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The Journal of Chemical Physics

Theory of one- and two-photon dissociation with strong laser pulses

Moshe Shapiro

Published Sep 1, 1994• 33 citations
Publisher

Abstract

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.

DOI
10.1063/1.467502

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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 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.
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.
We have developed a theory of three-pulse coherent control of photochemical processes. It is based on adiabatic passage and quantum coherence and interference attributed to the lower-lying dissociation continuum and excited upper discrete states, which are otherwise not connected to the ground state by one-photon transitions. Opportunities offered by the proposed scheme are demonstrated through extensive numerical simulations with the aid of a model relevant to typical experiments. The opportunities for manipulating the distribution of the population among discrete and continuous states with any necessary ratio by the end of the pulses are demonstrated.
We present a fully quantum-mechanical theory of the mutual light-matter effects when two laser pulses interact with three discrete states coupled to a (quasi)continuum. Our formulation uses a single set of equations to describe the time dependence of the discrete and continuum populations, as well as pulse propagation in electromagnetically induced transparency (EIT) and stimulated Raman adiabatic passage (STIRAP) situations, for both weak and strong laser pulses. The theory gives a mechanistic picture of the ``slowing down of light'' and the state of spontaneously emitted photons during this process. Surprising features regarding the time dependence of material and radiative transients as well as limitations on quantum light storage and retrieval are unraveled.
The theory of resonance Raman effect, resonantly enhanced two-photon absorption, and resonance fluorescence---valid also for strong fields---is treated in a unified and simplified way. Dressed states, Bloch equations, and perturbation theory are used to calculate line positions, and integrated intensities both for steady state and transient excitation. The case of adiabatic following is solved explicitly; it occurs when an off-resonance incident pulse is turned on and off slowly. It leads to the identification of Raman scattering, two-photon absorption, and Rayleigh scattering with an adiabatic process while fluorescence and consecutive two-photon absorption with nonadiabaticity. Time-dependent spectra are defined in a rigorous way. Our formulas agree in the various limits with those that appear in the literature.
Ongoing work aimed at developing highly efficient methods of populating a chosen sublevel of an energy level highlights the need to understand off-resonant effects in coherent excitation. This motivated us to re-examine some aspects of the theory of coherent excitation in a three-state system with a view to obtaining algebraic expressions for off-resonant eigenvalues and eigenvectors. Earlier work gives simple closed-form expressions for the eigenvalues this system, expressions applying even when the system is not on two-photon resonance. We present here expressions of similar simplicity for the components of the normalised eigenvectors. The analytic properties of these components explain the observed sensitivity of the stimulated-Raman-adiabatic-passage process (STIRAP) to the condition of two-photon resonance. None of the eigenstates is ‘trapped’ or ‘dark’ unless the system is on two-photon resonance; off resonance, all states have nonzero projections on the unperturbed intermediate state. A simple argument shows that no dressed state can be adiabatically connected to both the unperturbed initial and final states when the system is off two-photon resonance. That is, adiabatic transfer from initial to final state requires that these be degenerate before and after the STIRAP pulse sequence, and this implies zero two-photon detuning. However, substantial transfer probabilities are observed experimentally for very small two-photon detunings. We show that such systems are characterised by very sharp avoided crossings of two eigenvalues, and that the observed population transfer can be understood as an effect of non adiabatic transitions occurring at the avoided crossings.