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

arXiv:quant-ph/9710026 · Physical Review A

Atomic versus molecular diffraction: Influence of breakups and finite size

Gerhard C. Hegerfeldt, Thorsten Köhler

Published Mar 1, 1998• 26 citations
arXivHTMLPDF

Abstract

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${}_{2}$.

DOI
10.1103/physreva.57.2021

Related papers

Deviations from classical optics in matter diffraction and determination of the size of weakly bound molecules

Gerhard C. Hegerfeldt, Thorsten Köhler

In atom optics, optical wave theory has been very successful in describing the diffraction of atoms by microfabricated structures. For a molecule, however, with a binding energy smaller than the kinetic energy and with a non-negligible diameter, wave optics may no longer be adequate due to the effects of finite size and breakups. To study the role of the two effects we consider the diffraction of weakly bound diatomic systems such as the helium dimer. We find striking deviations from classical optics, in particular from Babinet's principle, and use the results to clarify the role of finite size and breakups, respectively, in the diffraction from strips, slits, and transmission gratings. As an application the determination of the ${\mathrm{He}}_{2}$ size by transmission through holes and by diffraction experiments is investigated.

Physical Review A•Jan 14, 2000•19 citations

Theoretical challenges in atom optics: Atomic and molecular diffraction by transmission gratings

Gerhard C. Hegerfeldt, Thorsten Köhler

A few years ago, diffraction of atoms by double slits and gratings was achieved for the first time, and standard optical wave-theory provided an excellent description of the experiments. More recently, diffraction of weakly bound molecules and even clusters has been observed. Due to their size and to possible breakup processes optical wave-theory is no longer adequate and a more sophisticated approach is needed. Moreover, surface effects, which can modify the diffraction pattern of atoms and molecules, give rise to further complications. In this article a fully quantum mechanical approach to these questions is discussed.

arXiv:quant-ph/9905090•May 26, 1999•0 citations

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

Mirjana Božić, D. Arsenović, Leposava Vušković

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, $D>{\ensuremath{\delta}}_{1}>{\ensuremath{\delta}}_{2}$.

Physical Review A•May 18, 2004•14 citations

QUANTUM EFFECTS IN MATTER-WAVE DIFFRACTION

Gerhard C. Hegerfeldt, Thorsten Köhler

Advances in micro-technology of the last years have made it possible to carry optics textbooks experiments over to atomic and molecular beams, such as diffraction by a double slit or transmission grating. The usual wave-optical approach gives a good qualitative description of these experiments. However, small deviations therefrom and sophisticated quantum mechanics yield new surprising insights on the size of particles and on their interaction with surfaces.

arXiv:quant-ph/0110163•International Symposium on Quantum Theory and Symmetries (QTS)•Jun 1, 2002•0 citations

Universal diffraction of atoms and molecules from a quantum reflection grating

Bum Suk Zhao, Weiqing Zhang, Wieland Schöllkopf

Since de Broglie's work on the wave nature of particles, various optical phenomena have been observed with matter waves of atoms and molecules. However, the analogy between classical and atom/molecule optics is not exact because of different dispersion relations. In addition, according to de Broglie's formula, different combinations of particle mass and velocity can give the same de Broglie wavelength. As a result, even for identical wavelengths, different molecular properties such as electric polarizabilities, Casimir-Polder forces, and dissociation energies modify (and potentially suppress) the resulting matter-wave optical phenomena such as diffraction intensities or interference effects. We report on the universal behavior observed in matter-wave diffraction of He atoms and He2 and D2 molecules from a ruled grating. Clear evidence for emerging beam resonances is observed in the diffraction patterns, which are quantitatively the same for all three particles and only depend on the de Broglie wavelength. A model, combining secondary scattering and quantum reflection, permits us to trace the observed universal behavior back to the peculiar principles of quantum reflection.

Science Advances•Mar 4, 2016•13 citations

Universal Diffraction of Atomic and Molecular Matter‐Waves: A Comparison of He and D2 Quantum Reflected from a Grating

Weiqing Zhang, Ju Hyeon Lee, Hye Ah Kim +5 more

Abstract Molecular beams of He and D2 are scattered from a ruled diffraction grating in conical‐mount geometry under grazing‐incidence conditions. Fully resolved diffraction patterns as a function of detection angle are recorded for different grating azimuth angles and for two different kinetic energies of the particle beams. Variations in diffraction peak widths are traced back to different velocity spreads of He and D2 determined by time‐of‐flight measurements. A comprehensive analysis of diffraction intensities confirms universal diffraction, that is, for identical de Broglie wavelengths, the relative diffraction intensities for He and D2 are the same. Universal diffraction results from peculiarities of quantum reflection of the atoms and molecules from the diffraction grating. In quantum reflection particles scatter many nanometers in front of the surface from the long‐range attractive branch of the particle–surface interaction potential without probing the potential well and the short‐range repulsive branch of the potential.

ChemPhysChem•Oct 17, 2016•7 citations
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​.
In atom optics, optical wave theory has been very successful in describing the diffraction of atoms by microfabricated structures. For a molecule, however, with a binding energy smaller than the kinetic energy and with a non-negligible diameter, wave optics may no longer be adequate due to the effects of finite size and breakups. To study the role of the two effects we consider the diffraction of weakly bound diatomic systems such as the helium dimer. We find striking deviations from classical optics, in particular from Babinet's principle, and use the results to clarify the role of finite size and breakups, respectively, in the diffraction from strips, slits, and transmission gratings. As an application the determination of the He2{\mathrm{He}}_{2}He2​ size by transmission through holes and by diffraction experiments is investigated.
A few years ago, diffraction of atoms by double slits and gratings was achieved for the first time, and standard optical wave-theory provided an excellent description of the experiments. More recently, diffraction of weakly bound molecules and even clusters has been observed. Due to their size and to possible breakup processes optical wave-theory is no longer adequate and a more sophisticated approach is needed. Moreover, surface effects, which can modify the diffraction pattern of atoms and molecules, give rise to further complications. In this article a fully quantum mechanical approach to these questions is discussed.
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 DDD: $D⪡{\ensuremath{\delta}}_{1}$ 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, $D>{\ensuremath{\delta}}_{1}>{\ensuremath{\delta}}_{2}$.
Since de Broglie's work on the wave nature of particles, various optical phenomena have been observed with matter waves of atoms and molecules. However, the analogy between classical and atom/molecule optics is not exact because of different dispersion relations. In addition, according to de Broglie's formula, different combinations of particle mass and velocity can give the same de Broglie wavelength. As a result, even for identical wavelengths, different molecular properties such as electric polarizabilities, Casimir-Polder forces, and dissociation energies modify (and potentially suppress) the resulting matter-wave optical phenomena such as diffraction intensities or interference effects. We report on the universal behavior observed in matter-wave diffraction of He atoms and He2 and D2 molecules from a ruled grating. Clear evidence for emerging beam resonances is observed in the diffraction patterns, which are quantitatively the same for all three particles and only depend on the de Broglie wavelength. A model, combining secondary scattering and quantum reflection, permits us to trace the observed universal behavior back to the peculiar principles of quantum reflection.
Abstract Molecular beams of He and D2 are scattered from a ruled diffraction grating in conical‐mount geometry under grazing‐incidence conditions. Fully resolved diffraction patterns as a function of detection angle are recorded for different grating azimuth angles and for two different kinetic energies of the particle beams. Variations in diffraction peak widths are traced back to different velocity spreads of He and D2 determined by time‐of‐flight measurements. A comprehensive analysis of diffraction intensities confirms universal diffraction, that is, for identical de Broglie wavelengths, the relative diffraction intensities for He and D2 are the same. Universal diffraction results from peculiarities of quantum reflection of the atoms and molecules from the diffraction grating. In quantum reflection particles scatter many nanometers in front of the surface from the long‐range attractive branch of the particle–surface interaction potential without probing the potential well and the short‐range repulsive branch of the potential.