Relativistic Effects for a Hydrogen Rydberg Atom in a High-Frequency Laser Field: Analytical Results

Nikolay Kryukov,Eugene Oks

doi:10.3390/foundations2010005

Abstract

Previously published analytical results for the effects of a high-frequency laser field on hydrogen Rydberg atoms demonstrated that the unperturbed elliptical orbit of the Rydberg electron, generally is engaged simultaneously in the precession of the orbital plane about the direction of the laser field and in the precession within the orbital plane. These results were obtained while disregarding relativistic effects. In the present paper, we analyze the relativistic effect for hydrogenic Rydberg atoms or ions in a high-frequency linearly- or circularly-polarized laser field, the effect being an additional precession of the electron orbit in its own plane. For the linearly-polarized laser field, the general case, where the electron orbit is not perpendicular to the direction of the laser field, we showed that the precession of the electron orbit within its plane can vanish at some critical polar angle θc of the orbital plane. We calculated analytically the dependence of the critical angle on the angular momentum of the electron and on the parameters of the laser field. Finally, for the particular situation, where the electron orbit is perpendicular to the direction of the laser field, we demonstrated that the relativistic precession and the precession due to the laser field occur in the opposite directions. As a result, the combined effect of these two kinds of the precession is smaller than the absolute value of each of them. We showed that by varying the ratio of the laser field strength F to the square of the laser field frequency ω, one can control the precession frequency of the electron orbit and even make the precession vanish, so that the elliptical orbit of the electron would become stationary. This is a counterintuitive result.

Highlights

Analytical studies of effects of a high-frequency laser field on various Rydberg atoms and ions—the studies using the method of separating rapid and slow subsystems—have been presented in the literature: see, e.g., book [1] and references therein
In the present paper we study the role of the relativistic effect for hydrogenic Rydberg atoms or ions in a high-frequency linearly- or circularly-polarized laser field, the effect being an additional precession of the electron orbit in its own plane
For the particular situation, where the electron orbit is perpendicular to the direction of the linearly-polarized laser field, we show that the relativistic precession and the precession due to the laser field occur in the opposite directions, so that their combined effect is smaller than the absolute value of each of them

Summary

Introduction

Analytical studies of effects of a high-frequency laser field on various Rydberg atoms and ions—the studies using the method of separating rapid and slow subsystems—have been presented in the literature: see, e.g., book [1] and references therein. The authors of paper [3] obtained analytical results for the situation where the high-frequency laser field is elliptically-polarized in the plane of the electron orbit They demonstrated that this situation is mathematically equivalent to a problem of celestial mechanics, where a satellite moves in an equatorial orbit about a slightly non-spherical planet. U1 is a perturbation of the Coulomb potential which makes the system mathematically equivalent to a satellite rotating around the oblate Earth [4], whose motion has the following property: the unperturbed elliptic orbit undergoes simultaneously two precessions, one of them being the precession of the orbit in its plane, and the other being the precession of the orbital plane about the vector F Both precession frequencies are of the same order of magnitude and are much smaller than the Kepler frequency. Equations (1.7.10) and (1.7.11) from book [4], we obtain the scaled frequencies of the precession of the orbit in its plane (“pip” stands for “precession in plane”) and the precession of the plane about the direction of the laser field (“pop” stands for “precession of plane”): Ωpip ωK

Ωpop ωK

Conclusions