An alignment factor which expresses the degree of alignment induced in an excited level by two-step excitation with short, broad-line pulses with parallel linear polarisations, is evaluated for various sequences of angular momenta J 0 to J 1 to J 2 . Unexpected zero alignments (in the short-pulse case) are found for two-step excitation involving the pairs of transitions J 0 =4 to J 1 =5 to J 2 =5 and J 0 =4 to J 1 =4 to J 2 =5. The results have application in the interpretation of Zeeman quantum beat signals, both direct and cascade beats, resulting from two-step excitation using pulsed laser sources.
For pt.I see ibid., vol.20, p.251 (1987). Theoretical expressions for cascade light intensity as a function of time have been evaluated for the case of cascade Zeeman beats produced by two-step excitation with broad-line laser pulses, and the results are compared with experimentally observed cascade Zeeman beats in Fe I. The beats were detected in time-resolved fluorescence from intermediate levels populated by cascades from highly excited levels of Fe I, using three different stepwise-excitation-cascade sequences. In the case of coincident laser pulses, good agreement between theory and experiment is obtained over a range of magnetic fields when allowance is made for Larmor precessions during the excitation period, for the width and shape of the exciting laser pulses and for the contribution of impurity processes. The effects of precession during the excitation period are especially important for the excitation sequence a 5 D 4 to z 5 F degrees 5 to e 5 F 5 , for which short-pulse theories predict no quantum beats for the experimental geometry used (parallel linear polarisations in the two excitation steps). For non-coincident pulses a predicted oscillation in the amplitude of the cascade beats with magnetic field has also been observed.
Aligned atomic Rydberg states of sodium can be prepared using two-step excitation from the ground state by linearly polarized pulsed lasers. Information that is normally inaccessible, e.g., sublevel partial cross sections in charge-transfer experiments, can be obtained when aligned targets are used. The calculations of orbital alignment must carefully allow for fine and hyperfine structure, laser linewidths, pulse widths and delays, sublevel coherences, and other factors. In this paper we derive the orbital alignments and time-averaged d-state sublevel populations for 3
2S1/2\ensuremath{\rightarrow}3
2PJ1\ensuremath{\rightarrow}n
2D excitations in Na using angular-momentum and density-matrix methods. We consider both quadrupole alignment
A(2) and hexadecapole alignment
A(4), with excitation through either
J1=1/2 or 3/2 intermediate states considered on the same footing. We show sublevel populations for \ensuremath{\Vert}
ML\ensuremath{\Vert}=0, 1, and 2 analytically and graphically. Finally, we formulate the experimental design problem quantitatively in order to ascertain how to optimize the choice of polarizer angles for extraction of sublevel partial cross sections. Although perhaps the commonest instance, two-step excitation of Na(nd) is but one of a large number of interesting cases, and this study is further intended to illustrate and guide the application of these methods to other light atoms.
A theory of stepwise pulsed-laser excitation of cascade Zeeman quantum beats has been developed for a four-level system. The laser pulses are treated in the broad-line approximation and the full optical-pumping equations for the atomic-density matrix of each level have been obtained. These can be used to describe saturation and light shift effects. The weak-pumping theory solutions to the optical pumping equations have been used to obtain expressions for the cascade quantum-beat intensity versus time curves. Larmor precession, spontaneous-emission decay and the populating of the final cascade level during the excitation pulse are all allowed for. A Wiener-Levy phase diffusion model with slowly varying amplitudes is used for the laser pulses, and the final theoretical expressions for the quantum beats depend on the time-dependent intensities of the laser pulses as well as on their polarisations. Hyperfine effects have been ignored. The theory applies to both coincident pulses and to pulses with a time delay between them. An illustrative application to the case of two very short but coincident pulses (during which Larmor precession, spontaneous emission etc. can be ignored) is given. In an accompanying paper the theoretical expressions are further evaluated and successfully applied to the interpretation of cascade Zeeman quantum beat experiments in Fe I.
A simple and accurate method of measuring the total angular momentum J of atomic energy levels is described. The method is essentially based on the J and photon-polarization dependence of the laser-induced two-step excitation in a three-level system. Four different combinations of polarizations in two lasers, which are tuned to each of the two Bohr frequencies, are utilized. They are co-circulating, counter-circulating polarizations and mutually parallel and perpendicular linear polarizations. It has been confirmed that the J-value of a level in the three-level system can be determined uniquely from relative strengths of the fluorescence originating in the top level. The determination of J is carried out by recognition of patterns in the excitation behaviour, which is peculiar to each J-value. The merit of the present method lies in the high reliability inherent in the pattern recognition procedure and also in the relative ease of the experiment.