Farhard Faisal

Multiple absorption of laser photons by atoms

Applying a space translation operation, the Schrodinger equation for an atom in an electromagnetic field is solved with sufficient accuracy to obtain probabilities for multiple absorption of photons from a monochromatic laser beam of arbitrary intensity or frequency. It is shown that the derived expression for the N-photon T-matrix contains the usual single photon matrix elements given by the perturbation theory and that the perturbative result is obtained in the limit of low intensity. Other explicit examples are considered. The conditions of applicability of the method are specified.

Definition of Lyapunov exponents and KS entropy in quantum dynamics

Abstract We propose a definition of quantum Lyapunov exponents and the associated KS entropy, which allows a rigorous characterization of regular or irregular quantum dynamics in the same terms as in classical dynamics. An illustration of the use of this concept is given for the quantum stardard map.

Unified theory of Lyapunov exponents and a positive example of deterministic quantum chaos

A unified theory of quantum Lyapunov exponents, based on the Hamilton-Jacobi formulation of quantum mechanics, is applied to Weigerts quantum cat map. It is shown to provide a definite positive example of deterministic quantum chaos in terms of extreme sensitivity on initial conditions and a positive definite Lyapunov exponent.

Time-dependent theory of non-Hermitian Schrodinger equation: Application to multiphoton-induced ionisation decay of atoms

A rigorous and practical time-dependent formulation of quantum decay processes is obtained by converting the Hermitian Schrodinger problem into an equivalent non-Hermitian Schrodinger equation. The properties of the original Hermitian and the reduced non-Hermitian Hamiltonians are compared and the non-Hermitian formulation is shown to be consistent with the theorem of Fock and Krylov for the description of truly decaying states. A self-consistent non-unitary algorithm is developed and used to obtain expressions for the time-dependent transition amplitudes of interest; they automatically preserve the total probability in the sum space at all future times tau >0. The formalism is coded for application to the important problem of ionisation decay of a ground-state hydrogen atom coupled to a strong radiation field with a sub-threshold photon frequency. The first quantitative information on the time dependence of two- and three-photon (resonant and non-resonant) ionisation of the hydrogen atom is obtained.

A model for dissociation of polyatomic molecules by multiple absorption of photons

Abstract A heuristic model is presented for dissociation of polyatomic molecules by absorption ofn-photons, that utilizes the idea of a resonance model along with the requirement of conservation of probability in a transition process. This leads explicitly to a formula for the rate of dissociation which is given by a probability factor multiplied by the single photon rate of dissociation, from the last resonant state to the continuum. The formula may be used to obtain the angular distribution of the dissociating fragments as well as to estimate the total rate of dissociation per unit time. The probability factor is conveniently calculated in the rotating wave approximation.

S-matrix analysis of ionization yields of noble gas atoms at the focus of Ti:sapphire laser pulses

We analyse the experimental data for the formation of different charge states of a whole sequence of noble gas atoms in the presence of intense femtosecond Ti:sapphire laser pulses, using a recently developed dynamical model of laser-induced n-fold ionization of a complex atom. The ion yields for single and double ionization, as well as their ratios, are calculated for He, Ne, Ar, Kr and Xe and are found to agree remarkably well with the corresponding experimental data (with the possible exception of Ne). Next, we compare the experimental ion yields for the triple ionization of Ar with the present theoretical results which also show excellent agreement over the entire intensity range and reproduce the measured knee structures. Our analysis indicates that direct escapes of up to three electrons can contribute significantly to the ion yields for the highest charge state of Ar (namely, Ar3+) observed so far. Finally, for the purpose of future experimental references, we present the predicted results for the yields of up to sixfold ionization from neutral Ar or Ar+ ion.

Collision of electrons with laser photons in a background potential

Electron-photon scattering in presence of a background potential is considered for arbitrary intensities of laser radiations. Cross sectional expressions are derived which automatically include the effect of the background on the electron states. If the electron states are approximated by plane waves, they are shown to reproduce the results given by previous authors. An explicit result for the total elastic cross section in the combined laser pulse Coulomb field, is given. A simple upperbound is obtained for the corresponding bremsstrahlung (inverse bremsstrahlung) cross sections.

Interplay of Polarization Geometry and Rotational Dynamics in High-Order Harmonic Generation from Coherently Rotating Linear Molecules

Recent reports on intense-field pump-probe experiments for high-order harmonic generation (HHG) from coherently rotating linear molecules have revealed remarkable characteristic effects of the simultaneous variation of the polarization geometry and the time delay on the high-order harmonic signals. We analyze the effects and give a unified theoretical account of the experimental observations. Furthermore, characteristic behavior at critical polarization angles are found that can help to identify the molecular orbital symmetry in connection with the problem of molecular imaging from the HHG data.

Computation of multiphoton IR spectra of small molecules: application to CO

A non-perturbative theoretical method has been generalised to compute rovibrational multiphoton excitation probabilities in small molecules. The practicability of the method is illustrated by direct computation for CO. Novel non-linear features emerge in the absorption spectrum when the power broadening of individual rovibrational lines becomes comparable to the rotational constant of the molecule. The results also establish that over-simplified N-level models should be treated with caution.

Dependence of strong-field photoelectron angular distributions on molecular orientation

We have analysed angular distributions of the photoelectron yields arising from strong-field ionization of diatomic and polyatomic linear molecules using a leading-order intense-field S-matrix theory. For molecules with active π electrons the distribution is found to strongly depend on the degree of molecular alignment, showing a nodal minimum along the laser polarization direction as a characteristic signature.