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Physical Review Letters

Is a circular Rydberg atom stable in a vanishing electric field?

M. Groß, J.-Q. Liang

Published Dec 22, 1986• 43 citations
Publisher

Abstract

It is shown both experimentally and theoretically that a Rydberg circular atom keeps its maximum momentum only if it is submitted to a nonzero static electric field whose direction is constant or slowly varying. The minimum characteristic time of the field-allowed rotation is determined. The implications of this effect for a future high-resolution microwave spectroscopy experiment on circular Rydberg atoms is discussed.

DOI
10.1103/physrevlett.57.3160

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It is shown both experimentally and theoretically that a Rydberg circular atom keeps its maximum momentum only if it is submitted to a nonzero static electric field whose direction is constant or slowly varying. The minimum characteristic time of the field-allowed rotation is determined. The implications of this effect for a future high-resolution microwave spectroscopy experiment on circular Rydberg atoms is discussed.
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.
Circular atoms, i.e., Rydberg atoms with maximum angular momentum, are semiclassical atoms of great interest for Rydberg constant metrology and QED tests. Following a suggestion by Delande and Gay, we have prepared circular atoms by a new method, involving the adiabatic switching of crossed electric and magnetic fields. The method, which is demonstrated for Rydberg states of lithium (principal quantum number n=20to25n=20 \mathrm{to} 25n=20to25, is applicable over a wide variety of experiment conditions.
We have studied in detail the continuous evolution from static field ionization to ionization by a circularly polarized microwave field by combining a z-polarized static field with a circularly polarized microwave field in the x-y plane. We have measured the ionization threshold for Na states of 27< n< 5027<~n<~5027< n< 50 in the precessing total field Ft,{F}_{t},Ft​, as a function of its angle \ensuremath{\theta} from the z axis. For low n, ${F}_{t}\ensuremath{\cong}{1/16n}^{4},$ independent of \ensuremath{\theta}. For n> 45,n>~45,n> 45, Ft{F}_{t}Ft​ decreases from 1/16n4{1/16n}^{4}1/16n4 to 0.8/16n4{0.8/16n}^{4}0.8/16n4 as \ensuremath{\theta} is increased from 0\ifmmode^\circ\else\textdegree\fi{} to 25\ifmmode^\circ\else\textdegree\fi{}, and it remains at this value until $\ensuremath{\theta}=90\ifmmode^\circ\else\textdegree\fi{}.$ We also observe ionization at quite low values of Ft,{F}_{t},Ft​, which we attribute to resonantly enhanced ionization, with the resonances driven by a stray static field in the x-y plane.
Preparation of a so-called circular state in a Rydberg atom where the projection of the electron angular momentum takes its maximum value is challenging due to the required amount of angular momentum transfer. Currently available protocols for circular state preparation are either accurate but slow or fast but error prone. Here we show how to use quantum optimal control theory to derive pulse shapes that realize fast and accurate circularization of a Rydberg atom. In particular, we present a theoretical proposal for optimized radio-frequency pulses that achieve high fidelity in the shortest possible time, given current experimental limitations on peak amplitudes and spectral bandwidth. We also discuss the fundamental quantum speed limit for circularization of a Rydberg atom when lifting these constraints.