Coherent Elliptic States Research Articles

Suppression of multiphoton intrashell resonances in Li Rydberg atoms

Multiphoton intrashell resonances are observed and measured quantitatively for coherent elliptic states, prepared in orthogonal DC electric and magnetic fields and perturbed by a linearly polarized RF-field. Strong suppressions of the resonances are found at certain values of the eccentricity e of the initial states.

Suppression of multiphoton intrashell resonances in Li Rydberg atoms

Multiphoton intrashell transitions in strongly driven Li ($n=25$) Rydberg atoms are studied experimentally. Orthogonal dc electric and magnetic fields lift the degeneracy of the $n$ shell and define the eccentricity $e$ of the initial coherent elliptic states, which are formed by laser excitation and subsequent adiabatic transformation. The intrashell transitions are driven by a time-harmonic electric field linearly polarized parallel to the major axis of the ellipse. $N$-photon resonances with $N=1\ensuremath{-}9$ are studied as a function of $e$. All resonances with $N\ensuremath{\geqslant}3$ are suppressed at certain $e$ values in between $0$ and $1$. A similar system was analyzed by Yabuzaki et al. [Phys. Rev. A 10, 1955 (1974)] who found a simple pattern of suppressions that applies also for the present experiments. The results of these experimentally confirm that each time $N$ is increased by two, an additional suppression is observed.

Transient intrashell resonances in Rydberg atoms

Rydberg atoms of principal quantum number n in a superposition of a harmonic and a slowly varying field pass through several resonances with the harmonic field of frequency Ω as the splitting ω of the shell by the slow field varies. These transient resonances which are met when ω ≃ NΩ, where N is an integer, have been studied for the n = 25 shell of Li. Coherent elliptic states were prepared and used as initial states, and the dynamics was probed by the probability Pa for the atom to remain in the initial state. The harmonic field was circularly polarized and had constant amplitude, and the slow field varied such that ω at first decreased, then went through a minimum and finally increased to bring the atoms into resonance at two different times. This led to interference patterns in Pa(ω0), where ω0 is the minimum splitting. These were quite regular for coherent elliptic states of low eccentricity e and for strong fields , but less regular for large e and weak . A few states of Li(n = 25) are not hydrogenic due to quantum defects from the (1s)2 core. Without quantum defects the dynamics can be reduced to that of two spin- particles and this reproduces the regular patterns quite well. A full quantal treatment, which is required if quantum defects are important, shows that the more irregular patterns are the result of quite complex dynamics involving non-hydrogenic quasi-eigenstates.

Core-induced chaos in intrashell transitions

Intrashell transitions in Rydberg atoms with a nonhydrogenic core were studied. The degeneracy of the energy shell was lifted by constant electric and magnetic fields and transitions from initial coherent elliptic states (CES) were driven by a harmonic electric field. Evenly spaced hydrogenic resonances dominate at low eccentricities $e$ of the CES. At high $e$, the hydrogenic structures disappear and new structures of a more irregular nature emerge. Classical and quantal calculations are described and are shown to agree fairly well with the experiment. Further, the classical calculations suggest that many of the observed phenomena are a consequence of the underlying classical dynamics being chaotic.

Control of autoionization widths: Doubly excited coherent elliptic states

Doubly excited coherent elliptic states (DECESs) of an atom could be produced by exciting an atomic electron to a Rydberg state, applying the adiabatic field-switching technique to obtain a coherent elliptic state (CES) and by subsequent excitation of an atomic core electron into a low-lying excited state. The DECESs decay by autoionization and radiative transitions. As an example, the autoionization widths are calculated for DECESs in He. The dependence of the widths on the eccentricity of the CES, principal quantum number of the Rydberg electron, orientation of the inner electron orbital and electron exchange is studied and interpreted.

ANALYSIS OF ALKALINE ATOMS IN ELLIPTIC STATES

This paper presents the coherent elliptic states (CES) of alkaline constructed from the spherical Rydberg wavefunctions generated by the B-spline method associated with Hartree–Fock approximation. To construct the elliptic orbit for alkaline is not straightforward. The core effect plays an important role for the formation of elliptic states especially in higher and lower eccentricity. When the eccentricity is not large (i.e. e=0.6), the physical quantities of CES of alkaline atoms can be theoretically calculated by the replacement with hydrogen atom.

QUANTUM ELLIPTIC STATES OF ALKALINE ATOMS

We generate the Hartree–Fock Rydberg wavefunctions of alkaline atoms using the/break B-spline finite basis method and then construct the coherent elliptic states from these spherical wavefunctions. We calculate the lifetimes of the elliptic states as a function of the eccentricities. The results are consistent with previous calculation using the quantum defect theory. The core effects play an important role for the elliptic states of high eccentricities.

The n-dependence of electron capture from Rydbergstates

The cross section, σn, for electron capture by Na+ions from coherent elliptic states (CES) of Li was studiedexperimentally. The dependences on the principal quantumnumber, n, the eccentricity, e, and the spatial orientationof the CES were determined at the two reduced ion velocitiesvr = 1.20 and 1.68 (vr≡v/ve, wherev is the ion speed and ve = 1/n the mean electron speedof the CES in atomic units). The ion velocity, v⃗, wasperpendicular to the minor axis of the CES throughout theexperiment, so the orientation is fully specified by the angle,φ, between v⃗ and the electric dipole moment,d⃗, of the CES. According to a generalized correspondenceprinciple, the reduced cross section,σ̃ = lim n→∞σn/n4, is givenaccurately by classical mechanics, and it is a universalfunction of the scaled parameters of the collision, which in thepresent experiment are vr, e and φ. It isassumed that this result can be extrapolated to the range ofn-values, 20-35, covered in this paper, i.e. σn = σ̃·np where σ̃ andp≃4 depend only weakly on n. The experimental datasupport the assumed existence of a universal cross sectionfunction and the expected n4-dependence is also confirmed atvr = 1.20, but at vr = 1.68 the n-dependence iscloser to n3.

Electron capture from elliptic Rydberg states: impact perpendicular to the minor axis

The total cross section, , for electron capture by Na+ ions from oriented coherent elliptic states (CES) of Li with principal quantum number n = 25 was studied experimentally for impact perpendicular to the minor axis of the elliptic orbit. The remaining geometrical parameters of the CES, which are the eccentricity, e, and the angle, , between the major axis and the beam direction, were varied in the course of the experiments, as was the reduced impact velocity vr = nv, where v is the projectile velocity in atomic units. Several representative cuts were chosen within the parameter space (vr,e,) = (0.74-2.09, 0-1, 0-2). The velocity range includes the region of matching velocities (vr1) where for given geometrical parameters attains its maximum value and the high-velocity region where is a strongly decreasing function of vr. The cross section depends sensitively on each geometrical parameter, and the dependences change dramatically as vr is varied. The spatial distribution of the CES apparently governs in some region of parameter space (vr,e,) and in another the momentum distribution prevails.

Dynamics of Rydberg states in crossed E and B fields: coherent elliptic states

The dynamics of the n = 25 shell of Li atoms in weak electric, E, and magnetic, B, fields was studied experimentally as a function of the rate of change of the electric field strength, , the strength, B, of a constant magnetic field and the angle between the two fixed field directions, . Prior to the variation of E, it was held constant at with strong enough to dominate the Stark-Zeeman manifold for the shell. The uppermost state, which is a coherent elliptic state (CES), was populated selectively by pulsed laser excitation. The field was subsequently varied without rotation from to at the constant rate . It is shown experimentally, in accordance with theory, that the dynamics is described by a single dimensionless parameter given by in atomic units. When the variation of E is so slow that the electron has time to adjust and the population then remains in the uppermost state of the manifold (adiabatic transformation), for smaller the population shifts to an interval of states centred near the middle of the manifold and at the wavefunction is almost frozen and the lowermost part of the manifold populated (diabatic transformation). The experimental findings for near-adiabatic evolution of the CES agree with theoretical results obtained in a non-relativistic, hydrogenic model but discrepancies are seen when non-hydrogenic states are populated for .

Electrostatic cage “Stark barrel” for rapidly switching a uniform electric field through arbitrary angles

A cylindrical arrangement of electrodes, together with control electronics, is described that provides uniform electric fields over cm3 volumes in a vacuum, whose angle and magnitude can be switched on a μs time scale. Full 360° field rotation is achieved, and the device allows access for particle or light beams from all sides. Both numerical and analytic descriptions of the general fields are given. Extension to full three-dimensional field control and other variations are described. The device, which was originally designed for crossed-beam collision experiments with keV energy ions and laser-excited Rydberg atoms in field-directed Stark states or coherent-elliptic states, may be more generally useful in atom trapping and cold collisions or in materials and surface science.

Coherent elliptic states of atoms in non-orthogonal E and B fields

The dynamics of coherent elliptic states in time-dependent electric and magnetic fields has been studied and it is shown that a linear Stark state may be transformed adiabatically into a circular Zeeman state through a continuous range of coherent elliptic states provided the fields vary slowly and are not parallel. The orientation vectors of the elliptic states rotate relative to the fields during the adiabatic transformation except when the fields are orthogonal. The condition for adiabatic behaviour is established for an easily realizable choice of field variation.

Electron capture from coherent elliptic Rydberg states

Experimental relative cross sections for electron capture by singly charged ions (Na{sup +}) from coherent elliptic states of principal quantum number n=25 are presented. An interval of reduced impact velocities from about 1{endash}2 is covered. Absolute reaction cross sections could not be determined precisely, but the eccentricity of the coherent elliptic states and their orientation relative to the ion-impact velocity were varied to expose the dependence of the electron-capture process on the initial motion of the electron. The dependencies on eccentricity and orientation are generally strong and they vary sharply with impact velocity. Qualitatively, the observations agree fairly well with classical trajectory Monte Carlo (CTMC) calculations, as expected for the large quantum numbers involved, but significant deviations of a systematic nature do remain, showing that some aspects of the capture reactions studied are described poorly by classical physics as represented by the CTMC model. {copyright} {ital 1997} {ital The American Physical Society}

Coherent elliptic states in lithium

A detailed comparison between experimental lifetimes for Rydberg atoms formed by the adiabatic crossed-field method and corresponding theoretical lifetimes has been performed to document that the crossed-field method indeed may be used to generate and control coherent elliptic states of highly excited Rydberg atoms. It is found that core effects play a negligible role except for states of very high eccentricity.

Formation of oriented elliptic Rydberg atoms

Oriented elliptic Rydberg atoms have been formed in a thermal beam of Li atoms by the adiabatic crossed-field method. All coherent elliptic quantum states from linear to circular can be produced by this method. The orientation and eccentricity is controlled by the external fields. While the formation of circular states by the crossed-field method has already been established experimentally, the radiative decay of the Rydberg atoms formed here was measured and compared with theory to verify that highly eccentric elliptic quantum states may also be formed.