Observation of quasi-Landau wave packets

Abstract

Atomic wave packets are produced in strong magnetic fields by exciting rubidium atoms with a short UV laser pulse. The strength of the magnetic field is varied from 0 to 3.3 T. In a classical model of these Rydberg atoms, this variation leads to a progression of the system from a regime of regular motion to one where chaotic motion dominates. The evolution of the wave packet is observed using a phase-sensitive technique and is compared to the predictions of a semiclassical model. The eft'ect of an electric field, applied parallel to the magnetic field, is also studied. As the electric field is increased, significant changes occur that are due in part to the appearance of new orbits.PACS numbers: 32.60+i, 32.30.Jc A satisfying connection between the classical snd quantal descriptions of a system in a classically chaotic regime has yet to be developed. Studies in the field of "quantum chaos" are aimed at resolving this difliculty. Our work focuses on the study of highly excited Rydberg atoms in a strong magnetic field. This system is among the simplest of physical systems whose classical analog displays chaotic behavior. Moreover, the rather complicated spectra observed in the presence of a strong magnetic field have been analyzed with great success by semiclassical models. Near the atom's ionization threshold, the spectra are strongly modulated [1). The peaks of the modulation are known as quasi-Landau (QL) resonances. Their frequency is the oscillation frequency of classical orbits of the electron [2,3]. Further measurements of QL resonances in magnetic fields [4,5] and in crossed B and E fields [6] emphasized this correspondence between the modulation of the spectra and classical orbits. Many theoretical studies [7 -10] give detailed methods to calculate spectra from the properties of classical trajectories.Although classical motion is used to calculate the spectra, the above ideas are mainly concerned with static properties. Here, we are interested explicitly in the dynamics of the problem. For pulsed excitation, it has been demonstrated that it is possible to produce nonstationary states of such systems [ll -13]. Usually, some spatial localization results and it is appropriate to describe the evolution of these states in terms of wave packets. This approach has also been considered theoretically [14].The general idea of this experiment is to explore the time-dependent behavior of these wave packets as the strength of the magnetic field is increased so that the classical system passes from a regular to a chaotic regime. The goal is to establish a link between the motion of these wave packets and the classical trajectories of the system.Previous observations of wave packets in external fieldsshow how the detection difficulty increases as the symmetries of the Coulomb potential are broken by the external fields [12,13]. A recently developed technique [15,16] greatly improves our ability to detect the evolution of such wave packets. This technique detects the interference between two wave packets. A short ultravi...

Non-dispersive wave packets in periodically driven quantum systems

“…This implies that the temporal dynamics is built from exactly the same frequencies; thus, the 3D dynamics is essentially the same as the 1D dynamics. 5 Indeed, collapses and revivals of the wave-packet were also observed, under various experimental conditions, in the laboratory [5,11,25,26]. Fig.…”

“…As opposed to that, the diamagnetic term in eq. (214) gives a stronger weight to the harmonic term, which is the basis of the above claim 26 . From our point of view, which, as already stated above, attributes the non-dispersive character of the wave-packet to a classical nonlinear resonance, the accuracy of the harmonic approximation (which, anyway, always remains an approximation) is irrelevant for the existence of non-dispersive wave-packets.…”

“…22,25,26). Quantum mechanically, the states with initial principal quantum number close to n 0 = ω −1/3 will enter progressively inside the resonance island.…”

Applications of wavepacket methodology

“…when p/q = 1 4 ), the wavepacket splits into two equal parts exactly out of phase, leading, at these characteristic times, to a doubling of the modulation frequency in the time delay scan (Vrakking et al 1996b). We note that revivals of wavepackets have been observed both in atomic Yeazel & Stroud 1991;Meacher et al 1991;Wals et al 1994;Marmet et al Figure 2. Typical wavepacket experiment.…”

Gradient Marker: A Universal Wave Pattern in an Inhomogeneous Continuum

“…Wave patterns in inhomogeneous media or confining structures are of great interest to quantum mechanics, optics and electrodynamics, acoustics, hydrodynamics, and chemistry. Examples include wave packets in atoms [1], Ghladny patterns in acoustics, EM resonator and waveguide modes [2], Anderson localization in disordered systems [3], soliton formation [4] due to nonlinearity, including atomic solitons in bosonic gas [5], as well as giant waves near caustics [6], waves in chemical reactions [7], dark-soliton grids [8], "scars" in "quantum billiard" [9], "quantum carpets" in QM potentials [10], nanostratification of local field in finite lattices [11], etc. In all of those, the presence of multi-modes or a broad-bend spectrum is pre-requisite for interference and pattern formation in inhomogeneous or confining structures.…”