448 research outputs found
Description of classical and quantum interference in view of the concept of flow line
Bohmian mechanics, a hydrodynamic formulation of quantum mechanics, relies on
the concept of trajectory, which evolves in time in compliance with dynamical
information conveyed by the wave function. Here this appealing idea is
considered to analyze both classical and quantum interference, thus providing
an alternative and more intuitive framework to understand the time-evolution of
waves, either in terms of the flow of energy (for mechanical waves, sound
waves, electromagnetic waves, for instance) or, analogously, the flow of
probability (quantum waves), respectively. Furthermore, this procedure also
supplies a more robust explanation of interference phenomena, which currently
is only based on the superposition principle. That is, while this principle
only describes how different waves combine and what effects these combinations
may lead to, flow lines provide a more precise explanation on how the energy or
probability propagate in space before, during and after the combination of such
waves, without dealing with them separately (i.e., the combination or
superposition is taken as a whole). In this sense, concepts such as
constructive and destructive interference, typically associated with the
superposition principle, physically correspond to more or less dense swarms of
(energy or probability) flow lines, respectively. A direct consequence of this
description is that, when considering the distribution of electromagnetic
energy flow lines behind two slits, each one covered by a differently oriented
polarizer, it is naturally found that external observers' information on the
slit crossed by single photons (understood as energy parcels) is totally
irrelevant for the existence of interference fringes, in striking contrast with
what is commonly stated and taught.Comment: 15 pages, 3 figure
Full quantum mechanical analysis of atomic three-grating Mach-Zehnder interferometry
Atomic three-grating Mach-Zehnder interferometry constitutes an important
tool to probe fundamental aspects of the quantum theory. There is, however, a
remarkable gap in the literature between the oversimplified models and robust
numerical simulations considered to describe the corresponding experiments.
Consequently, the former usually lead to paradoxical scenarios, such as the
wave-particle dual behavior of atoms, while the latter make difficult the data
analysis in simple terms. Here these issues are tackled by means of a simple
grating working model consisting of evenly-spaced Gaussian slits. As is shown,
this model suffices to explore and explain such experiments both analytically
and numerically, giving a good account of the full atomic journey inside the
interferometer, and hence contributing to make less mystic the physics
involved. More specifically, it provides a clear and unambiguous picture of the
wavefront splitting that takes place inside the interferometer, illustrating
how the momentum along each emerging diffraction order is well defined even
though the wave function itself still displays a rather complex shape. To this
end, the local transverse momentum is also introduced in this context as a
reliable analytical tool. The splitting, apart from being a key issue to
understand atomic Mach-Zehnder interferometry, also demonstrates at a
fundamental level how wave and particle aspects are always present in the
experiment, without incurring in any contradiction or interpretive paradox. On
the other hand, at a practical level, the generality and versatility of the
model and methodology presented, makes them suitable to attack analogous
problems in a simple manner after a convenient tuning.Comment: 17 pages, 6 figures (remarkably improved version
Evolution of the wave function of an atom hit by a photon in a three-grating interferometer
In 1995, Chapman et al. (1995 Phys. Rev. Lett. 75 2783) showed experimentally
that the interference contrast in a three-grating atom interferometer does not
vanish under the presence of scattering events with photons, as required by the
complementarity principle. In this work we provide an analytical study of this
experiment, determining the evolution of the atom wave function along the
three-grating Mach-Zehnder interferometer under the assumption that the atom is
hit by a photon after passing through the first grating. The consideration of a
transverse wave function in momentum representation is essential in this study.
As is shown, the number of atoms transmitted through the third grating is given
by a simple periodic function of the lateral shift along this grating, both in
the absence and in the presence of photon scattering. Moreover, the relative
contrast (laser on/laser off) is shown to be a simple analytical function of
the ratio d_p/\lambda_i, where d_p is the distance between atomic paths at the
scattering locus and \lambda_i the scattered photon wavelength. We argue that
this dependence, being in agreement with experimental results, can be regarded
to show compatibility of the wave and corpuscle properties of atoms.Comment: 8 pages, 4 figure
Understanding interference experiments with polarized light through photon trajectories
Bohmian mechanics allows to visualize and understand the quantum-mechanical
behavior of massive particles in terms of trajectories. As shown by
Bialynicki-Birula, Electromagnetism also admits a hydrodynamical formulation
when the existence of a wave function for photons (properly defined) is
assumed. This formulation thus provides an alternative interpretation of
optical phenomena in terms of photon trajectories, whose flow yields a
pictorial view of the evolution of the electromagnetic energy density in
configuration space. This trajectory-based theoretical framework is considered
here to study and analyze the outcome from Young-type diffraction experiments
within the context of the Arago-Fresnel laws. More specifically, photon
trajectories in the region behind the two slits are obtained in the case where
the slits are illuminated by a polarized monochromatic plane wave. Expressions
to determine electromagnetic energy flow lines and photon trajectories within
this scenario are provided, as well as a procedure to compute them in the
particular case of gratings totally transparent inside the slits and completely
absorbing outside them. As is shown, the electromagnetic energy flow lines
obtained allow to monitor at each point of space the behavior of the
electromagnetic energy flow and, therefore, to evaluate the effects caused on
it by the presence (right behind each slit) of polarizers with the same or
different polarization axes. This leads to a trajectory-based picture of the
Arago-Fresnel laws for the interference of polarized light.Comment: 36 pages, 6 figure
Trajectory-based interpretation of Young's experiment, the Arago-Fresnel laws and the Poisson-Arago spot for photons and massive particles
We present a trajectory based interpretation for Young's experiment, the
Arago-Fresnel laws and the Poisson-Arago spot. This approach is based on the
equation of the trajectory associated with the quantum probability current
density in the case of massive particles, and the Poynting vector for the
electromagnetic field in the case of photons. Both the form and properties of
the evaluated photon trajectories are in good agreement with the averaged
trajectories of single photons observed recently in Young's experiment by
Steinberg's group at the University of Toronto. In the case of the
Arago-Fresnel laws for polarized light, the trajectory interpretation presented
here differs from those interpretations based on the concept of "which-way" (or
"which-slit") information and quantum erasure. More specifically, the
observer's information about the slit that photons went through is not relevant
to the existence of interference; what is relevant is the form of the
electromagnetic energy density and its evolution, which will model consequently
the distribution of trajectories and their topology. Finally, we also show that
the distributions of end points of a large number of evaluated photon
trajectories are in agreement with the distributions measured at the screen
behind a circular disc, clearly giving rise to the Poisson-Arago spot.Comment: 8 pages, 5 figure
Lagrangian form of Schr\"odinger equation
Lagrangian formulation of quantum mechanical Schr\"odinger equation is
developed in general and illustrated in the eigenbasis of the Hamiltonian and
in the coordinate representation. The Lagrangian formulation of physically
plausible quantum system results in a well defined second order equation on a
real vector space. The Klein-Gordon equation for a real field is shown to be
the Lagrangian form of the corresponding Schr\"odinger equation.Comment: To appear in Foundation of Physic
Should particle trajectories comply with the transverse momentum distribution?
The momentum distributions associated with both the wave function of a
particle behind a grating and the corresponding Bohmian trajectories are
investigated and compared. Near the grating, it is observed that the former
does not depend on the distance from the grating, while the latter changes with
this distance. However, as one moves further apart from the grating, in the far
field, both distributions become identical.Comment: 10 pages, 7 figure
Metabolic profiling and phenotyping of central nervous system diseases: metabolites bring insights into brain dysfunctions
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