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Journal of Physics B Atomic and Molecular Physics

Cascade Zeeman quantum beats produced by stepwise excitation using broad-line laser pulses. II. Comparison of theory with experiment

Bryan J. Dalton, Chris R. Allton, Peter Hannaford, R. Martin. Lowe, David S. Gough

Published Jan 28, 1987• 7 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/20/2/011

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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.
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.
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.
levels of atomic sodium using ultrashort laser pulses in a stepwise excitation scheme. Two broadband femtosecond laser pulses are used to excite the 6S level from the 3S ground level in sodium vapor. The first one is simultaneously resonant with the D1 and D2 lines of the 3S→3P transition, and the second one with the 3P→6S transition. The delay between the two pulses is scanned in order to probe the dephasing between the two excited intermediate levels. Quantum beating is observed by monitoring the fluorescence signals at 330 nm and 515 nm, namely transition 4P→3S and 6S→3P, respectively. Signals are compared to a semi-classical model that reproduces the oscillations with a very good agreement.
The population gratings were created by two intersecting resonant light pulses in the ground state 3 2 S 1/2 and the excited state 3 2 P 1/2 in sodium vapor, and their developements in a static magnetic field were monitored by the diffraction of the resonant probe pulse. Intensity modulations of the diffraction signals at the Zeeman frequencies (Zeeman beats) were observed, which are due to the oscillation of the LIPG's. The detailed analysis of the creation, detection and the time development of the LIPG was made in a simple model system with total angular momentum J =1/2 in both the ground and the excited states. The observed beat patterns were compared with the theoretical calculations including the effects of hyperfine interaction in both states. Polarization characteristics were also examined. The agreement between theoretical predictions and experimental results was quite satisfactory.