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Physical Review Letters

Nonstationary, Nondispersive Wave Packets in a Rydberg Atom

Andrea F. Brunello, T. Uzer, David Farrelly

Published Apr 15, 1996• 44 citations
Publisher

Abstract

Immersing a Rydberg atom in circularly polarized microwave and magnetic fields spawns an equilibrium point, remote from the nucleus, which supports both regular and locally chaotic nonstationary, nondispersive eigenstates. Energy level spacing distributions typical of chaotic motion are found together with eigenstates scarred by classical periodic orbits. Five key advantages of this system as an atomic laboratory to study chaos are identified.

DOI
10.1103/physrevlett.76.2874

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Immersing a Rydberg atom in circularly polarized microwave and magnetic fields spawns an equilibrium point, remote from the nucleus, which supports both regular and locally chaotic nonstationary, nondispersive eigenstates. Energy level spacing distributions typical of chaotic motion are found together with eigenstates scarred by classical periodic orbits. Five key advantages of this system as an atomic laboratory to study chaos are identified.
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.
It is possible to make nondispersing Bohr wave packets in a straightforward way starting from Li Rydberg atoms in an np eigenstate[2]. These atoms are first exposed to a linearly polarized microwave field at the orbital frequency, 17.6GHz at n = 72. The linearly polarized field phase locks the electron wave packet to the microwave phase, making a nondispersing wave packet in which the electron oscillates in a highly eccentric, approximately linear orbit. We detect the phase locked motion of the electron with a 1/2ps half-cycle pulse synchronized with the microwave field. Slowly changing the microwave polarization from linear to circular polarization creates a nondispersing Bohr wave packet that survives for thousands of orbits.
Long-lived, nondispersing circular, or Bohr, wave packets are produced starting from Li Rydberg atoms by exposing them first to a linearly polarized microwave field at the orbital frequency, 17.6 GHz at principal quantum number n=72, which locks the electron's motion into an approximately linear orbit in which the electron oscillates in phase with the microwave field. The microwave polarization is changed to circular polarization slowly compared to the orbital frequency, and the electron's motion follows, resulting in a nondispersing Bohr wave packet.
We demonstrate the use of a periodic train of half-cycle pulses to maintain strongly-localized wave packets in very-high-nnn $(n\ensuremath{\sim}300)$ Rydberg atoms that travel in near-circular orbits about the nucleus. This motion can be followed for hundreds of orbital periods and mimics the original Bohr model of the hydrogen atom which envisioned an electron in circular classical orbit about the nucleus.