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Physical Review Letters

Nondispersive Two-Electron Wave Packets in a Helium Atom

Matt Kalinski, Loren Hansen, David Farrelly

Published Sep 2, 2005• 18 citations
Publisher

Abstract

We demonstrate the existence of stable nondispersing two-electron wave packets in the helium atom in combined magnetic and circularly polarized microwave fields. These packets follow circular orbits and we show that they can also exist in quantum dots. Classically the two electrons follow trajectories which resemble orbits discovered by Langmuir and which were used in attempts at a Bohr-like quantization of the helium atom. Eigenvalues of a generalized Hessian matrix are computed to investigate the classical stability of these states. Diffusion Monte Carlo simulations demonstrate the quantum stability of these two-electron wave packets in the helium atom and quantum-dot helium with an impurity center.

DOI
10.1103/physrevlett.95.103001

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We demonstrate the existence of stable nondispersing two-electron wave packets in the helium atom in combined magnetic and circularly polarized microwave fields. These packets follow circular orbits and we show that they can also exist in quantum dots. Classically the two electrons follow trajectories which resemble orbits discovered by Langmuir and which were used in attempts at a Bohr-like quantization of the helium atom. Eigenvalues of a generalized Hessian matrix are computed to investigate the classical stability of these states. Diffusion Monte Carlo simulations demonstrate the quantum stability of these two-electron wave packets in the helium atom and quantum-dot helium with an impurity center.
We demonstrate the existence of stable non-dispersing two-electron Trojan-like wave packets in the helium atom in combined magnetic and circularly polarized microwave fields. These packets follow circular orbits and we show that they can also exist in quantum dots. Classically the two electrons follow trajectories which resemble orbits discovered by Langmuir and which were used in attempts at a Bohr-like quantization of the helium atom. Eigenvalues of a generalized Hessian matrix are computed to investigate the classical stability of these states. Diffusion Monte Carlo simulations demonstrate the quantum stability of these two-electron wave packets in the helium atom and quantum dot helium with an impurity center.
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 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.