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Europhysics Letters (EPL)

A Wave Packet Can Be a Stationary State

Dominique Delande, Jakub Zakrzewski, Andreas Buchleitner

Published Oct 10, 1995• 41 citations
Publisher

Abstract

We establish the existence of strongly localized wave packets tracing without dispersion the classical dynamics of a Rydberg electron in a circularly polarized microwave field over up to 10 6 periods of the driving field, which at the same time are single eigenstates of the atom dressed by the microwave field. These “single-state wave packets” are shown to be robust towards small changes of the external field and can be prepared experimentally.

DOI
10.1209/0295-5075/32/2/003

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We establish the existence of strongly localized wave packets tracing without dispersion the classical dynamics of a Rydberg electron in a circularly polarized microwave field over up to 10 6 periods of the driving field, which at the same time are single eigenstates of the atom dressed by the microwave field. These “single-state wave packets” are shown to be robust towards small changes of the external field and can be prepared experimentally.
We find strongly localized wave packets tracing without dispersion the classical dynamics of a Rydberg electron in a circularly polarized microwave field using a full 3D quantum calculation. These wave packets are single eigenstates of the atom dressed by the microwave field and are very stable against ionization. Their widths fluctuate with microwave amplitude and/or frequency realizing an optical analog of the conductance fluctuations in mesoscopic systems. Similar behavior is observed for linear microwave polarization. We show that such behavior is expected when classical nonlinear resonances are important in an atomic system.
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.
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.
Nondispersive electronic Rydberg wave packets may be created in atoms illuminated by a microwave field of circular polarization. We discuss the spontaneous emission from such states, and show that the elastic incoherent component (occurring at the frequency of the driving field) dominates the spectrum in the semiclassical limit, contrary to earlier predictions. We calculate the frequencies of single-photon emissions and the associated rates in the ``harmonic approximation,'' i.e., when the wave packet has approximately a Gaussian shape. The results agree well with exact quantum-mechanical calculations, which validates the analytical approach.