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.
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 Li+H(X1\ensuremathΣ+)+\ensuremathν\ensuremathℏ\ensuremathω\ensuremath→Li+H(A1\ensuremathΣ+orB1\ensuremathΠ) where \ensuremathν\ensuremath≥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 Na(3s)+2\ensuremathℏ\ensuremathω\ensuremath→Na(5s) and of Li(2s)+8\ensuremathℏ\ensuremathω\ensuremath→Li(3s) are given.
A nonperturbative analysis is given for an n-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.
The resonant multiphoton resonances shifts and widths and ionization cross-sections for multielectron atoms in a intense laser radiation field are studied. It is carried out a new consistent approach to atom in a strong realistic laser field, based on the relativistic energy formalism (S-matrix adiabatic formalism), relativistic Dirac equation Green function method and relativistic many-body perturbation theory with the Dirac-Kohn-Sham zeroth approximation. In relativistic theory, the Gell-Mann and Low adiabatic formula for energy shift is connected with electrodynamical scattering matrice, which includes interaction with as a laser field as a photon vacuum field (radiative decay). The optimized basis of the relativistic orbitals is generated with using a minimization procedure for the gauge-non-invariant contribution (the fourth-order of the QED perturbation theory) to the radiation width of atomic state. An approach to treating the multiphoton atomic processes is outlined on example of H, Cs, Kr,Mg etc. Analysis shows that the shift and width of the multi-photon resonance line for the interaction “atom- multimode laser pulse” is greater than the corresponding shift and width for a case of the “atom- single-mode pulse” (the Lorenz pulse model) interaction. From the physical point of view it is naturally provided by action of the photon-correlation effects and influence of the laser pulse multi-modity.
The problem of calculating transition probabilities for an atom interacting with an intense radiation field is set up within the context of an effective Hamiltonian formalism. This has the virtue that resonance effects are properly accounted for at the outset; more generally, it provides a convenient framework for approximations. Through the restriction of the class of intermediate states to be included in the construction of the effective potential, a unitary (nonperturbative) model is obtained. A successive approximation procedure for determining the effective potential, which is based on continued-fraction representations, is described. While very likely intractable for the true problem, this successive approximation procedure can be implemented, for the model effective potential, with the aid of a generalized Rayleigh-Ritz procedure described here. The level-shift matrix is constructed from the effective potential; it determines the transition probabilities, linewidths, and energy-level displacements induced by the field. We derive variational expressions of the Kohn type for each of the elements of the model level-shift matrix.
They have analytically tested several quantum transitions in molecular dynamics. In addition, they have introduced applications of theoretical formalism in physics to economics. First, they have completed the semiclassical theory of nonadiabatic transitions in the exponential potential model. They treated a two-state quantum system, which commonly appears as a subsystem in many-state problems. They were concerned with one-dimensional Schroedinger equation, although the type or semiclassical approach which they used can be applied to higher-dimension potential surfaces by means of Fourier transform. In particular, they solved the case of repulsive exponentially growing potentials, that is the forward-back scattering. They re-expressed the nonadiabatic transition matrix, which describes the transition between the two states for one-direction passage, in terms of contour integrals in the complex coordinate plane. The integrands are adiabatic momenta derived from the eigenvalues of potential matrix. Such type of concept has the advantage that it can be applied to other models than just the exponential potential model. Based on this, they have obtained an analytical tool for describing one-transition point class of potential curve systems. Examples are Rosen-Zener-Demkov model and Landau-Zener-Stueckelberg model. The formalism, which they contributed to, is useful in describing physical processes such as the charge transfer, and it is suitable for shaping external fields or modulating their frequencies in order to achieve a desired state or a product with the theoretical 100% probability. Second, they have derived the first exact analytical solution for a diabatically avoided crossing model. The physical system is described with one-dimensional coupled potential well and barrier which do not intersect in the whole coordinate range. On the basis of special mathematical functions they derived the complete quantum mechanical solution for the wave functions and the transmission coefficient. They also analyzed this model semiclassically and compared it with the exact results. This comparison yields interesting implications on the validity and accuracy of semiclassical approximation. In particular, they solved the case of dramatically avoided crossing with exponentially steep potential curves, and obtained the probability of one-way passage through the interaction region. The overall behavior corresponds to the probability of tunneling through the single potential barrier. In addition, there are complete reflection resonances at discrete energies, resulting from the trapping of a wave in the potential well. The formalism of diabatically avoided crossing model is useful in laser control of molecular reactions. This is because the potential energy curves in realistic molecular systems can be shifted by the photon energy; the curves are coupled by the field intensity via the dipole moment. That is why the new topology of potential energy curves, which was so far broadly omitted, becomes practically interesting due to the development in lasers techniques. Third, they treated several two-state quantum systems common in molecular physics. The semiclassical conditions for the complete transmission and the complete reflection in one-dimensional scattering were given analytically. They discovered the possibility of these phenomena in energy ranges in which the complete reflection or the complete transmission are not commonly expected to occur. In particular, they have made use of the broadly shared assumption that the transitions between the states are localized phenomena. This enables them to separate the whole coordinate region into distinct subsets and to analyze the physics in each subset separately. Applying this approach, they obtained a fully algebraic problem, which can be treated e.g. by diagrammatic techniques. Let them also mention that the complete transmission or complete reflection conditions simplify the wave function, and hence the mathematical solution. The formalism which they used while deriving the semiclassical conditions for the resonant phenomena mentioned above can be further generalized. This will probably yield a whole spectrum of tools in the laser control of molecular processes. Fourth, they developed a powerful technique for solving integral equations with singular kernel. One of the physical formulations of scattering is the time-independent approach based on the Lippmann-Schwinger equation for the Green operator. They have developed a detailed technique how to treat the singularity in this equation. In particular, any scattering problem can be divided into two parts. The first one is the geometry of the system and the static interaction of its components. The second one is more dynamical: the singular equation for the Green operator including the variable energy of the scattering. They fix the most costly calculations in the static part. Then they solve the singularity analytically and thus obtain the cross section as a function of energy. The so far common approach is quite opposite: to fix the singularity first and then to recalculate heavily all the static part for any new value of energy. Obviously, their approach saves a considerable amount of computational time; therefore it is a good standpoint for treating large systems. The formalism above was proved to be extremely efficient taking the example of dissociative recombination H2+ + e- → H + H* because this is a diatomic system, quantum chemical data are easily available in the literature and they could demonstrate the superiority of their approach to the other approaches. Fifth, they suggested applications of basic physical concepts to economics. They introduced aggregate quantities in financial markets and interpreted these quantities as potential energy surfaces. They also formalized interactions between cyclic processes in terms of state to state transitions. Summarizing, they treated the exponential potential model of nonadiabatic transitions, introduced a new exactly solvable model of diabatically avoided crossing, discussed the semiclassical conditions for complete transmission and complete reflection from the viewpoint of laser control, contributed to scattering calculations, and introduced some interdisciplinary applications.
We develop a theory describing laser excitation of a Rydberg series by an intense laser field. Our theory is based on the fact that the radiative coupling is restricted to a region around the atomic nucleus (the reaction zone) which is small in comparison with the extent of the excited Rydberg states. The physical processes inside the reaction zone are characterized by a few parameters which are slowly varying functions of energy across the Rydberg threshold. This finite range of the radiative coupling allows us to apply methods from quantum-defect theory and to treat the laser interaction with the Rydberg series and the adjoining electron continuum as a whole. Within this approach we derive analytical expressions for transition probabilities as a function of time in either a dressed-state representation which is appropriate as long as only a few Rydberg states are excited or a multiple-scattering expansion which is particularly suited for a description of the excitation process close to threshold. The physical picture emerging in this limit is one of a radial electronic wave packet which is generated within the reaction zone and moves in the Coulomb potential of the ionic core. Every time it returns to the inner turning point of its orbit, i.e., to the reaction zone, it is either deexcited back to the initial atomic state or is scattered by the ionic core.
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.