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Communications in Theoretical Physics

Characteristics of Level Anticrossing in Parallel Electric and Magnetic Fields

Sihong Gu, Baiwen Li

Published Jun 15, 2000• 0 citations
Publisher

Abstract

Using the matrix diagonalization method, we have studied two kinds of level anticrosing of Rydberg cesium atom in parallel electric and magnetic fields. Our numerical results reveal that in the vicinity position of level crossing between different parity states in a magnetic field, the energy levels and other behaviors of the states are quite sensitive to the electric field. We tabulate some features which may be as a guide in experimental verification.

DOI
10.1088/0253-6102/33/4/525

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Numerical calculations of the positions and widths for anticrossings in Rydberg Stark states are scarce, largely due to the results' sensitive dependence on the wavefunctions chosen. With wavefunctions derived from a kind of potential model as a basis, we calculate the positions and sizes for the anticrossings of potassium Rydberg states in a static electric field by means of diagonalization, and show that the results are in good agreement with available experimental data. The results show that this potential model can be used to deal with the problem of anticrossings, and the accuracy of the potential model is sensitively and numerically tested in the situation of external fields for the first time.
Rydberg states in lithium have been excited from the ground state by absorption of \ensuremath{\pi}-polarized photons in the presence of parallel electric F and magnetic B fields. The magnetic field strength (B=3.11 T) is high enough to reach the inter-n-mixing regime, and a small electric field strength (F\ensuremath{\simeq}25 V/cm) is sufficient for the lowest state of the n=30 manifold to penetrate into the high-energy part of the n=29 manifold. The first anticrossing is thoroughly studied. Away from the anticrossing the spectrum exhibits two lines, but at the anticrossing a third component appears in the structure in the same energy range. This provides an experimental confirmation for the existence of pairs of almost-degenerate states with opposite parities in the high-energy part of the diamagnetic manifold of lithium. The two components of this doublet behave differently at the anticrossing. The experimental data have been interpreted in a global treatment in which core effects and intermanifold couplings are simultaneously taken into account. The different behavior of low- and high-lying states of the multiplet with respect to these two interactions is analyzed in detail.
With wavefunctions from a kind of atomic potential model including the fine-structure (FS) interaction as a basis, we calculate the positions and widths of anticrossings due to the FS interaction for the case of K Rydberg states in a static electrical field by using the diagonalization method. The results are in good agreement with experimental data; and we confirm that the influence of the FS interaction is very small on anticrossing brought about by core interaction. The accuracy of the potential model wavefunction including the FS interaction is sensitively and numerically tested in the situation of external fields.
The n=60, L z =0 angular momentum manifold in helium is studied in the presence of an electric field parallel to a fixed magnetic field (B=0.1539 T). Results obtained from a CW laser-atomic beam experiment are compared with diagonalization calculations and with a WKB approximation including core effects. Core-induced anticrossings have been analysed in detail. The supersymmetry, including quasi-crossings in hydrogen to occur at the same value of the electric field strength, does not apply for L z =0 manifolds in non-hydrogenic Rydberg atoms.
A spectroscopic study of Rydberg states of helium (n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear (n = 30, B ≤ 120 mT and F = 0-78 V cm⁻¹), and (ii) the diamagnetic term is dominant and the Stark effect is linear (n = 45, B = 277 mT and F = 0-8 V cm⁻¹). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin-orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m ₗ values and pronounced m ₁-mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg-Stark deceleration.