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Chinese Physics

Stark structure of the Rydberg states of alkaline-earth atoms

Zhi Miao-chan, Dai Chang-Jian, Shiben Li

Published Sep 25, 2001• 19 citations
Publisher

Abstract

The Stark effects of the Rydberg states in the alkaline-earth atoms are studied theoretically. Using a method similar to the treatment of alkali atoms, the properties of the Stark states of Mg, Ca, Sr and Ba atoms in the regions far away from the perturbers are investigated. The Stark maps for Mg ( n = 16, M = 0), Ca ( n = 10, M = 0), Sr ( n = 12, M = 0) and Ba ( n = 13, | M | = 0, 1) are presented. Topics such as the general methods of calculation, the treatment of fine structure and the structure of level anti-crossings are discussed. The comparison between the theoretical and experimental Stark maps is satisfactory.

DOI
10.1088/1009-1963/10/10/309

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The Stark effects of the Rydberg states in the alkaline-earth atoms are studied theoretically. Using a method similar to the treatment of alkali atoms, the properties of the Stark states of Mg, Ca, Sr and Ba atoms in the regions far away from the perturbers are investigated. The Stark maps for Mg ( n = 16, M = 0), Ca ( n = 10, M = 0), Sr ( n = 12, M = 0) and Ba ( n = 13, | M | = 0, 1) are presented. Topics such as the general methods of calculation, the treatment of fine structure and the structure of level anti-crossings are discussed. The comparison between the theoretical and experimental Stark maps is satisfactory.
The authors describe practical methods for calculating the Stark structure of Rydberg states of the alkali metals based on diagnolization of the energy matrix. A survey of Stark structures is presented for all of the alkali metals in the vicinity of n=15n=15n=15. Topics discussed include general methods for evaluating radial matrix elements, the treatment of fine structure, oscillator-strength distribution, scaling laws, the structure of a level anticrossing, and sources of error. Experimental Stark maps are compared with calculated results for lithium and cesium. Experimental studies of the oscillator-strength distribution within a Stark manifold and the structure of a level anticrossing are also presented.
The Stark effect in Rydberg atoms has potential applications in the areas of dipole-dipole interaction, quantum information, quantum control, and so on. Many reflevant theoretical calculations and experimental studies about the Stark effect of alkali metal and alkali earth metals have been reported, but the other atom’s Stark effect is studied still relatively less. Our goal in this paper is to reflearch the third main group atom’s Stark effect in a large electric field. First, according to the level data of gallium atom in zero-field, we obtain the quantum defects from the modified Ritz formula in each state by using a nonlinear least-squares-fitting algorithm. The quantum defects as a function of the principal quantum number are analyzed in detail. Influences of both the core polarization and the penetrating valence electron on the quantum defect are discussed according to the fitting results. Then we use the Numerov algorithm to calculate the radial wave functions of atomic gallium. Finally, the Stark structures of Rydberg states around n=7 and n=18 are numerically calculated by matrix diagonalization. Results show that at the levels above n=7 manifold states, (n+1)P is higher than nD state, and it is in contrast to the levels below the n=7 manifold states. This phenomenon is different from the usual Stark structure of alkali metal atoms, the level’s order of which does not change with the principal quantum number. The Stark levels with the identical |m| anti-cross each other, and those with different |m| cross. Our results give an important reflerence for related reflearches, and are of great significance for insight into the atomic structure and the interaction between the atomic core and the highly excited electrons.
Apropos to the growing interest in the study of long-range interactions which for their applications in cold atom physics, we have performed theoretical calculation for the two-dipole C6C_6C6​ and three-dipole C9C_9C9​ dispersion coefficients involving alkaline-earth atoms with alkaline-earth atoms and alkaline-earth ions. The C6C_6C6​ and C9C_9C9​ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated C6C_6C6​ coefficients for the considered alkaline-earth atoms among themselves are compared with the previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the C6C_6C6​ coefficients for alkaline-earth atoms with alkaline-earth ions and the C9C_9C9​ coefficients, we have performed separate fitting calculations and compared. Our calculations match in an excellent manner with the fitting calculations. We have also reported the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth ions, i.e., Mg+^++, Ca+^++, Sr+^++, and Ba+^++ as well as the alkaline-earth atoms, i.e., Mg, Ca, Sr, and Ba. These, when compared with the available experimental results, show good agreement.