Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSupersymmetry, half-bound states, and grazing incidence reflection
54
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Electromagnetic waves at grazing incidence onto a planar medium are analogous to zero energy quantum particles incident onto a potential well. In this limit waves are typically completely reflected. Here we explore dielectric profiles supporting optical analogues of `half-bound states, allowing for zero reflection at grazing incidence. To obtain these profiles we use two different theoretical approaches: supersymmetric quantum mechanics, and direct inversion of the Helmholtz equation.
rate research
Read More
Grazing incidence interferometry has been applied to rough planar and cylindrical surfaces. As suitable beam splitters diffractive optical phase elements are quite common because these allow for the same test sensitivity for all surface points. But a rotational-symmetric convex aspheric has two curvatures which reduces the measurable region to a meridian through the vortex of the aspheric, which is in contrast to cylindrical surfaces having a one-dimensional curvature which allows the test of the whole surface in gracing incidence. The meridional limitation for rotational-symmetric aspherics nevertheless offers the possibility to measure single meridians in a one-step measurement. An extension to the complete surface can be obtained by rotating the aspheric around its vortex within the frame of the test interferometer.
We here report coherent reflection of thermal He atom beams from various microscopically rough surfaces at grazing incidence. For a sufficiently small normal component $k_z$ of the incident wave-vector of the atom the reflection probability is found to be a function of $k_z$ only. This behavior is explained by quantum-reflection at the attractive branch of the Casimir-van der Waals interaction potential. For larger values of $k_z$ the overall reflection probability decreases rapidly and is found to also depend on the parallel component $k_x$ of the wave-vector. The material specific $k_x$ dependence for this classical reflection at the repulsive branch of the potential is explained qualitatively in terms of the averaging-out of the surface roughness under grazing incidence conditions.
Majorana bound states appearing in 1-D $p$-wave superconductor ($cal{PWS}$) are found to result in exotic quantum holonomy of both eigenvalues and the eigenstates. Induced by a degeneracy hidden in complex Bloch vector space, Majorana states are identified with a pair of exceptional point ($cal{EP}$) singularities. Characterized by a collapse of the vector space, these singularities are defects in Hilbert space that lead to M$ddot{rm o}$bius strip-like structure of the eigenspace and singular quantum metric. The topological phase transition in the language of $cal{EP}$ is marked by one of the two exception point singularity degenerating to a degeneracy point with non singular quantum metric. This may provide an elegant and useful framework to characterize the topological aspect of Majorana fermions and the topological phase transition.
More than eighty years ago, H. Bethe pointed out the existence of bound states of elementary spin waves in one-dimensional quantum magnets. To date, identifying signatures of such magnon bound states has remained a subject of intense theoretical research while their detection has proved challenging for experiments. Ultracold atoms offer an ideal setting to reveal such bound states by tracking the spin dynamics after a local quantum quench with single-spin and single-site resolution. Here we report on the direct observation of two-magnon bound states using in-situ correlation measurements in a one-dimensional Heisenberg spin chain realized with ultracold bosonic atoms in an optical lattice. We observe the quantum walk of free and bound magnon states through time-resolved measurements of the two spin impurities. The increased effective mass of the compound magnon state results in slower spin dynamics as compared to single magnon excitations. In our measurements, we also determine the decay time of bound magnons, which is most likely limited by scattering on thermal fluctuations in the system. Our results open a new pathway for studying fundamental properties of quantum magnets and, more generally, properties of interacting impurities in quantum many-body systems.
We construct the exact position representation of a deformed quantum mechanics which exhibits an intrinsic maximum momentum and use it to study problems such as a particle in a box and scattering from a step potential, among others. In particular, we show that unlike usual quantum mechanics, the present deformed case delays the formation of bound states in a finite potential well. In the process we also highlight some limitations and pit-falls of low-momentum or perturbative treatments and thus resolve two puzzles occurring in the literature.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
