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Physical Review A

Phase and intensity control of integral and differential above-threshold ionization rates

Ricardo A. Blank, Moshe Shapiro

Published Nov 1, 1995• 25 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.52.4278

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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.
Above‐threshold ionization (ATI) is the ionization of atoms by more than the minimum number photons necessary to overcome the Coulomb binding energy. Although ATI is contrary to the predictions of minimum‐order perturbation theory, it is the dominant mode of ionization whenever the light field becomes comparable to the static fields in the atom. We have learned a great deal by studying ATI over the past several years. We now know that by controlling these high intensity optical fields, we can control atomic and molecular processes such as ionization and dissociation. We can even engineer wave‐functions.
We present the first measurement of the ionization rate from above-threshold ionization (ATI) in an optical field whose phase dependence is known and controllable. Our method uses a harmonic two-color light field with a calibrated phase difference between the $1\ensuremath{\omega}$ and $2\ensuremath{\omega}$ fields. Our measurements confirm many of the predictions of recent semiclassical theories, but show an important discrepancy: An asymmetry in the ATI rates relative to the sign of the two-color phase difference supports recently suggested modifications to the models to include electron-core rescattering during ionization.
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 present a theoretical study of the main characteristics of two-color photoionization spectra obtained when atoms are subjected to an intense radiation pulse containing the fundamental of an infrared laser and one of its higher harmonics. The frequency of the latter is chosen to be high enough that the atom can be ionized by a single photon. The calculation is performed by numerical integration of the time-dependent Schrödinger equation for a (three-dimensional) hydrogen atom. We present the general properties of the spectra and angular distributions as well as the possible occurrence of interferences between the laser-assisted process and above-threshold ionization. Our results indicate that such interference effects, which can lead to partial coherent control of the photoionization process, can be observed at moderate laser intensities within the reach of currently operated laser and harmonic sources.
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.
We experimentally demonstrate one- and two-photon phase sensitive coherent control over the excitation and ionization of Rydberg states of Sr atom in the presence of a static homogeneous electric field. Without the field this excitation scheme can only be employed for the manipulation of angular distributions of photoelectrons and molecular photofragmentation products. Total atomic excitation-ionization yields cannot be modulated because the final states excited by each pathway are orthogonal to each other. When, however, a static electric field is applied, sss, ppp and ddd character is admixed into the final Rydberg state, which has no definite parity anymore. Hence, the excitation of the target Stark state from the ground state is possible with either two (fundamental laser frequency) photons or one (second harmonic frequency) photon and its population and further ionization can be controlled by varying the relative phase between the two radiation fields. The concept is successfully tested below as well as above the classical saddle point and with either mutually crossed or parallel linear laser beam polarizations (while the second harmonic beam polarization vector is always parallel to the static field direction). We examine the behavior of the obtained photoionization signal modulation depth VVV as a function of the static field strength FFF for otherwise identical experimental conditions. The V(F)V(F)V(F) curve exhibits a maximum (typically $\ensuremath{\sim}65%--85%$) at a field strength value that is dictated by the interplay between the employed laser power densities, one- and two-photon transition dipole moments, and relative amounts of field-dependent sss, ppp and ddd character. It is therefore shown that the static field strength may serve as an additional, experimentally adjustable, control parameter in a fashion complementary to both the intensities and relative phase of the two light beams.