Time-dependence of ionization and excitation by intense, short electric pulses

In this thesis studies of time-dependent electric pulse ionization and excitation of atomic systems (the hydrogen atom and its negative ion) are performed. Unidirectional (half-cycle) pulses are considered, as well as oscillating (up to several-cycle) pulses. The time scale of the pulses considered varies from very short to very long with respect to the time scale of the electron orbit in its initial state. The peak electric fields are mostly in the strong-field regime, although the weak-field case is considered as well. <br> <br>Several complementary methods are used to attack the above problem - numerical, semianalytic and analytic. In the case of the hydrogen atom a numerical code based on the discrete variable representation (DVR) of the state vectors is written. Another numerical method, based on the solution of the integral equation for the propagator is developed. This method provides numerical results for the negative ion modeled by a three-dimensional zero-range potential. The semianalytic advanced adiabatic approach is used to describe the process of ionization and excitation for slowly-varying pulses. Purely analytic methods are used in the limit of very short pulses, regardless of the field amplitude. These are the first-order time-dependent perturbation theory (FPA), first-order Magnus approximation (FMA) and a modification of the first-order Magnus approximation (modified FMA). The FPA is used in the weak-field case, for both half- and several-cycle pulses. In the strong-field case and half-cycle duration much smaller than the orbital time of the electron in its initial state the FMA and its modification are used. In the FMA the pulse is reduced, regardless of its shape, to a momentum kick with magnitude equal to the half-cycle pulse area. The modified FMA, developed in this thesis, in turn enables analysis beyond a half-cycle pulse by inclusion of the propagation in the Coulomb field of the nucleus between the kicks. <br> <br>In the case of unidirectional (half-cycle) pulses, the tunnelling formula is rigorously derived starting from the representation of the wavefunction in the advanced adiabatic approach. At smaller time scales the nonadiabatic transitions arising from the hidden crossings between the initial and the excited states dominate. This provides a fair estimate of the total inelastic probability for the electric field amplitudes studied. By considering the whole interval of pulse widths at various peak amplitudes of the pulse, an effect of nonmonotonic dependence on the pulse amplitude is identified and explained in detail. In particular, in the case of weak fields, ionization probability as a function of the pulse width (with peak electric field strength as a parameter) exhibits a local maximum and decreases to "lock" to the tunnelling curve and restore the monotonic rise. The probabilities of occupation of excited states in turn always exhibit a maximum and then decrease to zero. The maxima in the excitation and ionization probabilities are related to the situation where the pulse width is in resonance with the inverse transition frequency from the initial state to excited states or to the continuum. <br> <br>In the case of very short pulses, we have considered both half-cycle pulses and few-cycle pulses. A periodic occurrence of ionization and recombination in time is identified. More precisely, the ionization which occurs after an odd half cycle is reversed in the following even half cycle. In the weak-field case this periodicity leads to a high sensitivity of the energy distribution to the relative envelope-carrier phase. In the strong field the periodic occurrence of ionization and recombination in time is termed "Rabi flopping involving the continuum" because after each odd half-cycle of the field the atom is practically 100% ionized and then the even half-cycle returns most of this population back to the initial state. By considering this process in the modified FMA, analytic formulas for the population probability of the initial state after one cycle are derived. These formulas are asymptotic expressions in the limit of infinite momentum transfer. Remarkably, these analytic expressions are in excellent agreement with the numerical results even for small momentum transfers. Furthermore, the analysis of the few-cycle pulse with constant envelope is reduced to an equivalent one-cycle pulse. This enables application of the same asymptotic formulas derived in the one-cycle pulse for the few-cycle pulse as well.

Author dc:creator

• Dimitrovski, Darko

Contributors dc:contributor

• Briggs, John

• Ionisation durch elektrische Pulse
• Ionisation in starken Feldern
• Attosekundenpulse
• Magnusnäherung
• fortgeschrittene adiabatische Näherung
• electric pulse ionization
• strong-field ionization
• attosecond pulses, recombination
• Magnus approximation
• advanced adiabatic approach

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