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Journal of Physics B Atomic and Molecular Physics

Cascade quantum beats: the calculation of intensity profiles

Robert Luypaert, Jean Van Craen

Published Aug 28, 1979• 7 citations
Publisher

Abstract

A theoretical study of cascade quantum-beat intensity profiles is presented for the case of fine-structure beats. An explicit expression for the beat profiles, in the form of a multipole expansion, is derived using the graphical methods of angular momentum theory. The calculations take into account the possibility for the initial state being polarised. Analogous results for zero-field hyperfine-structure beats are listed.

DOI
10.1088/0022-3700/12/16/009

Related papers

Hyperfine-structure quantum beats: application of the graphical methods of angular-momentum theory to the calculation of intensity profiles

Robert Luypaert, Jean Van Craen

A theoretical study of quantum-beat intensity profiles is presented for the case of zero-field hyperfine-structure beats. By means of the graphical methods of angular-momentum theory, an explicit expression for the quantum-beat profiles, in the form of a multipole expansion is obtained.

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Theory of cascade effects on quantum beats

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A fully quantum mechanical theory of cascade effects on Zeeman quantum beats is presented. The work is mainly concerned with the case of selective optical excitation of the upper level of the cascade, but beam-foil excitation is also considered. The analogous steady-state cascade process in a magnetic field is considered as well, focusing on the polarisation of the cascade light. Calculations are made for specific cascade processes in Ar II.

Journal of Physics B Atomic and Molecular Physics•Aug 28, 1979•10 citations

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 +2 more

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.

Journal of Physics B Atomic and Molecular Physics•Jan 28, 1987•7 citations

Cascade Zeeman quantum beats produced by stepwise excitation using broad-line laser pulses. I. Theory

Bryan J. Dalton

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.

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Quantum beats revisited: a quantum jump approach

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The term quantum beats refers to a superposed oscillatory behaviour in the light intensity emitted by some suddenly excited atomic systems in their subsequent decay. In this paper we reinvestigate quantum beats for systems where two upper levels may decay to a common ground state by using the recently developed approach of quantum jumps. The treatment turns out to be very simple and intuitive. It gives explicit expressions for the time-dependent intensity of the radiating system and allows us to exhibit several phenomena which so far seem to have been overlooked. We show that quantum beats may also occur if only one of the upper levels is initially excited, a superposition is not needed. A possible experimental set-up for the verification of this effect is proposed. It is also shown that in some cases the beat frequency may differ considerably from the separation delta omega of the upper levels. For equal Einstein coefficients of the upper levels the beats are shown to be unexpectedly absent for small delta omega .

Quantum Optics Journal of the European Optical Society Part B•Feb 1, 1994•45 citations

Density-operator description of foil-excited atomic beams: Zero-field quantum beats in L-S coupling without cascades

David G. Ellis

The decay curve of a spectral line with unresolved structure produced by a foil-excited atomic beam is considered in terms of a spherical tensor analysis of the density operator. In the case of L-S coupling, no external field and no cascades, the general expression is displayed and the necessary conditions for the appearance of quantum beats are discussed. By considering a series of special cases, some observable implications of the commonly assumed properties of the beam–foil excitation process are derived.

Journal of the Optical Society of America•Oct 1, 1973•73 citations
A theoretical study of cascade quantum-beat intensity profiles is presented for the case of fine-structure beats. An explicit expression for the beat profiles, in the form of a multipole expansion, is derived using the graphical methods of angular momentum theory. The calculations take into account the possibility for the initial state being polarised. Analogous results for zero-field hyperfine-structure beats are listed.
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.
The term quantum beats refers to a superposed oscillatory behaviour in the light intensity emitted by some suddenly excited atomic systems in their subsequent decay. In this paper we reinvestigate quantum beats for systems where two upper levels may decay to a common ground state by using the recently developed approach of quantum jumps. The treatment turns out to be very simple and intuitive. It gives explicit expressions for the time-dependent intensity of the radiating system and allows us to exhibit several phenomena which so far seem to have been overlooked. We show that quantum beats may also occur if only one of the upper levels is initially excited, a superposition is not needed. A possible experimental set-up for the verification of this effect is proposed. It is also shown that in some cases the beat frequency may differ considerably from the separation delta omega of the upper levels. For equal Einstein coefficients of the upper levels the beats are shown to be unexpectedly absent for small delta omega .
The decay curve of a spectral line with unresolved structure produced by a foil-excited atomic beam is considered in terms of a spherical tensor analysis of the density operator. In the case of L-S coupling, no external field and no cascades, the general expression is displayed and the necessary conditions for the appearance of quantum beats are discussed. By considering a series of special cases, some observable implications of the commonly assumed properties of the beam–foil excitation process are derived.