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Physical Review A

Calculation of a linear-Stark effect inD-line absorption in rubidium

J. Hodgdon, B. R. Heckel, E. Norval Fortson

Published Apr 1, 1991• 7 citations
Publisher

Abstract

An external electric field can induce M1 and E2 amplitudes in the D lines of alkali-metal atoms, which interfere with the normal E1 amplitudes of these lines, causing the absorption to depend linearly upon the external field and upon the initial spin polarization of the atoms. We discuss this effect and calculate its size for the D lines of rubidium.

DOI
10.1103/physreva.43.3343

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An external electric field can induce M1 and E2 amplitudes in the D lines of alkali-metal atoms, which interfere with the normal E1 amplitudes of these lines, causing the absorption to depend linearly upon the external field and upon the initial spin polarization of the atoms. We discuss this effect and calculate its size for the D lines of rubidium.
We have measured the magnetic dipole (M1) and electric quadrupole (E2) amplitudes in the D1 transition of rubidium atoms placed in a static electric field, ${\mathit{scrE}\ensuremath{\rightarrow}}_{\mathit{s}}$. The interference of the Stark induced M1 and E2 amplitudes with the normal E1 amplitude gives the atomic absorptivity a linear dependence on ${\mathit{scrE}\ensuremath{\rightarrow}}_{\mathit{s}}$ and on the atomic spin polarization. We find that the fractional change in absorptivity due to the Stark interference is aM1{\mathit{a}}_{\mathit{M}1}aM1​+aE2{\mathit{a}}_{\mathit{E}2}aE2​=(-2.37\ifmmode\pm\else\textpm\fi{}0.37\ifmmode\pm\else\textpm\fi{}0.28)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ (kV/cm${)}^{\mathrm{\ensuremath{-}}1}$.
An externally applied static electric field, by mixing opposite-parity states, can add electric-quadrupole and magnetic-dipole transition amplitudes to an allowed electric-dipole transition. The resulting interference among the amplitudes causes the absorption of resonance radiation to depend linearly on the static field and on the atomic polarization state. We present a calculation of this effect for the 254-nm line of Hg where the atomic polarization is specified by the ground-state nuclear spin, and the excited-state hyperfine structure is resolved. Possible experiments to measure this effect are pointed out.
A static electric field may induce essential changes to the cross section for the magnetic-field-induced coherent frecuency mixing of two laser waves, modifying the cross-section dependence on the magnetic field and polarization vectors of incident waves, which depends on the ratio of M1/E2 contributions to n1 2P1/2 (3/2) - n2 2P3/2(1/2) radiation transition amplitude. Relations between the M1/E2 ratio and quantitative characteristics of polarization asymmetry in cross section are determined. Calculated numerical data are presented for coherent mixing of two laser waves on Cs, Rb and K atoms.
Experimental results on the photoionization spectra of excited rubidium atoms in a well-defined ml=1{m}_{l}=1ml​=1 state in the presence of an electric field are reported. Spectra corresponding to a definite polarization of the ionizing light exhibit characteristic resonances which are ascribed either to the non-Coulombic part of the central potential or to the spin-orbit interaction. The different line profiles are interpreted as being due to interferences between discrete states and continua, the observed structures depending directly on the density of oscillator strengths and not simply on the density of continuum states.
We have presented a novel method to calculate the widths of the avoided crossings of Rydberg states in a static electric field. The widths of avoided crossings can be decided not directly connected by scanning the static field, but indirectly connected through the Stark electric dipole moments. The method is restricted to the case in which both the two relevant states have linear Stark shifts or only one of the two involved states has linear Stark shifts, but another has no Stark shift. As test examples, we calculated the widths of avoided crossings of Li, Na and K. The Stark electric dipole moments are determined by using the Stark state wavefunctions which are obtained from the diagonalization method at a fixed static electric field amplitude. The results are in excellent agreement with experimental and other theoretical data.
Stark-induced electric dipole amplitudes between states of the same nominal parity can be important in experiments to observe parity nonconservation in atoms. The Stark-induced E1 amplitudes are expressed in terms of an irreducible spherical-tensor decomposition. This formalism is applied to the specific case of transitions between hyperfine sublevels of a single atomic state. It is shown that in the ground states of alkali atoms, such transitions are suppressed by many orders of magnitude relative to naive expectations.