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

Quantum mechanics and Talbot revivals on a tetrahedron

Jakub Bělín, S. A. R. Horsley, Tomáš Tyc

Published Sep 9, 2019• 3 citations
Publisher

Abstract

We analyze the propagation of waves on the surface of the simplest Platonic solid, the regular tetrahedron. We find that the time evolution of a quantum particle confined to such a surface is equivalent to the diffraction pattern from a certain grating profile and can therefore be investigated in a simple diffraction experiment. The quantum particle exhibits perfect quantum state revivals, which translate into the fractional Talbot effect in the diffraction pattern. We present the results of such an experiment and compare them with numerical simulations.

DOI
10.1103/physreva.100.033806

Related papers

The quantum Talbot effect on a sphere

J H Hannay, Amy Lockwood

Any quantum (Schrödinger) wavefunction on a sphere is necessarily periodic in time. The corresponding statement down one dimension, for a circular line instead, is the quantum version of the 'Talbot effect' for a diffraction grating in paraxial optics (which is fully analogous to quantum mechanics). In the circle case the 'revival' of any initial wavefunction at the period, or 'Talbot time', is accompanied by a kind of partial revival at any rational fraction of the period, increasing in complexity for less simple fractions. In particular, any piecewise constant initial wavefunction is again piecewise constant at such times. By contrast, in the sphere case, the simplest piecewise constant wave, constant on hemispheres is shown not to retain its piecewise constancy at rational fractions of the period, but instead, rather strikingly, to develop infinities at calculable locations. The calculation requires the uniform asymptotic form of the Legendre polynomials together with the Poisson sum formula leading to Gauss sums.

Journal of Physics A Mathematical and Theoretical•Sep 4, 2008•5 citations

Tetrahedron as a quantum self-imaging system

Jakub Bělín, S. A. R. Horsley, Tomáš Tyc

We found a full analytical solution to Schrodinger equation on a simple enclosed surface: a regular tetrahedron. The time evolution of a wavefunction on it is then completely equivalent to an optical Talbot effect.

Imaging and Applied Optics•Jan 1, 2019•0 citations

Optical simulation of quantum mechanics on the Möbius strip, Klein’s bottle and other manifolds, and Talbot effect

Jakub Bělín, Tomáš Tyc, S. A. R. Horsley

Abstract We analyse the evolution of the wavefunction of a quantum particle propagating on several compact manifolds, including the Klein bottle, Möbius strip and projective plane. We find analytically the stationary states and the energy spectrum and show that the wavefunction exhibits perfect revivals. Using the orbifold structure of the discussed manifolds, we establish the relation of wave evolution on the manifolds to Fresnel diffraction and consequently to the Talbot effect. This connection provides a novel method of optical simulation of the quantum motion on compact manifolds. We discuss some novel phenomena as well as the effects of topology on the properties of the waves on the manifolds.

New Journal of Physics•Feb 9, 2021•8 citations

A causal look into the quantum Talbot effect

Ángel S. Sanz, Salvador Miret-Artés

A well-known phenomenon in both optics and quantum mechanics is the so-called Talbot effect. This near field interference effect arises when infinitely periodic diffracting structures or gratings are illuminated by highly coherent light or particle beams. Typical diffraction patterns known as quantum carpets are then observed. Here the authors provide an insightful picture of this nonlocal phenomenon as well as its classical limit in terms of Bohmian mechanics, also showing the causal reasons and conditions that explain its appearance. As an illustration, theoretical results obtained from diffraction of thermal He atoms by both N-slit arrays and weak corrugated surfaces are analyzed and discussed. Moreover, the authors also explain in terms of what they call the Talbot-Beeby effect how realistic interaction potentials induce shifts and distortions in the corresponding quantum carpets.

arXiv:quant-ph/0702224•The Journal of Chemical Physics•Jun 18, 2007•71 citations

Quantum analysis on the Talbot effect of two-dimensional grating

Xing Xu, Gaokun Huang, Sumei Zhou

In this paper, we discuss some light diffraction phenomena with a simple quantum theory. Firstly, the wave function of the free particle in quantum mechanics is used to explain Fraunhofer diffraction of the light at a rectangular aperture, and the result is consistent with the Huygens-Fresnel principle. Secondly, probabilistic wave method is used to analyze the Talbot effect of a two-dimensional grating. The results show that the photons at the Talbot distance and incident photons are described by the same probability wave. Finally, Talbot effect is used to measure the wavelength of incident light.

Holography, Diffractive Optics, and Applications•Nov 7, 2018•1 citation

Demonstration of the temporal matter-wave Talbot effect for trapped matter waves

Manfred J Mark, Elmar Haller, Johann G Danzl +3 more

We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to tenth order.

arXiv:1105.0295•New Journal of Physics•Aug 10, 2011•25 citations
We analyze the propagation of waves on the surface of the simplest Platonic solid, the regular tetrahedron. We find that the time evolution of a quantum particle confined to such a surface is equivalent to the diffraction pattern from a certain grating profile and can therefore be investigated in a simple diffraction experiment. The quantum particle exhibits perfect quantum state revivals, which translate into the fractional Talbot effect in the diffraction pattern. We present the results of such an experiment and compare them with numerical simulations.
Any quantum (Schrödinger) wavefunction on a sphere is necessarily periodic in time. The corresponding statement down one dimension, for a circular line instead, is the quantum version of the 'Talbot effect' for a diffraction grating in paraxial optics (which is fully analogous to quantum mechanics). In the circle case the 'revival' of any initial wavefunction at the period, or 'Talbot time', is accompanied by a kind of partial revival at any rational fraction of the period, increasing in complexity for less simple fractions. In particular, any piecewise constant initial wavefunction is again piecewise constant at such times. By contrast, in the sphere case, the simplest piecewise constant wave, constant on hemispheres is shown not to retain its piecewise constancy at rational fractions of the period, but instead, rather strikingly, to develop infinities at calculable locations. The calculation requires the uniform asymptotic form of the Legendre polynomials together with the Poisson sum formula leading to Gauss sums.
Abstract We analyse the evolution of the wavefunction of a quantum particle propagating on several compact manifolds, including the Klein bottle, Möbius strip and projective plane. We find analytically the stationary states and the energy spectrum and show that the wavefunction exhibits perfect revivals. Using the orbifold structure of the discussed manifolds, we establish the relation of wave evolution on the manifolds to Fresnel diffraction and consequently to the Talbot effect. This connection provides a novel method of optical simulation of the quantum motion on compact manifolds. We discuss some novel phenomena as well as the effects of topology on the properties of the waves on the manifolds.
A well-known phenomenon in both optics and quantum mechanics is the so-called Talbot effect. This near field interference effect arises when infinitely periodic diffracting structures or gratings are illuminated by highly coherent light or particle beams. Typical diffraction patterns known as quantum carpets are then observed. Here the authors provide an insightful picture of this nonlocal phenomenon as well as its classical limit in terms of Bohmian mechanics, also showing the causal reasons and conditions that explain its appearance. As an illustration, theoretical results obtained from diffraction of thermal He atoms by both N-slit arrays and weak corrugated surfaces are analyzed and discussed. Moreover, the authors also explain in terms of what they call the Talbot-Beeby effect how realistic interaction potentials induce shifts and distortions in the corresponding quantum carpets.
In this paper, we discuss some light diffraction phenomena with a simple quantum theory. Firstly, the wave function of the free particle in quantum mechanics is used to explain Fraunhofer diffraction of the light at a rectangular aperture, and the result is consistent with the Huygens-Fresnel principle. Secondly, probabilistic wave method is used to analyze the Talbot effect of a two-dimensional grating. The results show that the photons at the Talbot distance and incident photons are described by the same probability wave. Finally, Talbot effect is used to measure the wavelength of incident light.