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Laser Physics Letters

Dynamic resonances in ultra-short laser pulses

N V Bordyug, В. П. Крайнов

Published Jan 4, 2007• 15 citations
Publisher

Abstract

Dynamic multiphoton resonances in ultra-short super-intense laser pulses consisting of 50-200 field periods are considered numerically for a two-level system. The impact of non-resonant (Bloch-Siegert) and carrier-envelope effects on the dynamics of a two-level system was studied numerically, and conditions for complete population inversion were derived. The widths of multiphoton resonances increase with the increasing of the laser field. Results do not depend practically on the pulse duration. Effective resonance frequencies for multiphoton resonances increases strongly in a super-intense field. Multiphoton resonances are shifted and unified with each other in super-intense laser fields.

DOI
10.1002/lapl.200610125

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Dynamic multiphoton resonances in ultra-short super-intense laser pulses consisting of 50-200 field periods are considered numerically for a two-level system. The impact of non-resonant (Bloch-Siegert) and carrier-envelope effects on the dynamics of a two-level system was studied numerically, and conditions for complete population inversion were derived. The widths of multiphoton resonances increase with the increasing of the laser field. Results do not depend practically on the pulse duration. Effective resonance frequencies for multiphoton resonances increases strongly in a super-intense field. Multiphoton resonances are shifted and unified with each other in super-intense laser fields.
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Bloch-Siegert shifts and widths of resonances in two-level systems are evaluated within an adiabatic approximation applicable in the multiphoton regime. The level splitting is controlled by a static field. Most attention is paid to the case of a circular driving field with the static field in the plane of rotation. This nonconventional setup was used in a recent experiment on intrashell resonances in Rydberg atoms where shifts and widths for NNN-photon resonance with NNN as large as 23 were observed [D. Fregenal et al., Phys. Rev. A 69, 031401(R) (2004)]. For this in-plane configuration the resonance widths are drastically enhanced compared to their values in the conventional configuration (linearly polarized driving field perpendicular to static field), whereas the shifts are only weakly affected.
Excitation of an atomic system subjected to a slowly varying external electromagnetic field is studied using a two-level model. Time evolution of the system is found using an approach which is nonperturbative in the field strength. There is no constraint to small values of the applied field, that is, the field (in appropriate energy units) need not be small compared to the difference in energies of the two levels. Rather, we use the fact that the situation of interest to us is where the frequency of the exciting field is small compared to the frequency associated with the level difference. Transition probabilities and resonance conditions are found which circumscribe both the large- and small-field limits. In the weak-field limit the previous results of high-order perturbation theory are readily recovered. For a monochromatic field the characteristic features of resonance excitation at high harmonic number of the applied field are (a) extremely narrow resonance widths and (b) shifts in resonance positions which are strong functions of field intensity. Because of this sensitivity, we are able to demonstrate that when slow temporal evolution of the field amplitude is taken into account (e.g., due to finite pulse duration) the appropriate mean excitation rate is that due to the uncorrelated contribution of many resonances. The results of this analysis are used to estimate excitation rates in a specific atomic system, Cd12+{\mathrm{Cd}}^{12+}Cd12+, which are then compared to multiphoton-ionization rates. Our calculations suggest that the ionization rate exceeds the excitation rate by several orders of magnitude.
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.