Double-slit Research Articles

Double Slit with an Einstein–Podolsky–Rosen Pair

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 drawing some specific connections between them.

Theoretical study on slit experiments in Rashba electron systems

We develop a theory of designing slit experiments in two-dimensional electron systems with the Rashba spin-orbit interaction. By simulating the spatiotemporal dynamics of electrons passing through a single slit or a double slit, we find that the interference fringes of the electron probability density attain specific spin orientations via the precession of spins around effective magnetic fields mediated by the Rashba spin-orbit interaction whose directions are determined by the propagation path. The spin orientations of the fringes can be controlled by tuning the Rashba spin-orbit parameter, which can be achieved by applying an electric gate voltage. This phenomenon can be exploited to implement electrically tunable transmission of spin information and to generate spin-polarized currents.

Fabrication of the Au Nano-Aperture Array Platform for Single Molecule Analysis

We have fabricated the Au nano-aperture array platforms on the Au films for single molecule analysis. Previously, we reported fabrication of the 200 nm wide double slits with various separations between two nanoslits, and the optical characteristics. In this paper, we will address the optical characteristics of various Au aperture platfoms; the double slits with a 50 nm opening width, the nanoslit array with its opening width less than 100 nm, and the circular type nano-aperture by using 30 keV focused Ga ion beam techniques, along with Au nanopore formation under the high energy electron beam irradiations at 200 keV. For the slit width less than 100 nm, we observed the surface plasmon polariton (SPP)-mediated intraband transmission peak at ∼500 nm, and the SPP-coupled peak around ∼650 nm. The optical intensities are measured to be dependent upon the size of the nano-aperture, the opening width of the slit, and the thickness of the Au film. For a 30 nm slit width, the broadband emission ranging from ∼600 nm to 800 nm were also observed. The fabricated Au plasmonic platforms can be utilized as single molecule bio-sensor.

Resolving strong-field tunneling ionization with a temporal double-slit interferometer

Laser-induced tunneling ionization is one of the most fundamental and ubiquitous quantum processes and it initiates various ultrafast phenomena in intense laser-atom and laser-molecule interactions. Accurately resolving tunneling ionization is essential for understanding these phenomena. Based on the advanced attosecond technologies, such as high-order harmonic spectroscopy and strong-field photoelectron holography, previous studies have resolved the temporal properties of the tunneling process for rescattering electron. Here, as a complement, we theoretically demonstrate the retrieval of the time information of the tunneling process for the direct electron with the temporal double-slit interferometer. In this scheme, a weak second harmonic parallel to the fundamental field is added. By solving the time-dependent Schr\odinger equation, the photoelectron momentum distribution (PEMD) from strong-field tunneling ionization is obtained. Varying the relative phase of the parallel two-color field, the path of the ionized electrons periodically changes, leading to a shift of the time double-slit interference fringes in PEMDs. By analyzing the response of the interference fringes to the perturbation, the time information of direct electron in strong-field tunneling ionization is reconstructed. Interestingly, our results present excellent agreement with the complex time obtained from the quantum-orbit model.

Fabrication of Plasmonic Optical Nanopore Platform for Single Molecule Sensing

Recently there have been significant interests about fabrication of optical nanopore with its diameter range of 5 nm to 10 nm for single molecule analysis and manipulation. However, due to very small amount of the optical intensity through the tiny size of the nano-aperture much smaller than the optical wavelength, the optical intensity enhancement via plasmonic effect by using pore array or periodic groove patterns have been tried. Also, the double slits with nanoscale width are reported to provide the constructive periodic modulation for the transverse-magnetic (TM) wave mode. In this report, the nanoscale double slit with an Au aperture array have been fabricated and optically characterized.

Singleshot polychromatic coherent diffractive imaging with a high-order harmonic source.

Singleshot polychromatic coherent diffractive imaging is performed with a high-intensity high-order harmonic generation source. The coherence properties are analyzed and several reconstructions show the shot-to-shot fluctuations of the incident beam wavefront. The method is based on a multi-step approach. First, the spectrum is extracted from double-slit diffraction data. The spectrum is used as input to extract the monochromatic sample diffraction pattern, then phase retrieval is performed on the quasi-monochromatic data to obtain the sample's exit surface wave. Reconstructions based on guided error reduction (ER) and alternating direction method of multipliers (ADMM) are compared. ADMM allows additional penalty terms to be included in the cost functional to promote sparsity within the reconstruction.

Double-slit interference of single twisted photons

Optical orbital angular momentum (OAM) is a special property of photons and has evoked research onto the light–matter interaction in both classical and quantum regimes. In classical optics, OAM is related to an optical vortex with a helical phase structure. In quantum optics, photons with a twisted or helical phase structure will carry a quantized OAM. To our knowledge, however, so far, no experiment has demonstrated the fundamental property of the OAM at the single-photon level. In this Letter, we have demonstrated the average photon trajectories of twisted photons in a double-slit interference. We have experimentally captured the double-slit interference process of twisted photons by a time-gated intensified charge-coupled device camera, which is trigged by a heralded detection. Our work provides new perspectives for understanding the micro-behaviors of twisted particles and enables new applications in imaging and sensing.

Light interference pattern measurements from automated low-cost Young’s double-slit experiments

Young’s double-slit experiment is commonly used in undergraduate physics laboratory to show the wave nature of light. As an alternative to expensive commercial kits, here we present an automated, low–cost light intensity measurement setup that allows real-time visualization of the interference pattern. The light intensity is measured by a light dependent resistor placed on the head of a dot matrix printer. The head motion is controlled by an Arduino which also collects the data and send them to a computer. The interference pattern obtained by the setup is in agreement with a model that includes the degree of the coherence of the light source and the effective size related to the light collecting area of the resistor. The apparatus allows quantitative data analysis from the measured light patterns and is suitable to be used in undergraduate physics laboratories.

A Double Slit Experiment with Human Subjects

We study a sequence of “double-slit” experiments designed to perform repeated measurements of an attribute in a large pool of subjects using Amazon’s Mechanical Turk. Our findings contrast the prescriptions of decision theory in novel and interesting ways. The response to an identical sequel measurement of the same attribute can be at significant variance with the initial measurement. Furthermore, the response to the sequel measurement depends on whether the initial measurement has taken place. In the absence of the initial measurement, the sequel measurement reveals additional variability, leading to a multimodal frequency distribution which is largely absent if the first measurement has taken place.

De Broglie Waves

There are many evidences in Quantum Mechanics about the existence of de Broglie waves: the two-slit experiment, self interference when a particle can follow two or more paths that converge, etc. There is not direct evidence of its existence because we use exclusively particle detectors. This paper presents a new evidence of the existence of de Broglie waves grounded in the action reaction principle. The action reaction principle is a fundamental ingredient of Physics: when two systems interact both change of state (i.e., they depart from the free, isolated evolution path in the phase space). A simple experiment using a Mach-Zehnder interferometer is analysed. A representation of the evolution in the phase space for different cases (isolated system and interaction with a detector) is shown. By applying the action reaction principle we show that some subsystem, different from the corpuscular photon, must follow one arm of the interferometer when we can infer that the photon follows the other arm. There cannot be interaction between the photodetector in one arm and the photon following the other arm. This new subsystem would be a distributed de Broglie wave.

On the Justification and Validity of the Kennard Inequality

In 1927, Earle Hesse Kennard derived an inequality describing Heisenberg’s uncertainty principle. Since then, we have traditionally been using the standard deviation as the measure of uncertainty in quantum mechanics. But Jan Hilgevoord asserts that the standard deviation is neither a natural nor a generally adequate measure of quantum uncertainty. Specifically, he asserts that the standard deviations are inadequate to use as the quantum uncertainties in the single- and double-slit diffraction experiments. He even tells that from these examples it will become clear that the standard deviation is the wrong concept to express the uncertainty principle generally and that the Kennard relation has little to do with the uncertainty principle. We will investigate what are adequate as the measures of quantum uncertainty. And, beyond that, we will investigate the effects of multiplying the two uncertainties; namely, characteristics which is hiding in deep interior of the Kennard inequality. Through investigations we’ll come to naturally realize that his assertions were wrong. All of our discussions will help raise understanding of the Heisenberg uncertainty principle. Our discussions will afford us an opportunity to think about the essence of the Fourier transform. The aim of this paper is to draw conclusions about whether the Kennard inequality is justified or not.

On the Semi-classical Approach to the Physical Axiomatic of Quantum Mechanics and the New Wave-Particle Interpretation of Light

A new approach to the physical axiomatic of quantum mechanics is proposed. The basis of this approach is the rejection of the idea of an electron as a point particle. To describe the dynamics of the material substance of the electron, a new AMT (Action-Matter-Transfer) equation based on the Hamilton-Jacobi equation is proposed. This nonlinear equation simply transforms into the Schrödinger equation which becomes an intermediate step for solving a more general equation that describes the actual mass and charge density of an electron cloud. The dimensionless density of the material substance of the electron is equal to the square of the wave function. The nonlinearity of the AMT-equation make us question the validity of the quantum mechanical principle of superposition. The representation of an electron as a cloud with a distributed density helps to explain the interference effects in the well-known double-slit experiment. It is shown that light emission can occur in full accordance with classical electrodynamics when the material substance of an electron is spatially redistributed. Our approach makes it possible to interpret light as a chain of photons, each of which represents a “particle” of an electromagnetic wave propagating in space. The direction of radiation can be determined by the axis of rotation of the electron cloud due to the presence of the spin which turns the electron into elementary magnet, so the two electron clouds can form in an atom a stable structure of paired electrons in the form of two hemispheres rotating in one direction. In the framework of the quasi-classical concept of photon generation, the processes of reflection of light, its transmission through a transparent medium, and birefringence are discussed as well as Compton effect and laser emission.

Slit structures: Fundamental mechanisms of mechanical trapping of granular flows

Slit-structures are rigid structures with one or more slits. To retard steep-creek hazards, slit-structures are sometimes installed to reduce the peak discharge, as well as to mechanically trap grains for frictional flows. However, designs are empirical. It is not possible to assess whether boulders will be trapped, or if smaller discharge of harmless flow material can pass downstream. This study starts by reviewing the inherent difficulties of characterising mechanical trapping processes for granular flows. A calibrated Discrete Element Method (DEM) model is then used to conduct a parametric study of the number of slits, the slit spacing, the Froude number and the ratio between grain and slit size. Results from the DEM study allow three interaction regions to be identified: ‘self-cleaning’, ‘unstable’ and ‘trapping’. These regimes are extremely sensitive to the slit number, width and spacing, as well as the Froude number. This study shows that existing recommendations may coincide with the unstable region. However, the unstable region should be avoided because of unpredictable trapping behaviour. Additionally, increasing the slit spacing can increase material trapping because of an increase in the duration of binary grain contacts. This increase in the slit spacing tends to prevent shear transmission from slit to slit. Narrowly-spaced double slits may be most effective at the controlling outflow rate whilst enabling ‘self-cleaning’.

New deep coronal spectra from the 2017 total solar eclipse

Context. The origin of the high temperature of the solar corona, in both the inner bright parts and the more outer parts showing flows toward the solar wind, is not understood well yet. Total eclipses permit a deep analysis of both the inner and the outer parts of the corona using the continuum white-light (W-L) radiations from electrons (K-corona), the superposed spectrum of forbidden emission lines from ions (E-corona), and the dust component with F-lines (F-corona). Aims. By sufficiently dispersing the W-L spectrum, the Fraunhofer (F) spectrum of the dust component of the corona appears and the continuum Thomson radiation can be evaluated. The superposed emission lines of ions with different degrees of ionization are studied to allow the measurement of temperatures, non-thermal velocities, Doppler shifts, and abundances to constrain the proposed heating mechanisms and understand the origin of flows that lead to solar wind. Methods. We describe a slit spectroscopic experiment of high spectral resolution to provide an analysis of the most typical parts of the quasi-minimum type corona observed during the total solar eclipse of Aug. 21, 2017 from Idaho, USA. Streamers, active region enhancements, and polar coronal holes (CHs) are measured well using deep spectra. Results. Sixty spectra are obtained during the totality with a long slit, covering ±3 solar radii in the range of 510 nm to 590 nm. The K+F continuum corona is exposed well up to two solar radii. The F-corona can be measured even at the solar limb. New weak emission lines were discovered or confirmed. The rarely observed Ar X line is detected almost everywhere; the Fe XIV and Ni XIII lines are clearly detected everywhere. For the first time hot lines are also measured inside the CH regions. The radial variations of the non-thermal turbulent velocities of the lines do not show a great departure from the average values. No significantly large Doppler shifts are seen anywhere in the inner or the middle corona. The wings of the Fe XIV line show some non-Gaussianity. Conclusions. Deep slit coronal spectra offered an opportunity for diagnosing several aspects of coronal physics during a well observed total eclipse without extended investments. The analysis of the ionic emission line profiles offers several powerful diagnostics of the coronal dynamics; the precise measurement of the F-continuum component provides insight into the ubiquitous dust corona at the solar limb.

Decrypting the Central Mystery of Quantum Mathematics:

This article proposes a solution to the double slit experiment of Quantum Mechanics. We attack the problem from a previously untried angle. Unsolved math problems must be attacked from unexpected angles because every conventional approach has already been tried and failed. Richard Feynman warned that the quantum world is such a strange place that humans can’t understand it. There is empirical evidence of particles following zero energy waves backwards, although that is counterintuitive. Schr˝odinger waves carry zero energy: they carry probability amplitudes instead. In our proposed model zero energy Schr˝odinger waves emanating from every point on the target screen pass backwards through the two slits, interfere at the particle gun, and a particle randomly chooses which wave to follow backwards. Once that decision is made the particle follows its wave with a probability of one, through only one slit (it doesn’t matter which slit) and inevitably strikes that point from which its wave emanates. This produces the same math and same pattern on the target screen. We propose three Axioms of the Theory of Elementary Waves (TEW) as a better platform for mathematics in this experiment than the Axioms of QM. This constitutes a paradigm shift.

Stereographic geometry of coherence and which-path information.

Recently, it was shown that quantum entanglement is an indispensable part of the duality behavior of light. Here we report a surprisingly intimate connection between the stereographic projection and the duality-entanglement nature of a single photon. We show that the duality-entanglement relation [Optica5, 942 (2018)OPTIC82334-253610.1364/OPTICA.5.000942] naturally emerges from the stereographic projection geometry. We demonstrate that this geometry is complementarity sensitive, in the sense that it is sensitive to the particle nature, wave nature, and entanglement nature of a single photon.

Schwinger’s picture of quantum mechanics III: The statistical interpretation

Schwinger’s algebra of selective measurements has a natural interpretation in the formalism of groupoids. Its kinematical foundations, as well as the structure of the algebra of observables of the theory, were presented in [F. M. Ciaglia, A. Ibort and G. Marmo, Schwinger’s picture of quantum mechanics I: Groupoids, Int. J. Geom. Meth. Mod. Phys. (2019), arXiv: 1905.12274 [math-ph]. https://doi.org/10.1142/S0219887819501196 . F. M. Ciaglia, A. Ibort and G. Marmo, Schwinger’s picture of quantum mechanics II: Algebras and observables, Int. J. Geom. Meth. Mod. Phys. (2019). https://doi.org/10.1142/S0219887819501366 ]. In this paper, a closer look to the statistical interpretation of the theory is taken and it is found that an interpretation in terms of Sorkin’s quantum measure emerges naturally. It is proven that a suitable class of states of the algebra of virtual transitions of the theory allows to define quantum measures by means of the corresponding decoherence functionals. Quantum measures satisfying a reproducing property are described and a class of states, called factorizable states, possessing the Dirac–Feynman “exponential of the action” form are characterized. Finally, Schwinger’s transformation functions are interpreted similarly as transition amplitudes defined by suitable states. The simple examples of the qubit and the double slit experiment are described in detail, illustrating the main aspects of the theory.

Three-dimensional dynamic numerical simulation of a Brazilian disc of concrete with variation of dip angle of parallel double slits

In order to study the influence of the change of the inclination angle of parallel double slits on concrete disk under dynamic load, we establish a three-dimensional dynamic numerical model of the flattened Brazilian disc by using finite element method. Non-uniform distribution of concrete materials has been realized in the model by adopting Weibull statistical theory. Moreover, we study the effect of variation of dip angle of parallel double slits on crack propagation pattern under stress wave, and obtain both diagrams of the complete failure process and acoustic emission of crack initiation, propagation and penetration. The results show that the failure of the specimen is cleavage and the direction of new crack growth is consistent with that of the dynamic load, the acoustic emission activity decreases with the increase of the dip angle of the prefabricated slits; the bigger the dip angle of prefabricated parallel double slits is, the bigger the peak load is, and the less the accumulated energy of acoustic emission is, the less likely the specimen is to be damaged.

Turbulence-free two-photon double-slit interference with coherent and incoherent light.

This article reports a study on a turbulence-free Young's double-slit interferometer. When the environmental turbulence blurs out the classic Young's double-slit interference completely, a two-photon interference pattern is still observable from the measurement of intensity or photon number fluctuation correlation. This two-photon interferometer always produces a turbulence-free interference pattern, when the double-slit interferometer is utilizing both first-order spatially incoherent light and spatially coherent light. This type of two-photon interferometer establishes new capabilities in optical observations and sensing measurements that require high sensitivity and stability.

Phasor field waves: experimental demonstrations of wave-like properties.

Time-of-flight (ToF) non-line-of-sight (NLoS) imaging reconstructs images of scenes with light that have undergone diffuse reflections. While, in the past, ToF light propagation and reconstruction methods have been described using their own inverse methods, it has recently been shown that ToF light transport can be described as the propagation of a wave, allowing it to be modeled by the same methods that are applied for direct imaging with electromagnetic or sound waves. This wave of fluctuating optical irradiance is called the phasor field (P-field) wave. Here, we perform a series of experiments to show the wave-like behavior of this P-field wave. We design a P-field source and detector and use them to demonstrate interference of P-field waves in a double slit experiment, as well as mutually-independent focusing and imaging of P-field waves and their optical carrier. Besides establishing the properties of P-field waves, our work demonstrates that imaging of ToF signals is possible without any computation enabling fast and energy-efficient NLoS imaging systems.