Related papers: Detecting level crossings without looking at the s…
We remind the reader that it is possible to tell if two or more eigenvalues of a matrix are equal, without calculating the eigenvalues. We then use this property to detect (avoided) crossings in the spectra of quantum Hamiltonians…
Avoided crossings are fundamental phenomena in quantum mechanics and photonics that originate from the interaction between coupled energy levels and have been extensively studied in linear dispersive dynamics. Their manifestation in open,…
We construct a non-perturbative approach based on quantum averaging combined with resonant transformations to detect the resonances of a given Hamiltonian and to treat them. This approach, that generalizes the rotating-wave approximation,…
The non-crossing rule for the energy levels of a parameter-dependent Hamiltonian is revisited and a flaw in a commonly accepted proof is revealed. Some aspects of avoided crossings are illustrated by means of simple models. One of them…
We investigate states of fermionic atoms across a broad Feshbach resonance in an optical superlattice which allows interaction only among a small number of lattice sites. The states are in general described by superpositions of atomic…
In this paper we consider the problem of avoided crossings (level repulsion) in phononic crystals and suggest a computationally efficient strategy to distinguish them from normal cross points. This process is essential for the correct…
We investigate exceptional points, which are branch point singularities of two resonance eigenstates, in spectra of the hydrogen atom in crossed external electric and magnetic fields. A procedure to systematically search for exceptional…
A highly sensitive, general, and preferably nondestructive technique to detect polar molecules would greatly advance a number of fields, in particular quantum science with cold and ultracold molecules. Here, we propose using resonant energy…
We examine structural and dynamical properties of quantum resonances associated with an avoided crossing and identify the parameter shifts where these properties attain maximal or extreme values, first at a general level, and then for a…
Magnetic Feshbach resonances are an invaluable tool for controlling ultracold atoms and molecules. They can be used to tune atomic interactions and have been used extensively to explore few- and many-body phenomena. They can also be used…
In a recent publication [Phys. Rev. A 79, 065602 (2009)] it was shown that an avoided-crossing resonance can be defined in different ways, according to level-structural or dynamical aspects, which do not coincide in general. Here a simple…
Ultracold atomic gases have realised numerous paradigms of condensed matter physics where control over interactions has crucially been afforded by tunable Feshbach resonances. So far, the characterisation of these Feshbach resonances has…
Due to the absence of degeneracy in one dimension, when a parameter, $\lambda$, of a potential is varied slowly the discrete energy eigenvalue curves, $E_n(\lambda)$, cannot cross but they are allowed to come quite close and diverge from…
We consider controlled collisions between two ultracold atoms guided by external harmonic potentials. We derive analytical solutions of the Schroedinger equation for this system, and investigate the properties of eigenergies and eigenstates…
We report the existence of exceptional points for the hydrogen atom in crossed magnetic and electric fields in numerical calculations. The resonances of the system are investigated and it is shown how exceptional points can be found by…
The ground electronic, vibrational and rotational state of the OH molecule is currently of interest as it can be manipulated by electric and magnetic fields for experimental studies in ultracold chemistry and quantum degeneracy. Based on…
We discover several magnetic Feshbach resonances in collisions of ultracold K(39) atoms, by studying atom losses and molecule formation. Accurate determination of the magnetic-field resonance locations allows us to optimize a quantum…
Feshbach resonances are fundamental to interparticle interactions and become particularly important in cold collisions with atoms, ions, and molecules. Here we present the detection of Feshbach resonances in a benchmark system for strongly…
We observe magnetically tuned collision resonances for ultracold Cs2 molecules stored in a CO2-laser trap. By magnetically levitating the molecules against gravity, we precisely measure their magnetic moment. We find an avoided level…
Given a surface with boundary and some points on its boundary, a polygon diagram is a way to connect those points as vertices of non-overlapping polygons on the surface. Such polygon diagrams represent non-crossing permutations on a surface…