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Journal of Physics B Atomic Molecular and Optical Physics

Dependence on relative phase for bichromatically driven atoms

Peter M. Koch, S. A. Zelazny, Leszek Sirko

Published Nov 20, 2003• 9 citations
Publisher

Abstract

We consider the interaction of atoms with a pulse of a linearly polarized electric field consisting of two phase-locked frequencies whose ratio ω H /ω L is the ratio of arbitrary integers h / l , with h > l . If the electric amplitudes vary in time, they do so with the same slow envelope. The relative phase can be used as a control parameter via variation of the phase ϕ H of ω H or ϕ L of ω L . We derive the physically important ranges of relative phase for total-yield processes as a function of h : l ; they depend on whether h , l are both odd or only one is odd. We tabulate a variety of relevant phase-dependent results for all h : l from 2:1 through 8:7. We use calculations and experimental data for helium and hydrogen Rydberg atoms driven by a bichromatic microwave field to confirm the physically important ranges of ϕ H and ϕ L for a few h : l ratios. Two experimental examples taken from the literature for the interactions of atoms with sub-picosecond, bichromatic laser pulses also confirm our conclusions.

DOI
10.1088/0953-4075/36/24/001

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We consider electron scattering by hydrogen atoms in a bichromatic linearly polarized laser field of frequencies ω and 3ω and we discuss the coherent control of the scattering process as a function of the relative phase φ between the two components of the radiation field. The electrons are assumed to have sufficiently high energies in order to permit the description of the scattering process in the first-order Born approximation. The scattered electrons, embedded in the bichromatic laser field of moderate power, as well as the laser dressing of the hydrogen atoms in their ground state are described by time-dependent perturbation theory. We discuss the angular dependence of the nonlinear differential scattering cross sections for the low values N = ±2 of absorbed or emitted laser photons as a function of the relative phase φ between the two radiation field components. We also compare our results with those obtained from the assumption of a static potential describing the target atom.
Coherent phase control under the interaction between bichromatic radiation with multiple frequencies and quantum systems is the topic of the last time investigations both experimental and theoretical. This type of nonlinear optical control enables one to manipulate the characteristics of radiation processes by the change of the relative phase of bichromatic field. The present study is devoted to the theoretical analysis of the coherent control of two-level system behavior under bichromatic excitation in the frame of perturbation approach. The general expressions have been derived which are valid for any integer ratio n between the frequencies of monochromatic components of radiation. Obtained formulas describe the system characteristics as functions of relative phase of bichromatic field and other radiation parameters. Bichromatic excitation of Rubidium atom is considered as numerical example.
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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.
A new method for coherent phase control of excitation of atoms in a discrete spectrum under the action of bichromatic laser radiation with the frequency ratio 1 : 2 is analysed. An important feature of this control method is the presence of a electrostatic field, which removes the parity selection rule for one of the control channels. It is shown that for the phase difference between the monochromatic radiation components, corresponding to the destructive interference between channels, there exists the electrostatic field strength at which the excited atomic transition is `bleached'. It is proposed to use luminescence at the adjacent atomic transition for detecting the phase dependence of optical excitation.