We report an observation of the long-term evolution of a radially localized electronic wave packet formed by the coherent superposition of Rydberg states of atomic potassium. Initially, the wave packet can be described classically. Subsequent dephasing of the discrete states in the superposition leads to a loss of spatial localization so that the evolution can no longer be described classically. However, the wave packet revives at a later time. Theory and experiment show good agreement including an accurate measurement of the phase shift of the wave packet on revival.PACS numbers: 32.90.+a, 31.50,+w, 32.60.+i Quantum-mechanical wave-packet states can approach the classical ideal of a spatially localized particle traveling along a well-defined trajectory. The uncertainty principle places a limitation on this localization. But, for bound systems excited appreciably above their ground states, this is not a very stringent limitation. A more serious limitation on the quasiclassical nature of the states is the fact that for most systems the wave packet does not remain localized, but rapidly spreads.Normally, as time goes on the wave packet continues to spread and becomes less and less classical in its nature. There are a few cases, however, in which the spreading reverses itself and the wave packet relocalizes, again approximating a particle moving on a classical trajectory. A closely related decay and revival of classical coherence has been predicted, *~3 and observed 4 recently in the micromaser realization of the Jaynes-Cummings problem. There it is the coherent Rabi oscillations of the inversion of a Rydberg atomic transition that decay and revive. In both cases the revival is possible only due to the discreteness of the quantized energy states. In the Jaynes-Cummings problem it is the quantized nature of the cavity field, while in the present case it is the quantized nature of the atomic energy. A second necessary feature in both cases is the fact that the coherent superposition state is made up of frequency components that are almost equally spaced.In this paper, we report the observation of the decay and revival of a spatially localized Rydberg electronic wave packet. Methods for exciting such wave packets have been reported in several papers 5 " 9 and several different types of these wave packets have been observed. 10~13 In this experiment, a radially localized wave packet is formed by the coherent excitation of Rydberg states by a short, optical pulse. The Rydberg states have a range of values for the principal quantum number n with an average value of n. The resulting wave packet has the appearance of a shell oscillating between the nucleus and the outer turning point. The oscillations are at the classical orbital period. The classical orbital period is inversely proportional to the first derivative of the average energy of the wave packet with respect to n (xQ^lKh* a.u.). 5 These oscillations have been observed experimentally for a few periods. u,nThe long-term evolution of the wave packet is more complex. ...

Rydberg atomic wave packets have demonstrated striking classical properties. In particular, the wave packets display regions in which they evolve like classical atoms. However, between these regions the wave packet is dispersed and its evolution departs from the classical model. In these nonclassical regions, the wave packet can either be dispersed or coalesced into a number of equally spaced sub-wave-packets.The regions in which the sub-wave-packets appear have come to be known as fractional revivals. This paper reports the observation of these fractional revivals and discusses their implications.Observations'

We have excited and detected an atomic electron wave packet that is localized in the polar and azimuthal angles. The wave packet is formed through the coherent superposition of Rydberg states of atomic sodium. The superposition is achieved by short-pulse optical excitation of the atom in the presence of a strong rf field. The wave packet is detected by dc field ionization. The behavior of this wave packet in a strong dc field is much different from that of an eigenstate. This behavior agrees well with a simple classical model. PACS numbers: 32.90.+a, 31.50,+w, Several recent papers 1 " 5 have discussed the possibility of forming a localized wave packet through the coherent superposition of atomic Rydberg states. The study of atomic coherent states began 6 shortly after the development of quantum mechanics and the theoretical treatment of these states has been extensive. 6 " 10 The fundamental concern of these studies is to understand the transition between classical and quantum physics. Recently, the interest in these states has increased because of the development of short-pulse lasers. The large coherent bandwidth of these pulses makes it likely that the result of this field acting upon an atom is best described in terms of atomic coherent states. In our previous paper 4 we proposed the excitation of a Rydberg atomic wave packet localized in two of the spherical coordinates, the polar and azimuthal angles. Here we report the observation of such a wave packet and examine its behavior in a strong dc field. This behavior agrees well with a simple classical model.The wave packet is formed in the high-angularmomentum Rydberg states of atomic sodium. The advantages of the use of such states are several, as has been demonstrated by the recent experiment on inhibited spontaneous emission. 11 The chief advantage, for this experiment, is the possibility of our obtaining a nearly uniform energy spacing between the excited eigenstates. This reduces the rate at which the wave packet disperses. Another feature is the exceedingly large electric dipole matrix elements that exist between neighboring states: A modest rf field is sufficient to dress strongly states with the same principal quantum number. This dressing plays a critical role in the excitation of the wave packet.The excitation of the angularly localized wave packet is achieved through the optical excitation of Rydberg states that are being strongly dressed by an rf field. A circularly polarized optical field is tuned to the twophoton resonance between the ground state and the ^=•50 (principal quantum number) manifold of states. This manifold of states is being strongly dressed by a circularly polarized rf field, tuned near the thirty-photon resonance between the 50d state and the / a =32 state. This high-angular-momentum state and several of its neighbors are strongly mixed with the 50d state. All of these rf-dressed states lie within the coherent bandwidth of the optical pulse and can be excited by it. Following an adiabatic turnoff of the rf field, the population ...

An experiment is described in which a coherent superposition of the Rydberg states of atomic potassium is excited by a short optical pulse. The coherent superposition forms a wave packet localized in the radial coordinate. The radial motion of the wave packet is periodic with the period of the classical Kepler orbit. The time evolution is probed by a second short pulse. The resulting photoionization signal, as a function of the delay between pulses, shows the classical periodicity.

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...