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Physical Review A

Multiphoton fragmentation of H2+ and D2+ with coherent and incoherent fields

Salvador Miret-Artés, David A. Micha

Published Oct 1, 1995• 1 citation
Publisher

Abstract

A theory of molecular photofragmentation is developed for coherent and incoherent light and for the case where dissociation lifetimes of field-induced resonances are shorter than pulse lengths. Using a mixed representation for the transition operator (a description of the initial state of the field with the coherent representation and of the final state with the number representation), we show how observables are modified at different field regimes by Poisson distributions. Applications to ${\mathrm{H}}_{2}^{+}$ and ${\mathrm{D}}_{2}^{+}$ are presented and discussed. They include line shapes and final distributions of kinetic energies for weak, intermediate, and strong fields. Results show that the interference of resonance states plays an important role even after averages over the field phases have been carried out to account for incoherent effects.

DOI
10.1103/physreva.52.2984

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A theory of molecular photofragmentation is developed for coherent and incoherent light and for the case where dissociation lifetimes of field-induced resonances are shorter than pulse lengths. Using a mixed representation for the transition operator (a description of the initial state of the field with the coherent representation and of the final state with the number representation), we show how observables are modified at different field regimes by Poisson distributions. Applications to H2+{\mathrm{H}}_{2}^{+}H2+​ and D2+{\mathrm{D}}_{2}^{+}D2+​ are presented and discussed. They include line shapes and final distributions of kinetic energies for weak, intermediate, and strong fields. Results show that the interference of resonance states plays an important role even after averages over the field phases have been carried out to account for incoherent effects.
Photodissociation probabilities for coherent and incoherent laser sources are described, using number- and coherent-state representations of the light field. Previous calculations of H2+{\mathrm{H}}_{2}^{+}H2+​ photodissociation in strong laser fields are used to calculate probabilities, for coherent and incoherent sources, that show increasing differences at lower light intensities.
Producing and controlling nonclassical light states are now the subject of intense experimental efforts. In this paper we consider the interaction of such a light state with a small molecule. Specifically, we develop the theory and apply it numerically to calculate in detail how a short pulse of nonclassical light, such as the high intensity Fock state, induces photodissociation in H(2)(+). We compare the kinetic energy distributions and photodissociation yields with the analogous results of quasi-classical light, namely a coherent state. We find that Fock-state light decreases the overall probability of dissociation for low vibrational states of H(2)(+) as well as the location of peaks and line shapes in the kinetic energy distribution of the nuclei.
We present a model calculation for two-photon autoionization of H2{\mathrm{H}}_{2}H2​ to the $X^{1}\ensuremath{\Sigma}_{g}$ state of H2+{\mathrm{H}}_{2}^{+}H2+​. The theory is based on a formulation that allows for strong-field effects. It is shown that, as a result of such effects, the autoionization profile will in general exhibit qualitatively new behavior at laser intensities needed for two-photon ionization. The magnitude of these effects depends significantly on the presence of resonance with intermediate states. The notion of autoionization width and qqq parameter are generalized to include this new behavior. Detailed calculations are reported for intensity effects on the line profile, the role of intermediate resonances, and the separate contribution of the vibrational states of H2+{\mathrm{H}}_{2}^{+}H2+​ as final states. The feasibility of observation with currently available sources is discussed.
Quantum Dynamics of H2+H_2^+H2+​ in Orthogonal Two-Color Fields
We present full-dimensional quantum simulations of H2+H_2^+H2+​ dissociative ionization driven by strong orthogonal laser fields. We consider equal-frequency orthogonal components, which generate elliptical or circular polarization depending on their relative phase and amplitude, as well as orthogonal 800800800- and 400400400-nm two-color fields. These two-dimensional fields strongly modify the fragmentation dynamics. Most notably, we identify a high-energy peak in the proton kinetic-energy-release (KER) spectrum at approximately 4−54-54−5 eV that is absent from the corresponding single-color, linearly polarized calculations. The yield of this peak can be coherently controlled by varying the relative carrier-envelope phase of the perpendicular field component. The perpendicular field also disrupts the clear electron-proton energy-sharing pattern observed in the main 3−3.53-3.53−3.5 eV dissociation channel, indicating more complex multichannel dynamics. Time-dependent state projections and calculations initiated from individual excited states attribute the additional peak to laser-induced vibrational excitation of H2+H_2^+H2+​. Furthermore, the perpendicular field rotates the fragment angular distributions, causing the most probable proton and electron emission directions to deviate substantially from the principal zzz axis. These findings demonstrate that the spatial and temporal geometry of orthogonal laser fields provides an additional degree of freedom for controlling ultrafast electron-nuclear dynamics.
A nonperturbative analysis is given for an nnn-level atom or molecule dressed by a Stark field and in single-photon or multiphoton (near) resonant interaction with coherent optical field modes, which may be intense. All the field amplitudes and phases may have nonadiabatic time variation. New formulas for probability amplitudes of states with finite lifetimes are given for atom-field levels swept or optical Stark shifted through resonance or into close approach. One of these includes the Landau-Zener formula as a special case. Power broadening is contained in these formulas. They are useful for both weak- and strong-field interaction. Further, it is shown that many familiar single-photon coherent transient phenomena have their analogs in the intense-field and the multiphoton domains. Two new effects, pulse-shape dependence in final transition probability and population inversion due to the nonadiabatic passage of an asymmetric pulse, are demonstrated with numerical results for the process $\mathrm{Na}(3s)+2\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\rightarrow}\mathrm{Na}(5s)$. Finally, double resonance (single-photon and/or multiphoton) is analyzed, with discussion of adiabatic following and a derivation of a formula for level crossing. Generalization of an earlier procedure for solving the adiabatic eigenvalue problem of the whole atom-field system is given.
We develop a consistent formalism for the treatment of temporal atomic or molecular coherence in multiphoton absorption. The formalism is fully quantum mechanical under the assumption that the exciting laser fields are well described by coherent states. We make use of the language and methodology of resonance physics to the extent possible, but deliberately avoid the rotating-wave approximation, and do not restrict the allowed atomic states to be finite in number or the electric field strengths to be small in magnitude. For compactness in the presentation only electric dipole transitions are considered. As all of the transitions, both stimulated and spontaneous, are due to the activation of quantum mechanical dipoles, it is most efficient to construct the formalism so that it emphasizes the role of dipole operators, and we do this. The one strong restriction imposed here, but avoided in a following paper, is to consider only multiphoton transitions that have one resonance between initial and final states and no intermediate resonance. We describe, in effect, the time dependences associated with the early multiphoton absorption calculations of Bebb and Gold.