Young's double-slit experiment requires two waves produced simultaneously at two different points in space. In quantum mechanics the waves correspond to a single quantum object, even as complex as a big molecule. An interference is present as long as one cannot tell for sure which slit is chosen by the object. The more we know about the path, the worse the interference. In the paper we show that quantum mechanics allows for a dual version of the phenomenon: self-interference of waves propagating through a single slit but at different moments of time. The effect occurs for time-independent Hamiltonians and thus should not be confused with Moshinsky-type time-domain interference, a consequence of active modulation of parameters of the system (oscillating mirrors, chopped beams, time-dependent apertures, moving gratings, etc.). The discussed phenomenon is counterintuitive even for those who are trained in quantum interferometry. For example, the more we know about the trajectory in space, the better the interference. Exactly solvable models lead to formulas deceptively similar to those from a Youngian analysis. There are reasons to believe that this new type of quantum interference was already observed in atomic interferometry almost three decades ago, but was misinterpreted and thus rejected as an artifact of unknown origin.
Young's double-slit experiment requires two waves produced simultaneously at two different points in space. In quantum mechanics the waves correspond to a single quantum object, even as complex as a big molecule. An interference is present as long as one cannot tell for sure which slit is chosen by the object. The more we know about the path, the worse the interference. In the paper we show that quantum mechanics allows for a dual version of the phenomenon: self-interference of waves propagating through a single slit but at different moments of time. The effect occurs for time-independent Hamiltonians and thus should not be confused with Moshinsky-type time-domain interference, a consequence of active modulation of parameters of the system (oscillating mirrors, chopped beams, time-dependent apertures, moving gratings, etc.). The discussed phenomenon is counterintuitive even for those who are trained in quantum interferometry. For example, the more we know about the trajectory in space, the better the interference. Exactly solvable models lead to formulas deceptively similar to those from a Youngian analysis. There are reasons to believe that this new type of quantum interference was already observed in atomic interferometry almost three decades ago, but was misinterpreted and thus rejected as an artifact of unknown origin.
Young's double-slit experiment \cite{Young} requires two waves produced simultaneously at two different points in space. In quantum mechanics the waves correspond to a single quantum object, even as complex as a big molecule. An interference is present as long as one cannot tell for sure which slit is chosen by the object. The more we know about the path, the worse the interference. In the paper we show that quantum mechanics allows for a dual version of the phenomenon: self-interference of waves propagating through a single slit but at different moments of time. The effect occurs for time-independent Hamiltonians and thus should not be confused with Moshinsky-type time-domain interference \cite{Moshinsky}, a consequence of active modulation of parameters of the system (oscillating mirrors, chopped beams, time-dependent apertures, moving gratings, etc.). The discussed phenomenon is counterintuitive even for those who are trained in quantum interferometry. For example, the more we know about the trajectory in space, the better the interference. Exactly solvable models lead to formulas deceptively similar to those from a Youngian analysis. There are reasons to believe that this new type of quantum interference was already observed in atomic interferometry almost three decades ago, but was misinterpreted and thus rejected as an artifact of unknown origin.
In Young's Double Slit Experiment (YDE) and improved versions, waves causing interference travel different distances.As speed of light is constant, waves require different time spans to reach the point of interference.Thereby, if the waves are generated simultaneously at the slits/source, they cannot meet on the screen anywhere outside the mid-line.Formation of fringes is commonly interpreted as interference caused by the meeting (super-positioning) of two waves generated simultaneously.The reality is that fringes are formed by interference of waves generated at different times.However, unless impacted by other phenomena, two waves generated at different times converging to form fringes, as this paper shows, will mandatorily come in same phase to the interference point, producing constructive interference.Interference observed, however, is not only constructive.The effect on the phase of waves while bending (diffraction) is also to be considered.Consequently, it addresses three phenomena causing phase shifts: (1)different starting times,(2)bending at slits, and (3)distances traveled (In contrast, the first two are overlooked by the conventional approach).(Dirac and Feynman Path Integral methods on quantum particles have different approaches).The paper reveals the widespread misconception in the analysis of YDE and would impact the wave/particle and other YDE interpretations.
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.
In recent years, matter-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and the study of fundamental aspects of quantum theory. Diffraction and interference of matter waves can be observed not only at a spatial aperture (such as a screen edge, slit, or grating), but also at a time-domain aperture (such as an absorbing barrier, or ``shutter,'' that is being periodically switched on and off). The wave phenomenon of the latter type is commonly referred to as ``diffraction in time.'' Here, we introduce a versatile, exactly solvable model of diffraction in time. It describes time evolution of an arbitrary initial quantum state in the presence of a time-dependent absorbing barrier, governed by an arbitrary aperture function. Our results enable a quantitative description of diffraction and interference patterns in a large variety of setups, and may be used to devise new diffraction and interference experiments with atoms and molecules.
For centuries Young’s double-slit interference continues to be a hot discussion subject about whether light is waves or particles. This work unravels the self-interference parados, and sheds light on such a concept that assumes a photon can split, self-interfere, and recombine. This work elucidates how coherent photons from a laser source could produce a double-slit interference pattern without the hypothesis of unphysical splitting and recombination of a single photon. Unlike the conventional single wave-function description for the whole ensemble of particles, we develop a pilot-wave trajectory approach to track every photon’s wave-packet propagation and calculate the evolution of the interference intensity in time. We demonstrate how wave packets and phase coherence affect the interference pattern. To resolve the century-old self-interference paradox, we show that such an hypothesis is unnecessary, and the illusion is due to the long coherence length of laser photons and overlaps of delocalized light wave packets.
Interference by division of wavefront. The two-slit experiment Preliminary remarks In this chapter we shall be concerned with various types of interference effects exhibited by matter waves. It might be argued that all quantum mechanical phenomena are ultimately a consequence of interference, being governed as they are by a linear wave equation. Of particular interest here is the analogue for material waves of Young's double-slit experiment in optics, a classic problem in the history of quantum theory. Feynman, Leighton & Sands (1965) state that it ‘ … has in it the heart of quantum mechanics. In reality, it contains the only mystery’. We shall also treat the process of tunnelling into classically forbidden regions, a phenomenon which also involves interference in an essential way. To observe the interference of waves issuing from a common source we must split the emerging beam into two spatially separated coherent parts and subsequently recombine them (the superposition of waves from physically independent sources is a many-body problem – see §§8.8 and 12.7). As in optics there are two methods of achieving this: by division of wavefront where, for example, a wave falls on a screen containing two apertures, and by division of amplitude in which a wave is incident on a semi-transparent barrier. Interference effects achieved by the first method, discussed in this section, have been observed for electrons (Jönsson, 1961; Lichte, 1986; Tonomura et al ., 1989), neutrons (Zeilinger et al ., 1988) and (helium) atoms (Carnal & Mlynek, 1991).