Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Interference of small and of large quantum particles behind an asymmetric grating

Mirjana Božić, D. Arsenović, Leposava Vušković

Published May 18, 2004• 14 citations
Publisher

Abstract

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 before the rise of molecular interferometry. In the experiments with large molecules, the diameter of the particle has approached the width of the slits. Therefore, an analytical description of these cases should include a finite particle size. An asymmetric double-slit grating seems to be very suitable for the study of the influence of a particle's size on the interference pattern. We identify three characteristic cases for the ratio of slit widths ${\ensuremath{\delta}}_{1}$ and ${\ensuremath{\delta}}_{2}$ and the particle diameter $D$: $D⪡{\ensuremath{\delta}}_{1}$ and $D⪡{\ensuremath{\delta}}_{2}$, ${\ensuremath{\delta}}_{1}>D>{\ensuremath{\delta}}_{2}$, and $D>{\ensuremath{\delta}}_{1}>{\ensuremath{\delta}}_{2}$. Taking into account the influence of both slits on the particle wave function, regardless of through which slit the particle passed, we treat the particle-wall interaction in a simple fashion, such that if the particle size is greater than the slit opening there is no transmission. The transverse momentum distribution is independent of the distance from the slits and the particle size, while the space distribution strongly depends on this distance and the particle size. We found that the interference is absent only when the particle's diameter is larger than both slit widths, $D>{\ensuremath{\delta}}_{1}>{\ensuremath{\delta}}_{2}$.

DOI
10.1103/physreva.69.053618

Related papers

An asymmetric double-slit interferometer for small and large quantum particles

Bozic, Mirjana, Arsenovic, Dusan, Vuskovic, Lepsa

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 asymmetric interferometer: the Fresnel-Kirchhoff form and the form derived from the transverse wave function in the momentum representation. The transverse momentum distribution is independent of the distance from the slits, while the space distribution strongly depends on this distance. Based on the transverse momentum distribution we determined the space distribution of particles behind the slits. We will present two cases: a) when the diameter of the particle may be neglected with respect to the width of both slits, and b) when the diameter of the particle is larger than the width of the smaller slit.

arXiv:quant-ph/0305189•May 30, 2003•3 citations

Theory Of Interference Of Large Molecules

Mirjana Božić, D. Arsenović, Milena Davidović

In the experiments with large molecules, the diameter of particles has approached the width of the slits. Therefore, a theoretical description of these cases should include a finite particle size. We are developing a theory of quantum interference which takes into account the trajectories and the size of particles. The theory uses a distribution of transverse momenta of particles to describe emergence of an interference pattern during accumulation of single particle arrivals to the screen. In this way we are accomplishing the task which Barut assigned to theoretical physicists by writing: “It now becomes a task of theoretical physics to build models and theories of single events, and a task of experimental physics to record more of single events”.

AIP conference proceedings•Jan 1, 2007•0 citations

Atomic versus molecular diffraction: Influence of breakups and finite size

Gerhard C. Hegerfeldt, Thorsten Köhler

Atomic diffraction through double slits and transmission gratings is well described in terms of the associated de Broglie waves and classical wave optics. However, for weakly bound and relatively large systems, such as the He${}_{2}$ dimer, this might no longer hold true due to the possibility of breakup processes and finite-size effects. We therefore study the diffraction of weakly bound two-particle systems. If the bar and slit widths of the grating are much larger than the diameter of the two-particle system, we recover the usual optics results. For smaller widths, however, deviations therefrom occur. We find that the location of possible diffraction peaks is indeed still governed by the usual grating function from optics, but the peaks may have a lower intensity. This is not unexpected when breakup processes are allowed. More unusually though, diffraction peaks that would be absent for de Broglie waves may reappear. The results are illustrated for diffraction of He${}_{2}$.

arXiv:quant-ph/9710026•Physical Review A•Mar 1, 1998•26 citations

A Crucial Experiment To Test The Broglie-Bohm Trajectories For Indistinguishable Particles

Michel Gondran, Alexandre Gondran

The standard quantum theory has not taken into account the size of quantum particles, the latter being implicitly treated as material points. The recent interference experiments of Zeilinger [3] with large molecules like fullerenes and the thought experiments of Bozic et al [7] with asymmetrical Young slits make it possible today to take into account the particle size. We present here a complete study of this phenomenon where our simulations show differences between the particles density after the slits and the modulus square of the wave function. Then we propose a crucial experiment that allows us to reconsider the wave-particle duality and to test the existence of the Broglie-Bohm trajectories for indistinguishable particles.

arXiv:quant-ph/0603200•Mar 22, 2006•0 citations

Quantum behavior in the Double Slit Experiment and the limitations of the equipment used.

Ernest Heinz

Abstract: Many problems exist in the Double Slit Experiment when you consider that the elements in the test are moving as waves. Outside of the pattern resembling peeks and troughs that overlap each other; there is no real scientific explanation on how this is taking place. In a more accurate and classical way, can we explain how the dark and light areas of the interference pattern are being made? Why is an Interference pattern being made when particles are being sent through the exercise one at a time? And how is it that through observation the Interference pattern collapses in on itself. Waves add more questions than they do answers, a very typical outcome of an incorrect solution. Maybe the unanswered questions left behind by the wave theory is a confirmation of its inaccuracy and not the mystique of its results. Rather than double down on the wave theory with time traveling particles, elements of duality, and the Copenhagen Interpretation; l reconsidered that elements tested in the double slit experiment behave as particles. But this time, I weighed the thought that these bits of matter are much smaller than previously thought. This new logic allowed particles with straight trajectories to interact with the edge of materials used in the double slit wall in a very detailed way. This created a storm of new ways to look at what is really taking place in the test; revealing the competence of the detectors utilized and the capacity of the Nonlinear Optical Crystal. Everything solved from just one idea, that quantum move as particles but on a much smaller scale. This is the enigma of the Double Slit Experiment.

•May 1, 2018•0 citations

Interference Phenomena: Exploring the Essential Mystery

Frank S. Levin

Abstract Chapter 11 introduces the essential mystery of quantum mechanics, shows how it is resolved, and then goes on to examine related phenomena. The mystery is how individual photons, not electromagnetic waves, can give rise to the interference pattern seen in the two-slit experiment. They are shown to do so because the relevant quantum amplitude is a linear combination of two terms, leading to the pattern when neither slit is identified as the one the photon went through, but collapsing to one term and no pattern if the slit is identified. Similar results are shown to occur when individual electrons are incident on the two slits, and when large molecules, which have de Broglie wavelengths, are scattered by diffraction gratings. Many other interference experiments are described, including those where a photon was shown to be in two places simultaneously and one where a photon displayed both wave and particle features.

•Sep 21, 2017•0 citations
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 before the rise of molecular interferometry. In the experiments with large molecules, the diameter of the particle has approached the width of the slits. Therefore, an analytical description of these cases should include a finite particle size. An asymmetric double-slit grating seems to be very suitable for the study of the influence of a particle's size on the interference pattern. We identify three characteristic cases for the ratio of slit widths \ensuremathδ1{\ensuremath{\delta}}_{1}\ensuremathδ1​ and \ensuremathδ2{\ensuremath{\delta}}_{2}\ensuremathδ2​ and the particle diameter DDD: D⪡\ensuremathδ1D⪡{\ensuremath{\delta}}_{1}D⪡\ensuremathδ1​ and D⪡\ensuremathδ2D⪡{\ensuremath{\delta}}_{2}D⪡\ensuremathδ2​, \ensuremathδ1>D>\ensuremathδ2{\ensuremath{\delta}}_{1}>D>{\ensuremath{\delta}}_{2}\ensuremathδ1​>D>\ensuremathδ2​, and D>\ensuremathδ1>\ensuremathδ2D>{\ensuremath{\delta}}_{1}>{\ensuremath{\delta}}_{2}D>\ensuremathδ1​>\ensuremathδ2​. Taking into account the influence of both slits on the particle wave function, regardless of through which slit the particle passed, we treat the particle-wall interaction in a simple fashion, such that if the particle size is greater than the slit opening there is no transmission. The transverse momentum distribution is independent of the distance from the slits and the particle size, while the space distribution strongly depends on this distance and the particle size. We found that the interference is absent only when the particle's diameter is larger than both slit widths, D>\ensuremathδ1>\ensuremathδ2D>{\ensuremath{\delta}}_{1}>{\ensuremath{\delta}}_{2}D>\ensuremathδ1​>\ensuremathδ2​.
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 asymmetric interferometer: the Fresnel-Kirchhoff form and the form derived from the transverse wave function in the momentum representation. The transverse momentum distribution is independent of the distance from the slits, while the space distribution strongly depends on this distance. Based on the transverse momentum distribution we determined the space distribution of particles behind the slits. We will present two cases: a) when the diameter of the particle may be neglected with respect to the width of both slits, and b) when the diameter of the particle is larger than the width of the smaller slit.
In the experiments with large molecules, the diameter of particles has approached the width of the slits. Therefore, a theoretical description of these cases should include a finite particle size. We are developing a theory of quantum interference which takes into account the trajectories and the size of particles. The theory uses a distribution of transverse momenta of particles to describe emergence of an interference pattern during accumulation of single particle arrivals to the screen. In this way we are accomplishing the task which Barut assigned to theoretical physicists by writing: “It now becomes a task of theoretical physics to build models and theories of single events, and a task of experimental physics to record more of single events”.
Atomic diffraction through double slits and transmission gratings is well described in terms of the associated de Broglie waves and classical wave optics. However, for weakly bound and relatively large systems, such as the He2{}_{2}2​ dimer, this might no longer hold true due to the possibility of breakup processes and finite-size effects. We therefore study the diffraction of weakly bound two-particle systems. If the bar and slit widths of the grating are much larger than the diameter of the two-particle system, we recover the usual optics results. For smaller widths, however, deviations therefrom occur. We find that the location of possible diffraction peaks is indeed still governed by the usual grating function from optics, but the peaks may have a lower intensity. This is not unexpected when breakup processes are allowed. More unusually though, diffraction peaks that would be absent for de Broglie waves may reappear. The results are illustrated for diffraction of He2{}_{2}2​.
The standard quantum theory has not taken into account the size of quantum particles, the latter being implicitly treated as material points. The recent interference experiments of Zeilinger [3] with large molecules like fullerenes and the thought experiments of Bozic et al [7] with asymmetrical Young slits make it possible today to take into account the particle size. We present here a complete study of this phenomenon where our simulations show differences between the particles density after the slits and the modulus square of the wave function. Then we propose a crucial experiment that allows us to reconsider the wave-particle duality and to test the existence of the Broglie-Bohm trajectories for indistinguishable particles.
Abstract: Many problems exist in the Double Slit Experiment when you consider that the elements in the test are moving as waves. Outside of the pattern resembling peeks and troughs that overlap each other; there is no real scientific explanation on how this is taking place. In a more accurate and classical way, can we explain how the dark and light areas of the interference pattern are being made? Why is an Interference pattern being made when particles are being sent through the exercise one at a time? And how is it that through observation the Interference pattern collapses in on itself. Waves add more questions than they do answers, a very typical outcome of an incorrect solution. Maybe the unanswered questions left behind by the wave theory is a confirmation of its inaccuracy and not the mystique of its results. Rather than double down on the wave theory with time traveling particles, elements of duality, and the Copenhagen Interpretation; l reconsidered that elements tested in the double slit experiment behave as particles. But this time, I weighed the thought that these bits of matter are much smaller than previously thought. This new logic allowed particles with straight trajectories to interact with the edge of materials used in the double slit wall in a very detailed way. This created a storm of new ways to look at what is really taking place in the test; revealing the competence of the detectors utilized and the capacity of the Nonlinear Optical Crystal. Everything solved from just one idea, that quantum move as particles but on a much smaller scale. This is the enigma of the Double Slit Experiment.
Abstract Chapter 11 introduces the essential mystery of quantum mechanics, shows how it is resolved, and then goes on to examine related phenomena. The mystery is how individual photons, not electromagnetic waves, can give rise to the interference pattern seen in the two-slit experiment. They are shown to do so because the relevant quantum amplitude is a linear combination of two terms, leading to the pattern when neither slit is identified as the one the photon went through, but collapsing to one term and no pattern if the slit is identified. Similar results are shown to occur when individual electrons are incident on the two slits, and when large molecules, which have de Broglie wavelengths, are scattered by diffraction gratings. Many other interference experiments are described, including those where a photon was shown to be in two places simultaneously and one where a photon displayed both wave and particle features.