Observation of the collapse and revival of a Rydberg electronic wave packet

Abstract

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. ...

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.…”

“…For a one-dimensional, time-independent system, it is even possible to estimate the time after which the wave-packet has significantly spread (this phenomenon is also known as the "collapse" of the wave-packet [5,6]). This is done by expanding the various energies E n around the "central" energy E n 0 of the wave-packet:…”

A linear atomic quantum coupler

“…2(a) and (b)). This mechanism reflects itself in very complicated Rabi oscillations Ω ± as well as in the double summations in the atomic inversions formulae (14). Fig.…”

“…Furthermore, the JCM has been experimentally implemented by various means, e.g. one-atom mazer [12], the NMR refocusing [13], a Rydberg atom in a superconducting cavity [14], the trapped ion [15] and the micromaser [16].…”

Open quantum system approach in multiple atomic collisions in solids and gases

“…Thus, our analysis of figure 3 was based on considerations of classical dynamics. At lower n a number of quantum phenomena such as revivals [15] should be within reach of experiment and might also be used to study the role of decoherence in the classical limit of quantum mechanics.…”