Summary. A modified version of the two-slit experiment is proposed in which the moveable detector/counter used to obtain the fringe distribution by counting single photons at different positions on the screen plane is replaced with a mirror positioned at an angle to the screen plane. A single photon arriving at the mirror through one of the slits is reflected at one of two angles along one of two divergent paths. It is then detected by one of two detectors, one on each of the paths, for different positions of the mirror on the screen plane. This modification results in the ability to generate which way information based on the path taken by the reflected photon as well as the distribution of photon counts on the screen plane, one for each slit. Since the photon does not experience any change other than the reflection at the mirror the question whether fringes are also present because of a priori interference effects when no mirror is present can be answered by examining the two a posteriori distributions. Three possible outcomes are considered and explanations proposed for them. The experiment is shown to be feasible with existing technology and can be performed in most physics laboratories.
Summary. A modified version of the two-slit experiment is proposed in which the moveable detector/counter used to obtain the fringe distribution by counting single photons at different positions on the screen plane is replaced with a mirror positioned at an angle to the screen plane. A single photon arriving at the mirror through one of the slits is reflected at one of two angles along one of two divergent paths. It is then detected by one of two detectors, one on each of the paths, for different positions of the mirror on the screen plane. This modification results in the ability to generate which way information based on the path taken by the reflected photon as well as the distribution of photon counts on the screen plane, one for each slit. Since the photon does not experience any change other than the reflection at the mirror the question whether fringes are also present because of a priori interference effects when no mirror is present can be answered by examining the two a posteriori distributions. Three possible outcomes are considered and explanations proposed for them. The experiment is shown to be feasible with existing technology and can be performed in most physics laboratories.
3.1 Interference of a Single Photon The kinds of study originally conducted by Thomas Young - in particular, the celebrated "double slit" experiment that we briefly examined in Chapter 1 (see Fig. 1) - provide a capacity to reveal far more than the wave nature of light, important as that is. True enough, the observed characteristic fringe pattern, when monochromatic light passes through two closely spaced slits onto a screen, appears to be simply explicable on the basis of waves from each slit undergoing constructive and destructive interference at different positions on the screen. Yet, astonishingly, these patterns of interference are still exhibited when individual photons of a low-intensity input beam reach the screen one at a time, showing that it cannot in fact be a matter of different photons having to interfere with each other. Indeed, Dirac enunciated the general principle that photons can never directly interact with each other. The double slit and other such experiments indicate that each photon interacts in a delocalized, wave-like manner with both slits at the same time. Successive experiments build interference patterns that conform to an exact mathematical distribution formula, but the position at which an individual photon is detected in any particular instance cannot be predicted; this is a quintessential illustration of quantum uncertainty. Using the path integral approach of quantum theory, the phenomenon is more accurately represented by introducing a summation over all possible routes between the source and the screen on which the pattern appears, signifying an entire "lifetime" for each photon involved in the experiment. This relates to the fact that the actual trajectory is unknown without an observation, and thus we only obtain the probabilities of the photon striking the screen at different positions and times; all trajectories (potentialities) must be considered in a superposition. Each route is considered equally probable, and the variation in phase produces quantum interference. The differences in phase of each trajectory, at varying positions on the screen, generates the fringe pattern. An intriguing variation on this experiment involves "marking" the photons so that the actual route of each photon to the screen is known. Remarkably, in such a case, the fringe patterns do not appear because quantum interference cannot occur. A consequence of the observation of the photon route is an effect that, in other quantum mechanical connections, is known as a collapse of the wavefunction. However, it is possible for the fringe patterns to reappear when information on the route of the photons is lost; this is known as a quantum eraser.
This research was conducted to note the changes in the interference patterns, by different means of reflection. For this, we have used a double slit, different mirrors, and a screen to obtain the image. The hypothesis behind this was that double slit produces a fringe patten on a screen when a coherent light source is passed through it, but what if we put a mirror after the slits and obtain an image on a screen. Not just that, what if we put different kinds of mirrors in between the slit and the screen. We conducted this research in an environment with negligible sources of light except the non-coherent light source, and with negligible vibrations which could affect the image obtained. When this research was conducted with a flat mirror, fringes were roughly the same as predicted by mathematical calculations. But when this research was conducted by a convex mirror, the fringes seemed to be virtual . When this same study was conducted with a concave mirror, the fringes seemed to be either concentrated at a single point, or they seemed to be have enlarged with a virtual image however the ratio of magnified image to the actual image that have been obtained if there was no mirror, remained the same. Whereas in the case of a convex mirror, the image was smaller. This property is useful as it can be used to observe the pattern more precisely by magnifying it and the actual numbers, i.e.- when mirror would not have been used can also be calculated because the magnification is the same.
We know that bright fringes on the observation-screen is the Fourier transform of light intensity that passes through diffraction slit (aperture) and we know according to Parseval and Rayleigh Theorems the power or energy of a function before and after Fourier transform is not changed that means the total intensity of light emerging slits is equal to the total intensity of bright fringes on the observation screen, but on the other hand according to destructive and constructive interference of light, some portions of the light passing through the slits destructively interfere to constitute dark fringes which means the total light intensity of fringes should be less than the total intensity passing through the slit. This is a violation of the Fourier transform. On the other hand, this paper is augmented by some very new experiments which show there are no photons in the dark fringes. A diffraction experiment by sticking narrow and small width mirrors on the dark fringes that according to the classical interpretation after destructive interference on the dark fringes should be reflected and could be found by sensors at other directions (specially reflection angle) and another experiment that by making a 1mm hole in the middle of the first dark fringe, we expect that photons can be detected by the light detector after destructive interference (passing through one another) behind the observation plan but no photon is detected. Finally, this paper provides a complete physical model associated with mathematical analysis and formulation that is based on the Schrödinger equation. This model answers to single Photon (electron) double-slit experiment with a high degree of accuracy.
We report a two-photon double-slit interference experiment. Two correlated photons, generated by spontaneous parametric downconversion and traveling in different directions, are made to pass through a double slit in such a way that the path of one photon can be identified with that of the other photon. No single-photon interference pattern is observed even if the path is not actually identified, but a spatial interference pattern appears in the joint detection counting rates of the photon pairs. It can easily be shown that these nonlocal phenomena cannot be exhibited by any kind of classical field.
Principle of quantum superposition permits a photon to interfere with itself. As per the principle of causality, a photon must pass through the double-slit prior to its detection on the screen to exhibit interference. In this paper, a double-slit quantum interference experiment with reversible detection of Einstein-Podolsky-Rosen quantum entangled photons is presented. Where a photon is first detected on a screen without passing through a double-slit, while the second photon is propagating towards the double-slit. A detection event on the screen cannot affect the second photon with any signal propagating at the speed of light, even after its passage through the double-slit. After the detection of the first photon on the screen, the second photon is either passed through the double-slit or diverted towards a stationary photon detector. Therefore, the question of whether the first photon carries the which-path information of the second photon in the double-slit is eliminated. No single photon interference is exhibited by the second photon, even if another screen is placed after the double-slit.
Abstract The double slit experiment was the first demonstrative proof of the wave nature of light. It was expounded by the English physician-physicist Thomas Young in 1801 and it soon helped lay to rest the then raging Newton–Huygens debate on whether light consisted of a fast-moving stream of particles or a train of progressive waves in the ether medium. In the experiment, light is made to pass through two very narrow slits spaced closely apart. A screen placed on the other side captures a pattern of alternating bright and dark bands called fringes which are formed as a result of the phenomenon of interference. In prior work by the same author, it was shown that the conventional analysis of Young’s experiment that is used in many introductory physics textbooks, suffers from a number of limitations in regards to its ability to accurately predict the positions of these fringes on the distant screen. This was owing to the adoption of some needless and paradoxical assumptions to help simplify the geometry of the slit barrier-screen arrangement. In the new analysis however, all such approximations were discarded and a hyperbola theorem was forwarded which was then suitably applied to determine the exact fringe positions on screens of varied shapes (linear, semi-circular, semi-elliptical). This paper further builds on that work by laying down the mathematical framework necessary for counting fringes and then comparing their distributions on differently shaped screens, using MATLAB software package for numerical–graphical simulation. In addition, a pair of equivalent laws of proportionality are predicted that govern the distribution of fringes independent of the shape of the detection screen employed.