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Journal of Experimental and Theoretical Physics

Resonant scattering of three-level Rydberg atoms in a microwave field

A. V. Bezverbnyĭ, Igor M. Beterov, Anatolii M Tumaikin, I. I. Ryabtsev

Published Mar 1, 1997• 0 citations
Publisher

Abstract

We examine the theory of potential scattering of Rydberg atoms in a microwave field. The model of a three-level atom is employed to calculate the radiative force emerging in the resonant coherent interaction with the microwave field for the case of a two-photon resonance and high intensities, using the method of quasienergies of the system consisting of the atom and the field. We determine the probabilities of Landau-Zener transitions in the spatial regions where under two-photon resonance conditions the quasienergies of the atoms approach one another by a small quantity. We also study the dynamics of the variation of the spatial profile of a beam of Rydberg atoms caused by resonant scattering. Finally, we give the results of the first experimental observation of the variation of the transverse beam profile when Rydberg atoms pass through a nonuniform microwave field formed in a rectangular waveguide and in resonance with the two-photon 36 P –37 P transition.

DOI
10.1134/1.558160

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We examine the theory of potential scattering of Rydberg atoms in a microwave field. The model of a three-level atom is employed to calculate the radiative force emerging in the resonant coherent interaction with the microwave field for the case of a two-photon resonance and high intensities, using the method of quasienergies of the system consisting of the atom and the field. We determine the probabilities of Landau-Zener transitions in the spatial regions where under two-photon resonance conditions the quasienergies of the atoms approach one another by a small quantity. We also study the dynamics of the variation of the spatial profile of a beam of Rydberg atoms caused by resonant scattering. Finally, we give the results of the first experimental observation of the variation of the transverse beam profile when Rydberg atoms pass through a nonuniform microwave field formed in a rectangular waveguide and in resonance with the two-photon 36 P –37 P transition.
Review of experiments on microwave spectroscopy of sodium Rydberg atoms carried out during last several years by our group, is presented. Most of the experiments have been done for the first time with Rydberg atoms. These are: static and dynamics Stark spectroscopy, two-photon dynamic Stark effect, double Stark resonance, scattering of Rydberg atomic beam by strong resonant microwave radiation. Also an experiment on pure amplification without the inversion in two-level Rydberg micromaser is discussed.
In this chapter experiments on rubidium Rydberg atoms in external fields are reviewed [1 – 8]. In the first part results on the interaction of microwave radiation with rubidium Rydberg atoms are described. The Rydberg atoms interact with a microwave pulse of a well-defined duration. When applying coherent microwave radiation with a frequency exceeding a certain value, the experimentally observed microwave field strength at which 10% of the atoms are ionized has to be much larger than the value found by classical trajectory calculations. The atoms are stabilized by the dynamical localization. An extremely weak microwave broadband noise which is added to the coherent wave at least partially destroys the localization. This phenomenon depends on the bandwidth of the added noise. In further experiments the dependence of the 10% ionization microwave field strength on the duration τ of the microwave pulse has been investigated. For increasing noise level the 10% ionization field strength ∈ 0.1 develops from a behavior ∈ 0.1 ∼ τ −1/4 to a ∈ 0.1 ∼ τ −1/2 dependence, which is characteristic for a classical diffusion process. The second part of the chapter deals with experiments in strong static crossed electric and magnetic fields. Below as well as above the ionization energy the observed quasi-Landau(QL)-resonances are explained using classical trajectories. The ionization behavior of the QL-resonances is clearly influenced by the spatial structure of the associated classical orbits. In further experiments the dependence of the observed ionization energy on the magnetic field was investigated in the presence of a fixed static electric field.
An analysis is made of the interaction of a three-level cascade atomic system with a resonant laser field. An investigation is made of the dynamics of the populations of the quasienergy states and of the atomic levels over times greater than the spontaneous transition times. In the steady-state regime the distribution of atoms over various quasienergy states is obtained under two-photon resonance conditions and for the case when all the resonances are strong. It is found that a suitable selection of the interaction parameters can establish an inversion between the quasienergy states and also due to atomic transitions. The total probability of spontaneous scattering is calculated. It is shown that, under two-photon resonance conditions, the scattering intensity increases sharply due to a self-induced resonance.
Rydberg helium atoms traveling in pulsed supersonic beams have been coupled to microwave fields in a superconducting coplanar waveguide (CPW) resonator. The atoms were initially prepared in the 1s55s ^{3}S_{1} Rydberg level by two-color two-photon laser excitation from the metastable 1s2s ^{3}S_{1} level. Two-photon microwave transitions between the 1s55s ^{3}S_{1} and 1s56s ^{3}S_{1} levels were then driven by the 19.556 GHz third-harmonic microwave field in a quarter-wave CPW resonator. This superconducting microwave resonator was fabricated from niobium nitride on a silicon substrate and operated at temperatures between 3.65 and 4.30 K. The populations of the Rydberg levels in the experiments were determined by state-selective pulsed electric field ionization. The coherence of the atom-resonator coupling was studied by time-domain measurements of Rabi oscillations.
We study experimentally and theoretically the detailed field-amplitude dependence of the multiphoton ionization and excitation probability of highly excited n0{\mathit{n}}_{0}n0​ 3^{3}3S helium atoms in a 9.924-GHz linearly polarized microwave electric field. For ionization, with principal quantum numbers in the range n0{\mathit{n}}_{0}n0​=25--32, we use a quasistatic analysis that employs integration of the time-dependent Schr\"odinger equation using basis states of the static field Hamiltonian. The calculated results are used to interpret the observed ionization threshold structure. For excitation, the results of n0{\mathit{n}}_{0}n0​ 3^{3}3S\ensuremath{\rightarrow}n0{\mathit{n}}_{0}n0​ 3^{3}3L, L>2 excitation experiments are explained quantitatively and precisely using a theory of multiphoton resonances. We present maps of quasienergy levels that allow the study of the dynamics of the field-switching transients. These transient effects are analyzed along the lines of standard atomic collision theory and are shown to determine the shape of the observed resonances.
The quasienergy spectrum of hydrogenlike Rydberg atoms in a precessing electric field of constant amplitude is found in simple form. Resonant intrashell transitions occur for specific field values when a (small) additional static electric field perpendicular to the precession axis is present. Sequences of such transitions may enhance the microwave ionization of a Rydberg atom. C. H. Cheng and T. F. Gallagher [Phys. Rev. A 61, 063411 (2000)] recently observed a one-photon resonance of this type. We evaluate the widths of one-photon intrashell resonances, and develop a general approach to the N-photon case within the framework of a quasienergy representation.