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Journal of Physics B Atomic Molecular and Optical Physics

Transient intrashell resonances in Rydberg atoms

Daniel E. Fregenal, Morten Førre, Erik Horsdal, Christian Fisker, N A Kjær

Published May 6, 2008• 2 citations

Abstract

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.

DOI: 10.1088/0953-4075/41/10/105003

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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.

We have investigated experimentally and theoretically the dynamics of Stark-Zeeman split states in Li(

n=25

) Rydberg atoms when they are exposed to a superposition of a slowly varying field and a harmonic RF field. Regular oscillatory structures are observed in the intrashell transitions. By solving the time-dependent Schr\"odinger equation for the problem it is shown that the dynamics is strongly influenced by the nonhydrogenic core which breaks the dynamical symmetry of the Coulomb problem. It is also shown that the dynamics effectively reduces to that of a two-level atom. The oscillations are remnants of interferences that arise partly due to a phase difference which develops between the two levels when they go through two consecutive one-photon resonances, and partly due to an effective change of the carrier-envelope phase of the coupling field.

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.

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.

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 .

One-photon intrashell transitions in strongly driven Li (

n=25

) atoms are studied experimentally. The degeneracy of the

n

shell is lifted by orthogonal dc electric and magnetic fields, which also define the eccentricity of the initial coherent elliptic state. The transitions are driven by a radio frequency pulse linearly polarized parallel to the major axis of the ellipse. A small dc electric field component parallel to the magnetic field splits the one-photon resonance into two, and transitions in between are studied by state-selective field ionization. Unexpected lines in the ionization spectra relating to unknown transitions are found and discussed.