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Journal of Physics B Atomic Molecular and Optical Physics

Dynamics of Rydberg states in crossedEandBfields: coherent elliptic states

P Sørensen, J. C. Day, Brett D DePaola, Thomas Ehrenreich, Erik Horsdal-Pedersen, L Kristensen

Published Jan 1, 1999• 11 citations

Abstract

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 .

DOI: 10.1088/0953-4075/32/5/013

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Physical Review A•Sep 20, 2005•5 citations

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 .

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.

The evolution of Rydberg states of Li in time-dependent fields was studied with special emphasis on the influence of the Li(1s2)+ core. The strengths and rates-of-change of the fields were such that the dynamics involves states of only a single shell (intrashell dynamics). For sufficiently slow variations, the Rydberg states are transformed adiabatically but for faster variations, intrashell transitions do occur. We present experimental approximate probabilities for adiabatic transformation of the Rydberg states and compare with theoretical predictions with and without core effects included. The core can perturb the dynamics significantly. Circumstances under which this is likely to be the case are discussed.

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 ? as the splitting ? of the shell by the slow field varies. These transient resonances which are met when ? N?, 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 ? 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(?0), where ?0 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.

Electron capture cross sections for coherent elliptic Rydberg states have been measured as a function of eccentricity. The ion impact velocity was parallel to the minor axis of the associated, classical elliptic orbit and both clockwise and anticlockwise orbital motion of the electron were studied. The incoming ions were 2.5 keV 23 Na + and the Rydberg target, with principal quantum number n=25, was formed by laser excitation of Li atoms with subsequent adiabatic switching of crossed, external electric and magnetic fields. A strong dependence on eccentricity and sense of orbital motion was found.

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.

Field ionization of high Rydberg manifold states

(n=112\text{--}137)

of rubidium-85 under a rotating electric field has been investigated experimentally and theoretically. Applying a rapidly reversed electric field with a small static perpendicular field to rotate the total electric field around zero, we have observed substantial increase of the fraction of the tunneling field-ionization process and a profound broadening of its ionization peak over a wide range of field strengths with increasing transverse electric field. The observed tunneling field-ionization fraction is almost independent of the slew rate of the applied electric field, and also on the principal quantum number

n

over the range investigated. To compare with these experimental results, theoretical calculations have been performed with a successive two-step regime. As the first step we calculated the redistributions of magnetic quantum number ${m}_{\ensuremath{\ell}}$ and parabolic quantum number ${n}_{1}\ensuremath{-}{n}_{2}$ of the states under the rotating electric field. Then the following time evolution of the manifold states with $\ensuremath{\mid}{m}_{\ensuremath{\ell}}\ensuremath{\mid}\ensuremath{\leqslant}3$ was traced on the Stark map in a coherent as well as an incoherent model. The calculated results are generally in good agreement with the experimental ones. The increase of the tunneling field-ionization fraction under a rotating electric field plays an essential role in achieving the high efficiency in the recently proposed selective-field-ionization scheme for high Rydberg atoms.