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Physical Review A

Rydberg atoms in circular polarization: Classical stabilization in optical frequency fields

Will Chism, L. E. Reichl

Published Jan 11, 2002• 2 citations
Publisher

Abstract

We investigate the classical dynamics of the Rydberg atom in circularly polarized laser fields, restricted to the two-dimensional plane of polarization. We use a Poincar\'e surface of section to study nonlinear resonance structures for optical frequency driving fields. We demonstrate the existence and morphology of these structures as the laser intensity transitions from moderate to intense.

DOI
10.1103/physreva.65.021404

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We investigate the classical dynamics of the Rydberg atom in circularly polarized laser fields, restricted to the two-dimensional plane of polarization. We use a Poincar'e surface of section to study nonlinear resonance structures for optical frequency driving fields. We demonstrate the existence and morphology of these structures as the laser intensity transitions from moderate to intense.
The interaction of a hydrogen or Rydberg atom with a circularly polarized microwave field leads to the creation of global equilibrium points that may be stable or unstable depending on the particulars of the applied field. The additional application of a magnetic field, perpendicular to the plane of polarization, can be used to manipulate both the nature and the stability of these points. We show that stable three-dimensional motion can be maintained that is localized at either a maximum or a minimum in the corresponding surface of zero velocity. At these equilibria, the zero-velocity surface may be locally quadratic in coordinates and stable harmonic-oscillator-like, nondispersive, coherent states can be supported. As the fields are varied, repeated order-chaos transitions may be observed, including various passages through rigorously integrable limits. Classical simulations are presented for a range of field strengths, and the effects of deviations of the microwave field from exactly circular polarization (i.e., elliptical polarization) are examined using a pulsating zero-velocity surface.
Quantitative results are presented for stabilization of atoms against ionization by strong laser fields over a wide range of frequencies for circular and linear polarization. With circular polarization, stabilization occurs for all frequencies. At high frequency (\ensuremath{\omega}>1 a.u.), the stabilization intensity is predicted by the occurrence of photon thresholds. This mechanism gives excellent numerical agreement both with present calculations and the results of Pont and Gavrila [Phys. Rev. Lett. 65, 2362 (1990)]. A different mechanism operates for \ensuremath{\omega}1 a.u. Linear polarization differs strongly from circular polarization in many respects.
A classical study of the dynamics of atomic Rydberg states interacting with both elliptically and circularly polarized microwave fields is presented. In recent experiments, enhanced ionization rates were observed in elliptically as opposed to circularly polarized fields. A classical phase-space simulation provides good qualitative agreement with experimental findings. These results are explained in terms of the breakdown of almost conserved quantities as the polarization of the field is changed from circular to elliptical.
We report the first observation of the ionization of Rydberg atoms by a circularly polarized 8.5-GHz microwave field. The observed threshold field for ionization is E=1/16n4{\mathrm{n}}^{4}n4, a value higher than that required for ionization by a linearly polarized microwave field. The origin of this threshold can be understood by transforming to a frame rotating at the microwave frequency. In the rotating frame no transitions occur, and level mixings alone are responsible for the ionization.
We demonstrate modulation-free laser stabilization to an atomic Rydberg transition using nonlinear polarization spectroscopy. To stabilize a laser to the upper transition of a three-level ladder scheme, the techniques of standard polarization spectroscopy are adapted to use a narrow, nonlinear coherence feature. We obtain a subnatural linewidth dispersive signal that is directly suitable for laser frequency stabilization. We examine the effect of laser polarization on the dispersive line shape. This technique stabilizes the laser to an absolute frequency reference, can be used with numerous Rydberg levels, and eliminates laser modulation, which can enable high bandwidth feedback.
We present the quantal dynamics of electronic wave packets in the hydrogen atom in the presence of circularly polarized microwave and magnetic fields in regions of classical stability. Whereas wave packets may disperse without the stabilizing influence of a magnetic field, in its presence stable motion can be maintained for wave packets that are localized either at global equilibria that are either a maximum or minimum in a zero-velocity surface. Because these extrema are locally harmonic their vacuum states are truly coherent states in the original sense of Schr\"odinger.