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New Journal of Physics

Scattering of a particle with internal structure from a single slit

Bruce W. Shore, Piroska Dömötör, Emerson Sadurní, Georg Süssmann, Wolfgang P. Schleich

Published Jan 27, 2015• 10 citations
Publisher

Abstract

Classically, rigid objects with elongated shapes can fit through apertures only when properly aligned. Quantum-mechanical particles which have internal structure (e.g. a diatomic molecule) also are affected during attempts to pass through small apertures, but there are interesting differences with classical structured particles. We illustrate here some of these differences for ultra-slow particles. Notably, we predict resonances that correspond to prolonged delays of the rotor within the aperture—a trapping phenomenon not found classically.

DOI
10.1088/1367-2630/17/1/013046

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Classically, rigid objects with elongated shapes can fit through apertures only when properly aligned. Quantum-mechanical particles which have internal structure (e.g. a diatomic molecule) also are affected during attempts to pass through small apertures, but there are interesting differences with classical structured particles. We illustrate here some of these differences for ultra-slow particles. Notably, we predict resonances that correspond to prolonged delays of the rotor within the aperture—a trapping phenomenon not found classically.
Scattering of a quantum particle with internal structure is fundamentally different from that of a point particle and shows quantum effects such as the modification of transmission due to tunnelling and trapping of the particle. As in a preceding paper (Shore et al 2014 New J. Phys. 17 013046 ) we consider a model of a symmetric, rigid rotor travelling through an aperture in a thin but impenetrable screen which is perpendicular to both the direction of motion and the rotation axis. We determine the quantum mechanical properties of this two-dimensional geometrical model using a quasi one-dimensional scattering problem with unconventional boundaries. Our calculations rely on finding the Green's function, which has a direct connection to the scattering matrix. Evaluated on a discrete lattice the Hamiltonian is 'dressed' by a self-energy correction that takes into account the open boundary conditions in an exact way. We find that the passage through the aperture can be suppressed or enhanced as a result of the rotational motion. These effects manifest themselves through resonances in the transmission probability as a function of incident energy and symmetry of the incident wavefunction. We determine the density-of-states to reveal the mode structure of resonant states and to exhibit the lifetimes of temporary trapping within the aperture.
The wave function of an atom, which passed through a diffraction grating, is characterized by a regular space structure. Correspondingly, the interaction of another particle with this atom can be viewed as scattering on an ‘atomic quantum grating’ made of just a single atom. Probing this ‘grating’ by collisions with a charged projectile reveals few-body interference phenomena caused by the coherent contributions of its ‘slits’ to the transition amplitude (the superposition principle) and quantum entanglement of the particles involved. In particular, the spectra of electrons emitted from the atom in collisions with swift ions exhibit a pronounced interference pattern whose shape can be extremely sensitive to the collision velocity.
This article presents a conceptual and experimentally illustrated reinterpretation of the double-slit experiment based on energetic coherence and Δφ-modulation within the Ilefos Model. Using a classical optical setup—including a 532 nm laser, multi-aperture plates, and photodiode detectors—the study investigates how interference patterns transform under different geometrical and observational conditions. Three coherence regimes are documented: (1) baseline interference, (2) complex multi-aperture diffraction, and (3) speckle-pattern coherence under polarization. The results demonstrate how small structural changes in the optical path lead to significant reorganizations of the field’s coherence distribution, supporting the hypothesis that measurement effects may be interpreted as field participation rather than particle-path detection. While the experiment operates in the classical regime (milliwatt intensities, not single photons), the illustrated coherence transitions align with the theoretical Δφ-framework describing how structured energy patterns respond to constraints and observation. This publication serves as a pilot study for future work involving higher-sensitivity detectors and single-photon sources, and provides a conceptual bridge between classical interference behavior and coherence-based interpretations of quantum measurement.
The quantum mechanical two-body problem is analyzed. Separating the center of mass from the relative motion Hamiltonian and focusing on “central potentials,” the stationary Schrödinger equation for the relative motion in spherical coordinates is split into radial and angular equations. The universal angular equation is identified as the eigenvalue equation of the angular momentum operator, whose proper solutions are the spherical harmonics. For fixed interparticle distance, the two-body system is mapped on a “rigid rotor” Hamiltonian, whose eigenstates coincide with the angular momentum eigenstates. In diatomic molecules, timescale separation between fast vibrations (radial motion) and slow rotations (angular motion) enables one to invoke a rigid rotor approximation for interpreting rotational absorption spectrum in the microwave regime. Deviations from the predictions of the rigid rotor model and their manifestation in experiments are analyzed by explicit solution of the stationary Schrödinger equation for two particles in the presence of vibration–rotation coupling.