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Journal of Physics B Atomic Molecular and Optical Physics

Large-scale quantum coherence of nearly circular wave packets

Carlos O Reinhold, S. Yoshida, Joachim Burgdörfer, B. Wyker, J. J. Mestayer, F. B. Dunning

Published Apr 27, 2009• 15 citations
Publisher

Abstract

We demonstrate that the quantum coherence of mesoscopic very-high- n , n ∼305, Rydberg wave packets travelling along nearly circular orbits can be maintained on microsecond time scales corresponding to hundreds of classical orbital periods. The coherence is probed through collapses and revivals of periodic oscillations in the average electron position. The temporal interferences of spatially separated Schrödinger cat-like wave packets are also observed. A novel hybrid quantum–classical trajectory method is employed to simulate the wave packet dynamics.

DOI
10.1088/0953-4075/42/9/091003

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We demonstrate that the quantum coherence of mesoscopic very-high- n , n ∼305, Rydberg wave packets travelling along nearly circular orbits can be maintained on microsecond time scales corresponding to hundreds of classical orbital periods. The coherence is probed through collapses and revivals of periodic oscillations in the average electron position. The temporal interferences of spatially separated Schrödinger cat-like wave packets are also observed. A novel hybrid quantum–classical trajectory method is employed to simulate the wave packet dynamics.
We demonstrate the use of a periodic train of half-cycle pulses to maintain strongly-localized wave packets in very-high-nnn $(n\ensuremath{\sim}300)$ Rydberg atoms that travel in near-circular orbits about the nucleus. This motion can be followed for hundreds of orbital periods and mimics the original Bohr model of the hydrogen atom which envisioned an electron in circular classical orbit about the nucleus.
A semiclassical propagator is applied to describe the dynamics of circular-orbit wave packets which are initially well localized in three dimensions. A sum over classical Kepler trajectories for the wave-packet autocorrelation function is obtained which is extremely accurate well past the classical regime of the evolution regime of the wave packet. The nonclassical nature of the wave-packet evolution at long times is associated with the interference between amplitudes from classical paths at different energies. The time scale of the wave-packet revivals is related to the shearing rate of the corresponding classical ensemble.
Quantum mechanical wave packet states can approach the classical ideal of a spatially localized particle traveling along a well-defined trajectory. These states offer a system in which the classical limit of quantum atomic theory can be studied. In this work, a wave packet that is radially localized and whose radial motion occurs at the classical orbital period is studied. Despite these strong classical features, the long-term evolution displays the quantum nature of the state. As the wave packet evolves, it becomes dispersed, and the radial motion becomes irregular. However, the wave packet does not remain dispersed, and classical motion returns with the return of the spatial localization. Both the collapse and revival of the wave packet occur because of the quantized nature of the atom. In this experiment, the wave packet was excited to the Rydberg slates by a short, ultraviolet pulse from the ground state of potassium. The probe pulse delay was scanned, and the resulting photo-ionization signal displayed the evolution of the wave packet. The collapse and revival of the radial wave packet were observed.1
We demonstrate a protocol to create localized wave packets in very-high-n Rydberg states which travel in nearly circular orbits around the nucleus. Although these wave packets slowly dephase and eventually lose their localization, their motion can be monitored over several orbital periods. These wave packets represent the closest analog yet achieved to the original Bohr model of the hydrogen atom, i.e., an electron in a circular classical orbit around the nucleus. The possible extension of the approach to create "planetary atoms" in highly correlated stable multiply excited states is discussed.
Quantum revivals in very-high-n (n ~ 300) high-l Rydberg wave packets generated from parent np states are used to examine decoherence induced by the application of 'coloured' noise from a random pulse generator and by collisions. In the absence of external perturbations, the high-l wave packets maintain their coherence for periods ~ 1 µs, i.e. for many hundreds of orbits. This coherence can be destroyed on sub-microsecond timescales by the application of even very small amounts of electrical noise at a rate that depends markedly on the spectral characteristics of the noise. In contrast, measurements over similar timescales with CO2 target gas densities of ~ 1011 cm−3 provided no evidence of collisional dephasing. The mechanisms responsible for decoherence are discussed with the aid of classical and quantum simulations. The results of these simulations are in good accord with the experimental data.