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Journal of the Optical Society of America B

Numerical studies of adiabatic population inversion in multilevel systems

Arlee V. Smith

Published Sep 1, 1992• 57 citations
Publisher

Abstract

A numerical analysis is presented of several potential pulsed-laser applications of adiabatic population inversion in atoms or molecules. A simple numerical method is demonstrated for evaluating adiabatic processes in multilevel systems for both swept-frequency and resonant, time-delayed pulses. Adiabatic inversion with time-delayed pulses is generalized to systems with any number of levels. The effect of Doppler broadening on time-delayed adiabatic pumping of a three-level system is investigated.

DOI
10.1364/josab.9.001543

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A numerical analysis is presented of several potential pulsed-laser applications of adiabatic population inversion in atoms or molecules. A simple numerical method is demonstrated for evaluating adiabatic processes in multilevel systems for both swept-frequency and resonant, time-delayed pulses. Adiabatic inversion with time-delayed pulses is generalized to systems with any number of levels. The effect of Doppler broadening on time-delayed adiabatic pumping of a three-level system is investigated.
We present detailed experimental and theoretical results on population transfer with frequency-swept picosecond laser pulses. Here, we demonstrate that intense frequency-swept pulses, when applied in the adiabatic limit, lead to both more efficient and more selective excitation than do unmodulated laser pulses. The experimental work is performed on quasi-two-level systems (pentacene/p-terphenyl crystal and Na vapor), quasi-three-level systems (Na vapor), and on more complex multilevel systems (I2 vapor). We discuss the different characteristics of adiabatic population transfer in both few-level, and multilevel cases, and, in particular, present computer calculations to explore the effects of molecular rotations in multilevel adiabatic population transfer.
Frequency swept pulses are used to invert population over a broad band of transition frequencies without the need for a precise calibration of the pulse amplitude. As long as the adiabatic approximation is valid, population is adiabatically inverted at each individual transition frequency of the swept range. Even though this picture fails to be true when the adiabatic approximation breaks down, population inversion can still be achieved for an appreciable range of transition frequencies and field amplitudes. We discuss population inversion in an ensemble of two-level systems by a frequency-swept pulse, the so-called constant adiabaticity pulse, without invoking the adiabatic approximation. The equations of motion are integrated by a seminumerical method to analyze population inversion in the regime where usually the adiabatic approximation is applied. The effects of resonance offset and variable pulse amplitude are described by an average Hamiltonian expansion to discuss pulse performance beyond the validity of the adiabatic approximation. As a function of the adiabaticity parameter (reciprocal of the pulse area), the inversion bandwidth increases in a stepwise fashion due to the consecutive cancellation of average Hamiltonians. The first inversion over a finite range of transition frequencies and pulse amplitudes is shown to occur for an adiabaticity parameter of 1/15.
We derive and discuss the behavior of several multilevel models relevant to the problem of molecular multiphoton excitation under the action of a quasimonochromatic laser field, the amplitude of which rises slowly and falls rapidly on a certain internal time scale. Our method is suitable for the numerical solution of problems involving the adiabatic excitation of large multilevel systems. We find adiabatic inversion to be a general characteristic of the models considered. The fact that adiabatic inversion is accompanied by marked qualitative and quantitative changes in the expectation value of the dipole operator makes our results useful for understanding the propagation of laser pulses. An explicit expression that is especially convenient for numerical evaluation is presented for determining the limiting internal time scale, which is determined by the energy levels and transition moments of the system and the laser frequency. We illustrate the criterion for adiabatic inversion by applying it to a particular multilevel model. From a density-matrix treatment we conclude that collisional damping destroys the coherence required for adiabatic inversion. On the basis of our results we believe that the adiabatic approximation may be appropriate for some experiments of current interest.
We applied our pictorial approach using the fundamental concept of the Hückel molecular orbital theory to the population inversion in the multilevel systems by the straddling-STIRAP (S-STIRAP). We showed that the mechanism of the population inversion in the multilevel system may be easily understood by our approach. It is also shown that our approach is useful to understand that the condition required for the laser frequency in the delayed pulse sequence is different for the even- and odd-level systems. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 1068–1075, 2000
Enhanced population transfer from the lowest to the highest level in the three-state ladder 5s\ensuremath{\rightarrow}5p\ensuremath{\rightarrow}5d of the rubidium atom by frequency-swept ultrashort laser pulses is observed if the frequency sweep first makes the pulse resonant with the 5s\ensuremath{\rightarrow}5p transition, and later with the 5p\ensuremath{\rightarrow}5d transition. With this ``intuitive'' scheme it is possible to achive complete population inversion via the intermediate level by two successive adiabatic passages. Complete inversion is also obtained by a ``counterintuitive'' direction of the frequency sweep, in which case population of the intermediate level during the pulse is strongly reduced.