases probability of a future detection, ruling out fire drill scenarios, having heard the fire alarm, increases probability of a past fire (using Bayesian inference). Cl…
Quantum theory of interference phenomena does not take the diameter of the particle into account, since particles were much smaller than the width of the slits in early observations. In recent experiments with large molecules, the diameter of the particle has approached the width of the slits. Therefore, analytical description of these cases should include a finite particle size. The generic quantum interference setup is an asymmetric double slit interferometer. We evaluate the wave function of the particle transverse motion using two forms of the solution of Schrodinger's equation in an asymm…
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…
A new class of generalized solutions related to the essential spectrum of linear Maxwell's equations is presented. The essential modes are given in terms of normalized singular Weyl's sequences, whose square represents Dirac's delta functions in spatial and angular frequency domains. The action integral associated with essential modes is well-defined. We claim that these modes represent the collapsed state of the electromagnetic field and, with some additional assumptions on the conservation of action, are suitable for describing the double-slit experiment in accordance with the orthodox point…
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 …
We carry out a numerical simulation about the occurrence of interference fringes in experiments where an initial Gaussian wave packet evolves inside a billiard domain with two slits on the boundary. Our simulation extends a previous work by Casati and Prosen and it is aimed to test their surprising conclusion that the fringes disappear in the experiments with fully chaotic billiards. According to the results found, we are led to reassess this remarkable effect of classical dynamics on quantum interference. Actually, we highlight another factor which acts on interference: a symmetry condition (…
Radical-ion-pair reactions were recently shown to represent a rich biophysical laboratory for the application of quantum measurement theory methods and concepts. We here show that radical-ion-pair reactions essentially form a non-linear biochemical double slit interferometer. Quantum coherence effects are visible when "which-path" information is limited, and the incoherent limit is approached when measurement-induced decoherence sets in. Based on this analogy with the optical double slit experiment we derive and elaborate on the fundamental master equation of spin-selective radical-ion-pair re…
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…
