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The Journal of Chemical Physics

Two-photon dissociation/ionization beyond the adiabatic approximation

Amichay Vardi, Moshe Shapiro

Published Apr 8, 1996• 39 citations
Publisher

Abstract

An accurate theory of two-photon dissociation with strong laser pulses, which goes beyond the adiabatic approximation, is developed. Criteria for adiabatic behavior in two photon dissociation (enabling via adiabatic passage the complete population transfer to the continuum), are derived. We obtain the minimal pulse duration needed to ensure adiabaticity as a function of the field intensities and detuning. In addition, we develop a simple, rapidly converging, iterative scheme, built on the adiabatic approximation, for the exact solution of the two-photon dissociation problem. Each iteration step requires a computational effort that scales as N2 (N being the system dimension) for full matrices, or N log N for sparse matrices. The iterative scheme is tested by comparing it to the Runge–Kutta–Merson direct integration algorithm. It is found to work well even when the adiabatic approximation fails completely.

DOI
10.1063/1.471788

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An accurate theory of two-photon dissociation with strong laser pulses, which goes beyond the adiabatic approximation, is developed. Criteria for adiabatic behavior in two photon dissociation (enabling via adiabatic passage the complete population transfer to the continuum), are derived. We obtain the minimal pulse duration needed to ensure adiabaticity as a function of the field intensities and detuning. In addition, we develop a simple, rapidly converging, iterative scheme, built on the adiabatic approximation, for the exact solution of the two-photon dissociation problem. Each iteration step requires a computational effort that scales as N2 (N being the system dimension) for full matrices, or N log N for sparse matrices. The iterative scheme is tested by comparing it to the Runge–Kutta–Merson direct integration algorithm. It is found to work well even when the adiabatic approximation fails completely.
The theory of one- and two-photon dissociation processes with strong laser pulses for slowly varying multiple continua (‘‘direct’’ dissociation) is developed. Closed form expressions for the state preparation and evolution during and after the excitation pulse are derived. We show how saturation of the photodissociation process as a function of the laser power sets in. We also show that for direct dissociation, the fragment state distribution is independent of the laser power. The dependence of spontaneous emission during dissociation (continuum Raman and resonance fluorescence) on the pulse intensity is studied. The formulation is extended to treating resonantly enhanced two-photon dissociation with strong laser pulses. Closed-form expressions for slowly varying pulses and slowly varying continua are derived. Using these expressions, the existence of adiabatic passage to the continuum (APC) by which a system executes a complete population transfer from an initial bound state to the continuum by following two guiding light pulses is established. A simple iterative scheme for going beyond the adiabatic approximation is introduced.
An analytic theory of resonantly enhanced two-photon excitation of N states with laser light of an arbitrary field is developed. Closed-form expressions for the time evolution of the system are derived. The formulation is used to explore adiabatic passage to a level embedded amongst N other levels. ``Counterintuitive'' pulse sequence is shown to lead to complete population transfer under adiabatic conditions. The reverse case of stimulated emission from N initial states is also studied. Complete population transfer to the ground state from an initial state satisfying the two-photon resonance condition is shown to be possible. \textcopyright{} 1996 The American Physical Society.
Coherent interactions between light fields and simple quantum systems, such as $\ensuremath{\pi}$-pulses and adiabatic passage through frequency chirps and stimulated Raman interactions, generally use one- or two-photon processes. This limits the use of such interactions to energy scales close to the photon energy of the control field. However, recent calculations have shown that a 3-level system, generic to ionized diatomic molecules, shows such a strong multiphoton coupling that $\ensuremath{\pi}$-pulses are possible on at least 12-photon transitions. In this paper, we show that adiabatic transfer of population is also possible on such high-order multiphoton transitions. Full one-dimensional quantum mechanical two-electron calculations confirm this effect even in a system with many excited states and an ionization continuum.
We discuss various theoretical issues that arise when one extends the conventional stimulated Raman adiabatic passage, involving a pump pulse preceded by a Stokes pulse, to situations in which the pump interaction involves a two-photon transition. As in the simpler cases, it is possible to obtain complete population transfer between an initial state and a targeted final state, if certain general conditions on the pulses are met. We point out important considerations, associated with dynamic Stark shifts and multiphoton ionization, which make successful population transfer more difficult in the multiphoton extension. We illustrate these problems and requirements by considering specific examples of excitation in metastable helium.
We propose a technique which produces nearly complete ionization of the population of a discrete state coupled to a continuum by a two-photon transition via a lossy intermediate state whose lifetime is much shorter than the interaction duration. We show that using counterintuitively ordered pulses, as in stimulated Raman adiabatic passage (STIRAP), wherein the pulse coupling the intermediate state to the continuum precedes and partly overlaps the pulse coupling the initial and intermediate states, greatly increases the ionization signal and strongly reduces the population loss due to spontaneous emission through the lossy state. For strong spontaneous emission from that state, however, the ionization is never complete because the dark state required for STIRAP does not exist. We demonstrate that this drawback can be eliminated almost completely by creating a laser-induced continuum structure (LICS) by embedding a third discrete state into the continuum with a third control laser. This LICS introduces some coherence into the continuum, which enables a STIRAP-like population transfer into the continuum. A highly accurate analytic description is developed and numerical results are presented for Gaussian pulse shapes.
Vibrationally selective population transfer in electronic transitions involving small Franck−Condon factors is studied by means of two-photon excitation with pulse sequences applied in counterintutive order. Depending on the intensity of the pulses, two schemes allow ultrafast adiabatic passage. Both schemes, called STIRAP and APLIP, are analyzed as a function of the geometry of the electronic states and of the time duration and intensity of the pulses that drive the transitions. Although both schemes imply adiabatic following, the APLIP scheme requires pulses of considerably larger intensity than STIRAP, hence operating in a strong adiabatic regime. Simple adiabatic criteria for high-quality transfer are proposed, and analytic proofs are provided that show under which conditions STIRAP and APLIP converge. The results of this paper are illustrated with numerical simulations for two different electronic transitions in the Na 2 molecule.