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Physical Review A

Symmetry and symmetry breaking in Rydberg-atom intrashell dynamics

Ingjald Pilskog, Daniel E. Fregenal, Øyvind Frette, Morten Førre, Erik Horsdal, A. Waheed

Published Apr 11, 2011• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.83.043405

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We have investigated experimentally and theoretically the dynamics of Stark-Zeeman split states in Li(n=25n=25n=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.
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.
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.
One-photon intrashell transitions in strongly driven Li (n=25n=25n=25) atoms are studied experimentally. The degeneracy of the nnn 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.
Multiphoton intrashell transitions in strongly driven Li (n=25n=25n=25) Rydberg atoms are studied experimentally. Orthogonal dc electric and magnetic fields lift the degeneracy of the nnn shell and define the eccentricity eee 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. NNN-photon resonances with $N=1\ensuremath{-}9$ are studied as a function of eee. All resonances with $N\ensuremath{\geqslant}3$ are suppressed at certain eee values in between 000 and 111. 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 NNN is increased by two, an additional suppression is observed.
In any atomic species, the spherically symmetric potential originating from the charged nucleus results in fundamental symmetry properties governing the structure of atomic states and transition rules between them. If atoms are exposed to external electric fields, these properties are modified giving rise to energy shifts such as the AC Stark-effect in varying fields and, contrary to this in a constant (DC) electric field for high enough field strengths, the breaking of the atomic symmetry which causes fundamental changes in the atom's properties. This has already been observed for atomic Rydberg states with high principal quantum numbers. Here, we report on the observation of effects linked to symmetry breaking in helium within the optical cycle of the utilized strong visible laser fields for states with principal quantum number n=2. These findings were enabled by temporally resolving the dynamics better than the sub-optical cycle of the applied laser field, utilizing the method of attosecond transient absorption spectroscopy (ATAS). We identify the spectroscopic fingerprint of instantaneous polarization and breaking of the symmetry of the atom in the intense visible femtosecond pulse used in an ATAS experiment and develop a time domain picture describing the dipole response that leads to these signatures. In the future, this general experimental approach can be used to measure strong-field induced symmetry-breaking effects in other atomic or molecular systems also consisting of two or more active electrons and thus to examine new routes to their bound-state and transition-state control by laser fields.
We report the observation of a controlled Landau-Zener transition (LZT) in Rydberg atoms by breaking the symmetry of the underlying Hamiltonian. For a nonhydrogenic Rydberg atom inside a changing electric (F) field, a LZT occurs between the avoided crossing energy levels of neighboring Rydberg states only for a sufficiently high changing rate. If a transverse magnetic (B) field is applied as we implement, the atomic level symmetry is broken, which causes the Stark manifolds denoted by a different |m| (m is the magnetic quantum number) to interact with each other. The mixed state levels end up pushing the adiabatically repelled target states closer and additionally they serve as stepping stones for the sequential LZTs between the neighboring sublevels. Such a feature significantly decreases the changing rate required for an efficient LZT inside a pure electric field. We report experimental observations that support the above scenario. It opens a versatile approach for engineering a controlled LZT in more general systems.