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The Journal of Chemical Physics

Atomic and molecular collisions in pulsed laser fields

Dane K. Madsen, Yiwen Xiao, Larry Eno

Published Dec 15, 1998• 0 citations

Abstract

We examine collisions in pulsed laser fields within the framework of multimode Floquet theory; the approach as outlined in a recent paper allows us to deal with collisional problems in pulsed fields without having to explicitly follow the varying field amplitude. Our focus here is on pulses which are on a time scale of the order of the collision time or less; the interest follows from an analysis made by Lee and George suggesting that unusually strong radiative transitions are possible in such fields. We examine transitions in a model problem based on the Na–Ar collision system and conclude, as others have done for this system, that a short, intense pulse is indeed effective in promoting transitions. Our assessment is, however, only partly based upon the traditional measure of examining how transition probabilities vary as the pulse length is shortened/lengthened. This traditional measure, we argue, is not sufficient for investigation of the mechanism of Lee and George because the measure includes varying contributions to the pulse effect as the pulse frequency profile changes—and this is not accounted for in the analysis of Lee and George. We combine, then, the traditional measure with an examination of the effect of changes in pulse-frequency profile. More particularly, results are determined which embody the same frequency profile as the pulse train, but are generated from a series of fixed-amplitude sources and these results are, in turn, compared with ones generated from a single fixed-amplitude source operating at the central frequency of the train. While, as noted above, we conclude for the Na–Ar system that a short, intense pulse is indeed effective in promoting transitions, we find that combining the traditional measure with an investigation of the role of frequency-profile changes significantly alters assessment of the pulse effect.

DOI: 10.1063/1.477717

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We examine collisions in pulsed laser fields within the framework of multimode Floquet theory; the approach as outlined in a recent paper allows us to deal with collisional problems in pulsed fields without having to explicitly follow the varying field amplitude. Our focus here is on pulses which are on a time scale of the order of the collision time or less; the interest follows from an analysis made by Lee and George suggesting that unusually strong radiative transitions are possible in such fields. We examine transitions in a model problem based on the Na–Ar collision system and conclude, as others have done for this system, that a short, intense pulse is indeed effective in promoting transitions. Our assessment is, however, only partly based upon the traditional measure of examining how transition probabilities vary as the pulse length is shortened/lengthened. This traditional measure, we argue, is not sufficient for investigation of the mechanism of Lee and George because the measure includes varying contributions to the pulse effect as the pulse frequency profile changes—and this is not accounted for in the analysis of Lee and George. We combine, then, the traditional measure with an examination of the effect of changes in pulse-frequency profile. More particularly, results are determined which embody the same frequency profile as the pulse train, but are generated from a series of fixed-amplitude sources and these results are, in turn, compared with ones generated from a single fixed-amplitude source operating at the central frequency of the train. While, as noted above, we conclude for the Na–Ar system that a short, intense pulse is indeed effective in promoting transitions, we find that combining the traditional measure with an investigation of the role of frequency-profile changes significantly alters assessment of the pulse effect.

A theoretical study of radiative transitions in molecular collisions occurring in the presence of short laser pulses is carried out within the semiclassical two-state formalism. Transition probabilities are calculated by numerically integrating the Bloch equation for two model systems and the Na-Ar system. At high laser intensities where a short pulse is more effective in inducing transitions than cw radiation, the transition probability exhibits nonlinear character with respect to the pulse intensity. At such high intensities, noncollisional atomic transitions may also be present, which need to be eliminated for an observation of collisional transitions.

It has been widely believed that short-pulse multiphoton ionization is dominated by a resonance process: excited states of the atom are shifted by the radiation field into multiphoton resonance with the ground state, are populated, and then rapidly ionized. A recent experiment, shows significant population remaining in excited states at the end of the laser pulse, and this result has been interpreted as indicating that ionization proceeds slowly out of these states. We investigate this issue in the framework of Floquet theory, supplemented by direct numerical solution of the time-dependent Schrodinger equation. In this framework, the standard picture is portrayed as an adiabatic transition between Floquet eigenstates, which occurs as the amplitude of the laser field is ramped through the resonance value (i.e. through an avoided crossing of Floquet quasienergies). Thus it follows that the same type of transition must occur as the field is turned off. This mechanism can yield significant populations of excited states that do not suffer appreciable ionization. We exhibit this effect by numerical studies of a model atom with two bound states and two continua.

It is shown theoretically that Ramsey fringes can be produced when a laser-assisted reaction of the form

{\mathrm{A}}_{2}

+${\mathrm{A}}_{1}^{\ensuremath{'}}$+\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\rightarrow}

{\mathrm{A}}_{1}

+${\mathrm{A}}_{2}^{\ensuremath{'}}$ is driven by a pair of ultrafast radiation pulses, each of whose temporal widths is less than the duration ${\mathrm{\ensuremath{\tau}}}_{\mathrm{c}}$ of a collision between the A and A\ensuremath{'} atoms. The excitation profile of the laser-assisted collision is calculated as a function of detuning of the laser field frequency from the initial- to final-state transition frequency. For radiation pulses separated by time T, Ramsey fringes appear separated in frequency by ${\mathrm{T}}^{\mathrm{\ensuremath{-}}1}$. The modulation depth and shift of the central Ramsey fringe as a function of (T/${\mathrm{\ensuremath{\tau}}}_{\mathrm{c}}$) provide information about the collisional interaction. Both the weak- and strong-field regions are considered and comparison with laser-assisted collisions using excitation pulses having temporal widths greater than ${\mathrm{\ensuremath{\tau}}}_{\mathrm{c}}$ is made.

The authors present an investigation of the modification caused by an intense laser field to the rates of m J changing collisions for Hg perturbed by argon. They have studied experimentally the competition between radiative and collisional coupling between m J states with a strong laser field tuned to the Hg J=1 to J=1 transition at lambda 435.8 nm. Population is pumped into the strongly dressed manifold from the ground state with a weak UV 'probe' laser detuned slightly from the lambda 253.7 nm intercombination line. The fluorescence observed at lambda 404.7 nm depends critically on whether the excitation proceeds via collisional redistribution or resonance through Stark shifted levels. The authors present data that clearly exhibit the effects of this competition. The data show in particular how one can produce excitation to transient Stark shifted levels in the presence of collisions. This will be critical in future experiments on collisions in strong fields.

The quantum nonperturbative analysis of Kroll and Watson for a two-level system of near-adiabatic atom-atom scattering in an intense laser-field mode is extended to treat a general multilevel system interacting with intense single- or many-field modes. A procedure for rigorously solving the adiabatic eigenvalue problem for the whole charge-field system is given. A new transition-probability formula is derived. Cross sections are calculated for the processes $\mathrm{Li}+\mathrm{H}(X^{1}\ensuremath{\Sigma}^{+})+\ensuremath{\nu}\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\rightarrow}\mathrm{Li}+\mathrm{H}(A^{1}\ensuremath{\Sigma}^{+} or B^{1}\ensuremath{\Pi})$ where $\ensuremath{\nu}\ensuremath{\ge}1$. Analysis of transition in an atom due to intensity variation of a laser pulse shows that desired transition probability per pulse (e.g., \textonehalf{}) may be achieved by varying the pulse parameters. For this, numerical results of $\mathrm{Na}(3s)+2\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\rightarrow}\mathrm{Na}(5s)$ and of $\mathrm{Li}(2s)+8\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\rightarrow}\mathrm{Li}(3s)$ are given.

We study multiphoton transitions in helium Rydberg atoms subjected to a microwave electric field of fixed frequency but varying intensity. For each principal quantum number in the range n=25--32, the

{n}^{3}

S to

{n}^{3}

(L>2), n=25--32, transition probability exhibits very sharp structures as a function of the field amplitude. Their positions could be reproduced precisely using a Floquet Hamiltonian for the interaction between atom and field. Their shapes are determined by the transients of field turn-on and turn-off in a way that makes a close analogy with the theory of slow atomic collisions.