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Physical Review A

Nonadiabatic transitions between quasistationary states in a laser field

Predrag Krstić, R.K. Janev

Published Jul 1, 1986• 8 citations
Publisher

Abstract

We consider two quasimolecular states, one discrete and one quasistationary, whose dynamical coupling becomes possible only by absorption or emission of laser-field photons. In the presence of the laser field the initially discrete state also becomes quasistationary, with an energy continuum shifted with respect to the continuum into which the initially quasistationary state decays. For such an interacting system, the corresponding system of coupled equations is derived and then solved within the Landau-Zener and Demkov nonadiabatic-coupling models, with various assumptions about the time variation of decay widths. Closed-form expressions for the transition probabilities of the half and full collision are obtained. The considered general physical problem is related to electron-capture processes in slow ion--excited-atom (or atom--excited-ion) collisions in a laser field or to laser-assisted excitation-transfer processes in atom--excited-atom slow collisions.

DOI
10.1103/physreva.34.157

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We consider two quasimolecular states, one discrete and one quasistationary, whose dynamical coupling becomes possible only by absorption or emission of laser-field photons. In the presence of the laser field the initially discrete state also becomes quasistationary, with an energy continuum shifted with respect to the continuum into which the initially quasistationary state decays. For such an interacting system, the corresponding system of coupled equations is derived and then solved within the Landau-Zener and Demkov nonadiabatic-coupling models, with various assumptions about the time variation of decay widths. Closed-form expressions for the transition probabilities of the half and full collision are obtained. The considered general physical problem is related to electron-capture processes in slow ion--excited-atom (or atom--excited-ion) collisions in a laser field or to laser-assisted excitation-transfer processes in atom--excited-atom slow collisions.
The authors consider a new case of collision-induced transitions between two discrete (quasistationary) states embedded in a continuum. The energy difference ( delta =E 1 -E 2 ) between the two states is assumed to remain constant throughout the collision whereas the difference between their individual decay widths ( Gamma 1 - Gamma 2 ) and their imaginary couplings (iV 1,2 ) via the continuum have a common exponential dependence: (E 1 -i Gamma 1 /2)-(E 2 -i Gamma 2 /2)= delta -ig exp(- eta R) iV 1,2 =iF 1,2 exp(- eta R). Transition probabilities are determined in closed analytical form for this problem.
The presence of coherent radiation fields can modify various atomic, ionic, and molecular processes. We examine cases where the changes can be effected without actual absorption or emission of photons. The radiation fields cause optical Stark shifts of the energies and dress the nonadiabatic couplings between states. Rates of processes such as dissociation, predissociation, atomic and molecular collisions can be radiatively controlled. Formation of new avoided crossings due to radiative interaction gives rise to new phenomena. We give both exact numerical results from which the influences of the radiation field on arbitrary configurations can be calculated, and simple but accurate analytic results, from which these effects can be conveniently assessed. It is shown that the inelastic transition probability is decreased at a true crossing and is increased at an avoided crossing as a result of the presence of the nonresonant radiation field. Furthermore, for two parallel levels with constant nonadiabatic coupling, it is shown that the amplitudes of the nonadiabatic transition are invariant, but its flopping frequency is reduced by the field. Depending on final measurements with the field on or off, general behaviors of the inelastic transition probability as a function of the field parameters and the charge-system parameters are predicted and the possibility of inversion (from a field-free value of less than \textonehalf{} to a value greater than \textonehalf{}) is demonstrated. Experimental investigation with iodine molecules is suggested. Comparison of our nonperturbative results with those of stationary perturbation theory shows that the latter is inadequate in an important parameter region where the field modification of processes is greater than 1%.
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.
Ion-pair formation processes are studied in collisions of Rydberg atoms with neutral particles possessing small electron affinities. Nonadiabatic transitions from a Rydberg covalent term to an ionic term of a quasi-molecule are considered using the modified Landau-Zener theory supplemented with calculation of survival factors of an anion decaying in the Coulomb field of a positive ion core. Using the technique of irreducible tensor operators and the momentum representation of the wavefunction of a highly excited atom, exact expressions are obtained for transition matrix elements and the ionic-covalent coupling parameter. The approach developed in the paper provides the description beyond the scope of a conventional assumption about a small variation of the wavefunction of the Rydberg atom on the range of electron coordinates determined by the characteristic radius of the wavefunction of the anion. This allows one to correctly consider long-range effects of the interaction between a weakly bound electron and the neutral core of a negative ion in processes under study. It is shown by the example of thermal collisions of Xe( nf ) atoms with CH 3 CN molecules that this is very important for a reliable quantitative description of anion formation with a low binding energy. The results are compared with experiments and calculations performed within the framework of a number of approximate methods.
The nonstationary Schr\"odinger equation is considered in a finite basis of states. The model Hamiltonian matrix corresponds to a single diabatic potential curve with a Coulombic $\ensuremath{\sim}1/t$ time dependence. An arbitrary number of other diabatic potential curves are flat, i.e., time independent and have arbitrary energies. Related states are coupled by constant interactions with the Coulomb state. The resulting nonstationary Schr\"odinger equation is solved by the method of contour integral. Probabilities of transitions to any other state are obtained as $\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{\infty}$ in a simple analytical form for the case when the Coulomb state is populated initially (at instant of time $\stackrel{\ensuremath{\rightarrow}}{t}+0).$ The formulas apply both to the cases when a horizontal diabatic potential curve is crossed by the Coulomb one and to a noncrossing situation. In the limit of weak coupling, the transition probabilities are interpreted in terms of a sequence of pairwise Landau-Zener-type transitions. Mapping of the Coulomb model onto an exactly solvable exponential multistate model is established. For the special two-state case, the well-known Nikitin model is recovered.