Theory of the inverse hook method for measuring oscillator strengths

Abstract

The theory of a new method to measure oscillator strengths is presented. The method exploits the ac Stark interaction of a laser pulse detuned from a transition between an initially populated state a and a second state b of an atom. We assume the density matrix \ensuremath{\rho} of state a initially has only diagonal elements given by 〈m\ensuremath{\Vert}\ensuremath{\rho}\ensuremath{\Vert}m〉=C+${\mathrm{Dm}}^{2}$ where C and D\ensuremath{\ne}0 are constants and m is the Zeeman sublevel quantum number. The laser pulse is linearly polarized along an axis different from the quantization axis and therefore rearranges the atoms among the various Zeeman sublevels. Changes of the relative Zeeman sublevel populations induced by the laser pulse can be readily detected by monitoring changes in the angular distribution or polarization of fluorescent light emitted when the atoms radiatively decay to some final state f. This paper considers the general problem where states a, b, and f have arbitrary angular momentum. We derive the functional dependence of the polarized fluorescent light fluence on the laser pulse fluence (pulse energy per unit area).For spatially uniform laser pulses, these signals are periodic functions of the laser fluence. When the laser is completely speckled, we show that the signal is well approximated by a Lorentzian curve. This latter case is of considerable experimental interest since most pulsed dye lasers have poor transverse mode structure which can readily be converted into a statistically well-defined speckle pattern. The oscillator strength of the transition between states a and b is found using (1) the fluence half-width of the ``depolarization curve,'' the Lorentzian-like dependence of the fluorescence polarization on the laser pulse fluence, (2) the detuning of the laser from the transition frequency ${\ensuremath{\omega}}_{\mathrm{ab}}$, and (3) some known constant factors which depend on the angular momenta of states a, b, and f. The physics of the situation is very similar to that of the conventional hook method with this difference: the roles of the atoms and the photons have been interchanged. We therefore call this new method the inverse hook method. The inverse hook method is relatively insensitive to the details of the atomic absorption line shape and also to the temporal and spatial profile of the laser pulse. It yields absolute oscillator strengths and it is especially suitable for measurements of transitions between excited atomic states, including autoionizing states.