Phase-space picture of resonance creation and avoided crossings (original) (raw)

Dynamics of quasibound state formation in the driven Gaussian potential

Physical Review E, 2008

The quasibound states of a particle in an inverted-Gaussian potential interacting with an intense laser field are studied using complex coordinate scaling and Floquet theory. The dynamics of the driven system is different depending on whether the driving field frequency is less than or greater than the ionization frequency. As the laser field strength is increased, a new quasibound state emerges as the result of a pitchfork bifurcation in the classical phase space. Changes in the time-averaged "dressed potential" appear related to this bifurcation and provide additional confirmation of the role of the bifurcation on the emergence of a new quasibound state. The Husimi plots of the quasibound state residues reveal strong support on the periodic orbits of the bifurcation at frequencies above the ionization frequency.

Avoided crossing resonances: Structural and dynamical aspects

Physical Review A, 2009

We examine structural and dynamical properties of quantum resonances associated with an avoided crossing and identify the parameter shifts where these properties attain extreme values. Thus the concept of avoided crossing resonance can be defined in different ways, which do not coincide in the general case. These definitions are described first at a general level, and then for a two-level system coupled to a harmonic oscillator, of the type commonly found in quantum optics. Finally the results obtained are exemplified and applied to optimize the fidelity and speed of quantum gates in trapped ions.

Orbiting resonances and bound states in molecular scattering

Physical Review A, 2002

A family of orbiting resonances in molecular scattering is globally described by using a single pole moving in the complex angular momentum plane. The extrapolation of this pole at negative energies gives the location of the bound states. Then a single pole trajectory, that connects a rotational band of bound states and orbiting resonances, is obtained. These complex angular momentum singularities are derived through a geometrical theory of the orbiting. The downward crossing of the phase-shifts through π/2, due to the repulsive region of the molecular potential, is estimated by using a simple hard-core model. Some remarks about the difference between diffracted rays and orbiting are also given.

Classical resonances in quantum mechanics

Physical Review A, 1992

%e study the role of classical resonances in quantum systems subjected to a periodic external force. It is demonstrated that classical invariant vortex tubes determine the structure of Floquet states "captured" by resonances in the classical phase space. In addition, resonance quantum numbers are introduced. The analysis of simple model calculations leads to a qualitative description of nonperturbative phenomena relevant for the interaction of atoms or molecules with strong, short laser pulses.

The influence of classical resonances on quantum energy levels

The Journal of Chemical Physics, 1993

In this paper, we examine the behavior of the quantum energy levels of a coupled oscillator system as the zero-order frequencies are varied to carry the corresponding classical system through a resonance. We find that the levels exhibit a pattern that is characteristic of the resonance. This pattern consists of clusters of levels, each containing a number of curves that run roughly parallel to one another and a number of curves that undergo pairwise narrowly avoided crossings. Adiabatic switching calculations show that the "parallel" curves are associated with states within the classical resonance region, while the narrowly avoiding curves are associated with states that are outside this region. It is further shown that the curves describing resonance states are formed from zero-order nonresonant curves by the overlap of many avoided crossings. This reorganization of multiply intersecting lines into parallel curves reflects the classical reorganization of phase space at a resonance.

Periodic orbits of perturbed non-axially symmetric potentials in 1:1:1 and 1:1:2 resonances

Discrete & Continuous Dynamical Systems - B, 2018

We analytically study the Hamiltonian system in R 6 with Hamiltonian H = 1 2 (p 2 x + p 2 y + p 2 z) + 1 2 (ω 2 1 x 2 + ω 2 2 y 2 + ω 2 3 z 2) + ε(az 3 + z(bx 2 + cy 2)), being a, b, c ∈ R with c = 0, ε a small parameter, and ω1, ω2 and ω3 the unperturbed frequencies of the oscillations along the x, y and z axis, respectively. For |ε| > 0 small, using averaging theory of first and second order we find periodic orbits in every positive energy level of H whose frequencies are ω1 = ω2 = ω3/2 and ω1 = ω2 = ω3, respectively (the number of such periodic orbits depends on the values of the parameters a, b, c). We also provide the shape of the periodic orbits and their linear stability.

Instability of Pre-Existing Resonances Under a Small Constant Electric Field

Annales Henri Poincaré, 2014

Two simple model operators are considered which have pre-existing resonances. A potential corresponding to a small electric field, f , is then introduced and the resonances of the resulting operator are considered as f → 0. It is shown that these resonances are not continuous in this limit. It is conjectured that a similar behavior will appear in more complicated models of atoms and molecules. Numerical results are presented.

Classical resonance overlapping and quantum avoided crossings

Physical Review Letters, 1987

It is pointed out that for pulsed rotators the classical resonance-overlapping criterion for the onset of chaotic motion implies the existence of avoided crossings among an arbitrarily large number of quantum levels at the classical limit 6 small, nb =2 close to a classical resonance.

Correspondence between classical and quantum resonances

Physical Review E, 2021

Bifurcations take place in molecular Hamiltonian nonlinear systems as the excitation energy increases, leading to the appearance of different classical resonances. In this paper, we study the quantum manifestations of these classical resonances in the isomerizing system CN-Li Li-CN. By using a correlation diagram of eigenenergies versus Planck constant, we show the existence of different series of avoided crossings, leading to the corresponding series of quantum resonances, which represent the quantum manifestations of the classical resonances. Moreover, the extrapolation of these series toh = 0 unveils the correspondence between the bifurcation energy of classical resonances and the energy of the series of quantum resonances in the semiclassical limith → 0. Additionally, in order to obtain analytical expressions for our results, a semiclassical theory is developed.

Computation of resonances by two methods involving the use of complex coordinates

Physical Review A, 1993

We have studied two different systems producing resonances, a highly excited multielectron Coulombic negative ion (the He 2s2p P state) and a hydrogen atom in a magnetic field, via the complexcoordinate rotation (CCR) and the state-specific complex-eigenvalue Schrodinger equation (CESE) approaches. For the He 2s2p P resonance, a series of large CCR calculations, up to 353 basis functions with explicit r;, dependence, were carried out to serve as benchmarks. For the magnetic-field problem, the CCR results were taken from the literature. Comparison shows that the state-specific CESE theory allows the physics of the problem to be incorporated systematically while keeping the overall size of the computation tractable regardless of the number of electrons.