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Physical Review A

Multiple phase control in Mg through the continuum

A. Lyras, H. Bachau

Published Dec 1, 1999• 27 citations
Publisher

Abstract

We present results from perturbative calculations on a scheme of coherent control in Mg. The scheme involves the excitation of Mg in the vicinity of an autoionizing resonance lying above the first two ionization thresholds by a two-color field composed of a fundamental frequency and its third harmonic, whose relative phase can be continuously controlled. Four as well as two-photon coherent excitation pathways, involving appropriate combinations of the two frequencies, proceed through the atomic continuum simultaneously contributing to the excitation, while three-photon ionization by the fundamental is also energetically possible. As a result, some of the excitation processes involve above-threshold ionization (ATI). The calculated ionization yields for the various groups of photoelectrons reveal significant modulation as the relative phase of the field component frequencies is varied. The modulation patterns for the different photoelectron groups are mutually shifted due to the multiphoton matrix element phases associated both with the ATI process and the multichannel nature of the final state. The effect is particularly pronounced when the autoionizing state is in near four-photon resonance with the fundamental frequency. The role of an autoionizing state as a final state as well as that of the continuum as an intermediate state in coherent control processes is discussed.

DOI
10.1103/physreva.60.4781

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We present results from perturbative calculations on a scheme of coherent control in Mg. The scheme involves the excitation of Mg in the vicinity of an autoionizing resonance lying above the first two ionization thresholds by a two-color field composed of a fundamental frequency and its third harmonic, whose relative phase can be continuously controlled. Four as well as two-photon coherent excitation pathways, involving appropriate combinations of the two frequencies, proceed through the atomic continuum simultaneously contributing to the excitation, while three-photon ionization by the fundamental is also energetically possible. As a result, some of the excitation processes involve above-threshold ionization (ATI). The calculated ionization yields for the various groups of photoelectrons reveal significant modulation as the relative phase of the field component frequencies is varied. The modulation patterns for the different photoelectron groups are mutually shifted due to the multiphoton matrix element phases associated both with the ATI process and the multichannel nature of the final state. The effect is particularly pronounced when the autoionizing state is in near four-photon resonance with the fundamental frequency. The role of an autoionizing state as a final state as well as that of the continuum as an intermediate state in coherent control processes is discussed.
We examine the excitation dynamics of a model atom excited by a two-colour laser field. Here the two colours or frequencies are the fundamental and its third harmonic. The atomic model consists of two bound states which are near-resonantly coupled by a three-photon excitation by the fundamental and a one-photon excitation by the third harmonic, and a structureless continuum. We investigate how the laser parameters (intensity and frequency) and the relative phase between the two colours affects the degree of phase modulation in the ionization signal. We compare our findings from this simple model atom with those from more realistic atomic models by carrying out numerical integration of the hydrogenic Schrodinger equation in both one and three dimensions.
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We report the observation of coherent control of the ionization rate in four-photon resonant, five-photon ionization schemes in Kr and Xe. The intermediate resonance is excited via different interfering channels involving four-photon absorption of the fundamental laser frequency ( ionization) as well as one third harmonic and one fundamental frequency photon absorption ( excitation), a particular aspect of the scheme being that interference occurs at a virtual level. By varying the relative phase of the two electromagnetic fields, a large modulation depth has been observed which is due to the chosen non-linear excitation scheme. In the Xe excitation experiment the interference between the different channels could be additionally probed through the modulation of the third-harmonic signal.
A theory of coherent control of above-threshold ionization (ATI) of hydrogen using light fields composed of a fundamental frequency and its third harmonic is developed. Phase control and intensity control over integral and differential quantities is demonstrated. Modulation of the first ATI kinetic-energy peak height by more than 70%, variation in the ratio of the first two peaks of up to a factor of 4, and separation in the alignment of the first two ATI peaks by as much as \ensuremath{\sim}50\ifmmode^\circ\else\textdegree\fi{}, as a function of the relative phase between the two fields, are demonstrated. Intensity control, in which both partial and total integral ATI rates attain a local maximum at a specific combination of light intensities, is predicted to occur.
Using the R -matrix Floquet theory we have carried out non-perturbative, ab initio one- and two-colour calculations of the multiphoton ionization of magnesium with the laser frequencies chosen such that the initial state of the atom is resonantly coupled with autoionizing resonances of the atom. Good agreement is obtained with previous calculations in the low-intensity regimes. The single-photon ionization from the excited state of magnesium has been studied in the vicinity of the autoionizing resonance at non-perturbative laser intensities. Laser-induced degenerate states (LIDS) are observed for modest laser intensities. By adding a second laser which resonantly couples the and autoionizing levels, we show that, due to the small width of the state, LIDS occur between this state and the state at intensities of the first laser below . We next investigate the case in which the first laser induces a resonant two-photon coupling between the ground state and the autoionizing state, while the second laser again resonantly couples the respective and autoionizing states. At weak intensities, our calculations compare favourably with recent experimental data and calculations. We show that when the intensity of the first laser is increased, the effect of an additional autoionizing state, the state, becomes significant. This state is coupled to the autoionizing level by one photon, inducing a triply resonant processes. We show that LIDS occur among the three autoionizing levels and we discuss their effect on the decay rate of the ground state. We consider dressed two- and three-level atoms which can be used to model the results of our calculations.
In coherent control schemes, pathways connecting an initial and a final state can be independently controlled by manipulating the complex amplitudes of their transition matrix elements. For paths characterized by the absorption of multiple photons, these quantities depend on the magnitude and phase between the intermediate steps, and are expected to be strongly affected by the presence of resonances. We investigate the coherent control of the photoemission process in neon using a phase-controlled two-color extreme ultraviolet pulse with frequency in proximity of an excited energy state. Using helium as a reference, we show that the presence of such a resonance in neon modifies the amplitude and phase of the asymmetric emission of photoelectrons. Theoretical simulations based on perturbation theory are in fair agreement with the experimental observations.