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Dynamical Stark Effect for Atoms in a Static Magnetic Field: Dressed Atom Model

Stanisław Chwirot, S. Łęgowski, Jarosław Zaremba

Published Jan 1, 1981• 0 citations
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Abstract

By means of the dressed atom model the effects of a modulated nonresonant electric field are investigated for atoms in a static magnetic field. Expression for the transition probability between Zeeman sublevels is derived. The resonant character of this probability is shown.

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According to the quantum theory of the optical-pumping cycle, one can describe the effect of a nonresonant light beam on the different Zeeman sublevels of an atomic ground state by an effective Hamiltonian He{\mathcal{H}}_{e}He​ which depends on the polarization and spectral profile of the incident light. In order to check the structure of He{\mathcal{H}}_{e}He​, we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to He{\mathcal{H}}_{e}He​. We have been able to obtain experimentally in the ground state of 199Hg^{199}\mathrm{Hg}199Hg, 201Hg^{201}\mathrm{Hg}201Hg, and 87Rb^{87}\mathrm{Rb}87Rb, Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ is added. We have checked that the effect of He{\mathcal{H}}_{e}He​ can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.
Based on the dressed-atom approach, we discuss a two-dimensional (2D) radio-frequency trap for neutral atoms, in which the trap potential derives from the magnetic-dipole transitions among the hyperfine Zeeman sublevels. By adjusting the detuning of the radiation from resonance, the trapping states will be changed predominantly from the bare states of m F g F >0 to other states of m F g F <0, where m F and g F are the quantum numbers of Zeeman sublevels and the Landé factor, respectively. This character contrasts finely with that of a static magnetic trap that can only trap or guide the states of m F g F >0. In comparison to the optical field, the radio-frequency trap eliminates the spontaneous emission heating of the atoms. Unlike other oscillating traps reported in the literature, the configuration of the radio-frequency trap is suitable for realization of a miniature magnetic guide.
Theoretical study and computer modeling results of the spectra of coherent dark resonances resulted from excitation of Zeeman sublevels of the Fg=2→Fe=1 transition of the D1 line in 87Rb atoms by a frequency-modulated laser field are presented and discussed in detail. The influence of the nonlinear Zeeman effect on the structure of the coherent dark resonances is observed. It is shown that calculated for different values of the magnetic field spectra are in a good agreement with the experimental data.
The effect of a dc magnetic field on the rate at which a ground-level, Zeeman-degenerate atom is photoionized via a short-lived autoionizing level is calculated. We consider single-step as well as two-step photoionization; in the latter case we allow the light to be either resonant or far from resonance with an intermediate level. In all cases we find that the magnetic field may raise the fraction of the atoms available for photoionization and consequently increase the photoion fraction produced by a light pulse of given fluence. In the resonant case we find that if the magnetic-field Zeeman splitting of the ground and intermediate level is much larger than the rate at which population enters or leaves that level then the Zeeman-state populations are decoupled from one another and there exist simple conditions under which they obey rate equations. In the nonresonant case an additional condition for two-photon rate equations is that the optical Stark shift of the ground state be much smaller than the magnetic Zeeman splitting. These results apply specifically to excitation by lasers whose spectral widths are narrow compared to the homogeneous linewidths of the corresponding atomic transitions, but appear to be generalizable to the opposite limit, in which the laser spectral widths are much broader than the homogeneous linewidths.