Avoided Crossings Research Articles

Computational study of the electronic structure of the Srm+Kr (m = 0, 1) van der Waals complexes

A computational study of the electronic structure of the SrKr and Sr+Kr molecular systems is presented in this paper. The theoretical approach is based on the pseudo-potential technique for Sr++Kr interaction and core-valence correlation for the one and two electrons-Sr++Kr interaction. The potential energy surfaces (PESs), spectroscopic parameters, electric dipole moments (EDM), and the vibrational levels’ spacing for all electronic states are calculated. The accuracy of the current spectroscopic results is discussed by comparing them to the available experimental and theoretical data. It is interesting to note that several avoided crossings (ACs) have occurred between the high-lying 2Σ+ excited states. Each curve exhibits ionic and neutral branches in the AC region, yielding the appearance of the ionic character and the illustration of charge transfer.

Spectroscopic and structural investigation for the ground and excited states of CaNa+ molecular ion

In the current theoretical study, we investigated several electronic states correlated with the {Ca+Na+} and {Ca++Na} asymptotic limits of different symmetries (Σ+, Π, Δ). Our calculations were based on ab intio method using semi-empirical pseudo-potential theory of both cores Na+ and Ca2+ and Full Configuration Interaction (FCI). Hence, we computed the adiabatic potential energy curves (PECs) and vibrational levels of the ground state along with several higher states of (CaNa)+ molecular ion. From these curves, we extracted all related spectroscopic parameters (De, D0, Te, Re, Be, ωe and ωeχe). Dipolar properties of (CaNa)+ such as Permanent and Transition Dipole Moments (PDM, TDM) were determined and analyzed. Numerous Avoided Crossings (ACs) were detected in PECs and their reflections were clearly observed in PDM and TDM functions. The strong interactions could lead to significant charge or excitation transfer for atom–ion collisions in the diverse charge or excited states.

Enhancement of quantum speed limit time due to cooperative effects in multilevel systems

Deriving minimum evolution times is of paramount importance in quantum mechanics. Bounds on the speed of evolution are given by the so called quantum speed limit (QSL). In this work we use quantum optimal control methods to study the QSL for driven many level systems which exhibit local two-level interactions in the form of avoided crossings (ACs). Remarkably, we find that optimal evolution times are proportionally smaller than those predicted by the well-known two-level case, even when the ACs are isolated. We show that the physical mechanism for such enhancement is due to non-trivial cooperative effects between the AC and other levels, which are dynamically induced by the shape of the optimized control field.

Avoided-crossing spectroscopy technique based on detection of atoms in metastable states

We present a highly efficient technique for observing an avoided-crossing signal resulting from modified decay branching ratios of excited atomic states in the vicinity of avoided crossings (ACs) formed in tunable external fields. The technique is based on detection of atoms in metastable (MS) states, and we apply it to the case of photoexcited helium atoms which cascade to the singlet and triplet $1s2s$ states in a dc electric field. We show that narrow structures present in the MS atom yield are due to the increased probability to cascade to the triplet MS states at the field strengths at which the ACs emerge. The resolution of the present technique is not limited by the excitation bandwidth, only by the extent to which a homogeneous field can be produced over a limited region of space. Using results of high-precision calculations which include relativistic and QED corrections, we are able to reproduce the dependence of the measured MS atom yield on the electric-field strength.

Low-frequency atomic stabilization and dichotomy in superintense laser fields: Full Floquet results

In the preceding paper we have shown, based on the high-intensity, high-frequency Floquet theory (HIHFFT), that atomic quasistationary stabilization (QS) and dichotomy are not necessarily high-frequency phenomena as widely believed, but can occur also at photon energies small with respect to the unperturbed ground state binding energy, provided that the field is strong enough. In this paper we approach the issue from the point of view of accurate numerical Floquet computations. We have made a comprehensive determination of the Floquet quasienergies for a one-dimensional (1D) atomic model with a soft-core Coulomb potential (ground state energy ${W}_{0}=\ensuremath{-}0.500\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$) in a laser field of constant amplitude ${E}_{0}$ and frequency $\ensuremath{\omega}$. The excursion parameter ${\ensuremath{\alpha}}_{0}={E}_{0}∕{\ensuremath{\omega}}^{2}$ was varied over the range $0l{\ensuremath{\alpha}}_{0}l100$, at two low frequencies $\ensuremath{\omega}=0.12$ and $0.24\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ $(\ensuremath{\omega}l\ensuremath{\mid}{W}_{0}\ensuremath{\mid})$; the lowest-lying 18 states were computed. We present graphs for the ${\ensuremath{\alpha}}_{0}$ dependence of the energies of the states in the field, $W({\ensuremath{\alpha}}_{0})=\mathrm{Re}\phantom{\rule{0.2em}{0ex}}E$ (``Floquet maps''), and their ionization rates $\ensuremath{\Gamma}({\ensuremath{\alpha}}_{0})$. An intricate behavior of $W({\ensuremath{\alpha}}_{0})$ was revealed at low ${\ensuremath{\alpha}}_{0}$, with many crossings, avoided crossings (ACs), and Floquet states materializing or disappearing at multiples of $\ensuremath{\omega}$ energy thresholds. At large ${\ensuremath{\alpha}}_{0}$, however, the uneventful pattern encountered at high frequencies is regained, in which the levels tend monotonically to zero modulo $\ensuremath{\omega}$ (i.e., the binding energies of all states vanish). Also $\ensuremath{\Gamma}({\ensuremath{\alpha}}_{0})$ varies substantially at low ${\ensuremath{\alpha}}_{0}$, attaining sometimes large values, but at large ${\ensuremath{\alpha}}_{0}$ it decreases to zero in an oscillatory manner (QS). The form of the components of the Floquet wave function was also followed from low to large ${\ensuremath{\alpha}}_{0}$, and abrupt changes were found in most cases at ACs. The Floquet results were then compared to a computation of the HIHFFT formulas for the quasienergies and good agreement was found (to within the expected accuracy of HIHFFT). This confirms that HIHFFT is fully capable of describing the low-frequency regime at large enough ${\ensuremath{\alpha}}_{0}$, and in particular the existence of QS and dichotomy.