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The Journal of Chemical Physics

Effects of arbitrary laser or NMR pulse shapes on population inversion and coherence

Warren S. Warren

Published Dec 15, 1984• 210 citations
Publisher

Abstract

We present a new perturbation expansion for calculating the effects of arbitrary pulse shapes in two-level systems, even when the effects are grossly nonlinear. The first two terms have simple physical interpretations. This expansion converges rapidly for all values of resonance offset with simple shapes, and for any pulse shape far from resonance. We generate very simple, symmetric, single phase pulse shapes which produce uniform inversion or polarization and which can be combined into multiple pulse sequences. We also show that pulse shape modification is superior to construction of composite pulse sequences, since such sequences must become erratic far from resonance.

DOI
10.1063/1.447644

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We present a new perturbation expansion for calculating the effects of arbitrary pulse shapes in two-level systems, even when the effects are grossly nonlinear. The first two terms have simple physical interpretations. This expansion converges rapidly for all values of resonance offset with simple shapes, and for any pulse shape far from resonance. We generate very simple, symmetric, single phase pulse shapes which produce uniform inversion or polarization and which can be combined into multiple pulse sequences. We also show that pulse shape modification is superior to construction of composite pulse sequences, since such sequences must become erratic far from resonance.
In this series of papers we report on the generation and application of multiple pulse phase coherent sequences in optical spectroscopy.In this paper the effects of intense pulse trains on systems with only two resonant energy levels are analyzed, with particular attention to the effects of extreme inhomogeneous broadening and population depletion to nonresonant levels.It is shown that these effects, which are present in virtually all optical systems, make the simple gyroscopic model of optical coherent transients invalid.Exact calculations show, e.g., that a two-pulse photon echo is not maximized by a 1:2 length ratio for the pulses; that the maximum excited state population is not created by a 180" pulse; and that three equal pulses are almost as effective as a 1:2:1 ratio for producing three pulse echoes.The role of pulse phase is extensively analyzed.Pulse sequences are proposed and experimentally demonstrated which permit optical phase sensitive detection and measurement of ground state relaxation parameters.The experimental results are based on an extension of the acousto-optic modulation and fluoresence detection techniques of Zewail and Orlowski [Zewail et al., Chem.Phys.Lett.48, 256 (1977); Orlowski et al., ibid.54, 197 (1978)).The relative merits offluorescence and transverse polarization detection are discussed, and fluorescence detection is shown to be more generally useful for these new sequences.Finally, composite pulse trains are shown to be capable of substantially increasing the signal available from highly inhomogenously broadened transitions.In paper II we extend the treatment to multilevel systems with some emphasis on solid state applications.
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We introduce a method to rotate arbitrarily the excitation profile of universal broadband composite pulse sequences for robust high-fidelity population inversion. These pulses compensate deviations in any experimental parameter (e.g., pulse amplitude, pulse duration, detuning from resonance, Stark shifts, unwanted frequency chirp, etc.) and are applicable with any pulse shape. The rotation allows one to achieve higher-order robustness to any combination of pulse area and detuning errors at no additional cost. The latter can be particularly useful, e.g., when detuning errors are due to Stark shifts that are correlated with the power of the applied field. We demonstrate the efficiency and universality of these composite pulses by experimental implementation for rephasing of atomic coherences in a Pr3+:Y2SiO5{\text{Pr}}^{3+}\text{:}{\text{Y}}_{2}{\text{SiO}}_{5}Pr3+:Y2​SiO5​ crystal.
In this series of papers we report on the generation and application of multiple pulse phase coherent sequences in optical spectroscopy. In this paper the effects of intense pulse trains on systems with only two resonant energy levels are analyzed, with particular attention to the effects of extreme inhomogeneous broadening and population depletion to nonresonant levels. It is shown that these effects, which are present in virtually all optical systems, make the simple gyroscopic model of optical coherent transients invalid. Exact calculations show, e.g., that a two-pulse photon echo is not maximized by a 1:2 length ratio for the pulses; that the maximum excited state population is not created by a 180° pulse; and that three equal pulses are almost as effective as a 1:2:1 ratio for producing three pulse echoes. The role of pulse phase is extensively analyzed. Pulse sequences are proposed and experimentally demonstrated which permit optical phase sensitive detection and measurement of ground state relaxation parameters. The experimental results are based on an extension of the acousto-optic modulation and fluoresence detection techniques of Zewail and Orlowski [Zewail et al., Chem. Phys. Lett. 48, 256 (1977); Orlowski et al., ibid. 54, 197 (1978)]. The relative merits of fluorescence and transverse polarization detection are discussed, and fluorescence detection is shown to be more generally useful for these new sequences. Finally, composite pulse trains are shown to be capable of substantially increasing the signal available from highly inhomogenously broadened transitions. In paper II we extend the treatment to multilevel systems with some emphasis on solid state applications.
Control of multiphoton transitions is demonstrated for a multilevel system by generalizing the instantaneous phase of any chirped pulse as individual terms of a Taylor series expansion. In the case of a simple two-level system, all odd terms in the series lead to population inversion while the even terms lead to self-induced transparency. The results hold for multiphoton transitions that do not have any lower-order photon resonance or any intermediate virtual state dynamics within the laser pulse width.