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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. I. Theory

Bryan J. Dalton

Published Jan 28, 1987• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/20/2/010

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Mark P. Silverman, S. Haroche, M. Groß

A general theory of laser-induced quantum beats introduced in paper I is extended to include the effects of sequential laser excitation by several lasers for atomic systems either free or subjected to external static fields. A detailed study is made of the dependence of the quantum beat signal on the polarizations of the exciting laser pulses and detected spontaneous emission. The theory is applied to the echelon excitation of sodium $\mathrm{nD}$ Rydberg states. An analysis of the Zeeman beats produced by excitation in an external magnetic field suggests new ways to measure the fine-structure interaction constant of the Rydberg levels.

Physical Review A•Oct 1, 1978•18 citations
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.
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 quantum beats in a Stokes signal observed in pump-probe experiments upon excitation of four-level atoms with two close upper lying levels by femtosecond laser pulses is developed. Quantum beats arise in the intensity of the Stokes field due to the interference of two atomic wave packets generated by ultrashort pump and probe pulses. An analytical solution of the non-steady-state Maxwell-Bloch equations is obtained, and the dependence of the Stokes radiation intensity on the delay time between two laser pulses is investigated. The theoretical results describe qualitatively well the observed features of quantum beats.
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.
A general theory of laser-induced quantum beats introduced in paper I is extended to include the effects of sequential laser excitation by several lasers for atomic systems either free or subjected to external static fields. A detailed study is made of the dependence of the quantum beat signal on the polarizations of the exciting laser pulses and detected spontaneous emission. The theory is applied to the echelon excitation of sodium nD\mathrm{nD}nD Rydberg states. An analysis of the Zeeman beats produced by excitation in an external magnetic field suggests new ways to measure the fine-structure interaction constant of the Rydberg levels.