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Physical Review A

Multiple-laser excitation of multilevel atoms

F. T. Hioe, Joseph H. Eberly

Published Mar 1, 1984• 37 citations
Publisher

Abstract

The probability of preparing multilevel atoms in high-lying levels by multiphoton excitation using one or more laser pulses can be increased by suitably tailoring the pulse amplitudes and frequencies. Few, if any, systematic methods designed specifically for multilevel excitation have been proposed. We present in this paper specific pulses and phase modulations which give specific degrees of inversion of multilevel atoms in analytic form.

DOI
10.1103/physreva.29.1164

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The probability of preparing multilevel atoms in high-lying levels by multiphoton excitation using one or more laser pulses can be increased by suitably tailoring the pulse amplitudes and frequencies. Few, if any, systematic methods designed specifically for multilevel excitation have been proposed. We present in this paper specific pulses and phase modulations which give specific degrees of inversion of multilevel atoms in analytic form.
Rabi frequencies for multiphoton absorption by atoms or molecules that can be characterized as two- or three-level systems are obtained in the cases of single and double laser perturbations. If the ambiguity in the origin of absolute energy is conveniently gauged off in the three-level model, there appears an additional non linear frequency which is originated from the separate evolution of a relative-frequency component induced in the whole system by the simultaneous action of the two perturbations.
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 develop the group-theoretical approach for analytically solving the time-dependent Schrodinger equations for multilevel atoms driven by amplitude- and/or frequency-modulated concurrent laser fields. The time evolution of externally driven N-level atoms is calculated in an explicit matrix form. The exact analytical conditions for complete population transfer and its return are simply connected with the parameters of the symmetry. We consider in detail the case of a four-level system driven by concurrent laser pulses of different forms.
We propose a method of laser isotope separation based on the phenomenon of adiabatic inversion and illustrate the method in a multilevel system consisting of a single ground state and multiplet excited states. In this model, population may be transferred from the ground state to one of the excited manifolds with nearly 100% efficiency by using laser pulses, the envelope of which rises slowly and then decays rapidly on an internal time scale that can be precisely calculated. Adiabatic inversion in this model is strongly dependent on the laser frequency, thus permitting separation of isotopes by faking advantage of small shifts in molecular or atomic energy level spacings. The criterion that determines whether a laser pulse is adiabatic also depends strongly on the laser frequency and thereby enhances the separation. We demonstrate the effectiveness of the method with a solution of the time-dependent Schroedinger equation for a specific model of two isotopes.