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Chinese Physics B

Dependence of above-threshold ionization spectrum on polarization directions of two-color laser fields

Min Liu, Yingchun Guo, Bingbing Wang

Published Jun 25, 2015• 9 citations

Abstract

Using the frequency-domain theory, we investigate the above-threshold ionization (ATI) process of an atom in two-color laser fields. When both photon energies of the two-color laser fields are much smaller than the atomic ionization threshold, the ATI spectrum depends on the angle between the two lasers' polarization directions. While when the photon energy of one laser is comparable with or larger than the atomic ionization threshold, the ATI spectrum is independent of the angle, and only several dips appear at certain angles. By analyzing the contributions of different quantum channels, we find that, for the case that both frequencies of the two color lasers are low, the quantum interferences between the channels are strong, and hence the spectrum changes with the angle between the two lasers' polarization directions. While for the case that the frequency of one of the two color lasers is high, the contributions of the channels to the ATI spectrum decrease dramatically with increasing channel order, hence the interferences between the channels disappear, and the ATI spectrum has a step-like structure, which is independent of the angle between the two lasers' polarizations. These results can shed light on the study of the corresponding relation between classical and quantum mechanisms of the matter–laser interaction in high-frequency laser fields.

DOI: 10.1088/1674-1056/24/7/073201

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Using the frequency-domain theory, we investigate the above-threshold ionization (ATI) process of an atom in two-color laser fields. When both photon energies of the two-color laser fields are much smaller than the atomic ionization threshold, the ATI spectrum depends on the angle between the two lasers' polarization directions. While when the photon energy of one laser is comparable with or larger than the atomic ionization threshold, the ATI spectrum is independent of the angle, and only several dips appear at certain angles. By analyzing the contributions of different quantum channels, we find that, for the case that both frequencies of the two color lasers are low, the quantum interferences between the channels are strong, and hence the spectrum changes with the angle between the two lasers' polarization directions. While for the case that the frequency of one of the two color lasers is high, the contributions of the channels to the ATI spectrum decrease dramatically with increasing channel order, hence the interferences between the channels disappear, and the ATI spectrum has a step-like structure, which is independent of the angle between the two lasers' polarizations. These results can shed light on the study of the corresponding relation between classical and quantum mechanisms of the matter–laser interaction in high-frequency laser fields.

We investigate a polarization control scheme in two-color two-photon atomic ionization. Experiments employing free-electron laser or high-order harmonic generation sources have shown light polarization dependencies in above threshold ionization of atoms assisted with an IR field. These were mostly performed at relatively high photoelectron energies where the soft-photon approximation remains valid. We use here a perturbation theory approach to show the larger degree of control that can be attained when the short wavelength photon energy is below the ionization threshold. This largely unexplored energy region offers unique possibilities to achieve polarization control of the reaction.

We formulate a quantum theory of photon emission during strong-laser-field-induced ionization and show that such photons can be emitted in a single-step process. The probability of this process is many orders of magnitude higher than that of the well-known high-order harmonic generation, which is a three-step process. We analyzed photon emission for various wavelengths and intensities of the laser field and found that the probability of photon emission is maximal for energies near 5 eV and that it can be shifted to higher energies for higher intensity. For a bichromatic linearly polarized laser field the photon emission rate can be controlled with the relative phase between the field components and can be one order of magnitude higher than in the monochromatic case. For circular laser polarization the rate of photon emission is lower than for the linear one and it depends on the emitted photon direction (it is much lower if the emitted photon polarization is perpendicular to the laser-field polarization plane). For the counterrotating bicircular field the rate is much higher than for the corotating bicircular field, monochromatic circularly and linearly polarized fields, and bichromatic linearly polarized field. The rate is the highest for orthogonally polarized two-color field for the relative phase $\ensuremath{\pi}/2$.

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 an atomic model to study above-threshold ionization (ATI). We show that when the laser field is sufficiently intense the usual perturbation theory is not valid. We solve the model dynamics exactly, and several interesting quantities, including the initial-state decay rate and photoelectron spectrum, are calculated. These quantities are related to recent ATI experiments, and qualitatively they agree with these experiments. We specify the strong-field condition for continuum–continuum transitions and explore its physical meaning. Finally some comments on perturbation theory are made.

We present our study on complete measurements of two-photon ionization in atomic rubidium. In this study we developed an effective technique to measure the angular distributions of photoelectrons. Through the measurements with this technique and using elliptically-polarized light we have successfully determined the atomic parameters—the relative cross sections for various ionization channels as well as the phase difference between s- and d-continuum waves. The measured phase differences are in excellent agreement with expected values over the entire range of photoelectron kinetic energy from 0 to 0.5 eV. The measured relative cross sections for ionization into S and D channels are also in good agreement with theoretical data. Both the relative cross sections and phase differences show a slow variation as a function of photoelectron energy. The ratios of cross sections of the two D channels are not in agreement with the expected value, suggesting fine structure effects. We also studied a quantum mechanical interference using two-color laser fields and observed the extremely asymmetric photoelectron angular distribution produced by interfering even- and odd-order photoionization processes in atomic rubidium as the optical phase was varied. We observed these effects with both perpendicularly and parallel-polarized fields components. It is worthy to note that the quantum interference observed with perpendicularly-polarized two-color fields is unique. Based on the analysis of measured angular distributions we derived the phase difference between even and odd continuum waves for the first time. The measured value of the phase difference is in good agreement with the calculated value from quantum defect theory.

A nonperturbative method is used to study the two-color multiphoton ionization of atoms by solving the Schr\"odinger equation in momentum space, which facilitates the extraction of the rapidly varying part of the wave function. Our method generalizes the problem for cases where an arbitrary number of ionization photons are absorbed, and also takes into account the threshold shifts due to both the high- and low-frequency fields. The photoelectron energy spectra of the hydrogen atoms are calculated and the dependence on the laser field strengths and frequencies is discussed. \textcopyright{} 1996 The American Physical Society.