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Rydberg atom wavepacket dynamics in one and two-dimensions

J. J. Mestayer

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Atoms in high-lying Rydberg states with large values of principal quantum number n, n ≥300, form a valuable laboratory in which to explore the control and manipulation of quantum states of mesoscopic size using carefully tailored sequences of short electric field pulses whose characteristic times (duration and/or rise/fall times) are less than the classical electron orbital period. Atoms react to such pulse sequences very differently than to short laser or microwave pulses providing the foundation for a number of new approaches to engineering atomic wavefunctions. The remarkable level of control that can be achieved is illustrated with reference to the generation of localized wavepackets in Bohr-like near-circular orbits, and the production of non-dispersive wavepackets under periodic driving and their transport to targeted regions of phase space. New protocols continue to be developed that will allow even tighter control with the promise of new insights into quantum-classical correspondence, information storage in mesoscopic systems, physics in the ultra-fast ultra-intense regime, and non-linear dynamics in driven systems.

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Atoms in high-lying Rydberg states with large values of principal quantum number n, n ≥300, form a valuable laboratory in which to explore the control and manipulation of quantum states of mesoscopic size using carefully tailored sequences of short electric field pulses whose characteristic times (duration and/or rise/fall times) are less than the classical electron orbital period. Atoms react to such pulse sequences very differently than to short laser or microwave pulses providing the foundation for a number of new approaches to engineering atomic wavefunctions. The remarkable level of control that can be achieved is illustrated with reference to the generation of localized wavepackets in Bohr-like near-circular orbits, and the production of non-dispersive wavepackets under periodic driving and their transport to targeted regions of phase space. New protocols continue to be developed that will allow even tighter control with the promise of new insights into quantum-classical correspondence, information storage in mesoscopic systems, physics in the ultra-fast ultra-intense regime, and non-linear dynamics in driven systems.
Atoms in high-lying Rydberg states with large values of the principal quantum number n, n {ge} 300, form a valuable laboratory in which to explore the control and manipulation of quantum states of mesoscopic size using carefully tailored sequences of short electric field pulses whose characteristic times (duration and/or rise/fall times) are less than the classical electron orbital period. Atoms react to such pulse sequences very differently than to short laser or microwave pulses providing the foundation for a number of new approaches to engineering atomic wavefunctions. The remarkable level of control that can be achieved is illustrated with reference to the generation of localized wavepackets in Bohr-like near-circular orbits, and the production of non-dispersive wavepackets under periodic driving and their transport to targeted regions of phase space. The testing of these control schemes, together with their reversibility, through the creation of electric dipole echoes in Stark wavepackets, is also described. New protocols continue to be developed that will allow even tighter control with the promise of new insights into quantum-classical correspondence, information storage in mesoscopic systems, physics in the ultra-fast ultra-intense regime and nonlinear dynamics in driven systems.
We describe how, almost 100 years after the introduction of the Bohr model of the atom, it is now possible using pulsed electric fields to create localized wavepackets in high n (n≈300) Rydberg atoms that travel in near-circular Bohr-like orbits mimicking the behavior of a classical electron. The protocols employed are explained with the aid of quantum and classical dynamics. Although many aspects of the underlying behavior can be described using classical arguments, purely quantum effects such as revivals can be seen even for n≈300.
In this article, we review a different approach to controlling quantum systems. We show that the quantum control problem can be greatly simplified by limiting the duration of the driving force to less than one characteristic period of the system. (For an atomic-electron Rydberg wavepacket this would be the Kepler period, for example, or the vibrational period in the case of a molecule.) If the target state is a bound state of the system, then for times less than the characteristic period, the particle does not have the opportunity to reach the system's boundary and acts essentially as a classical free particle. Such a restriction on the duration of the driving field allows an analytic solution to be found, even in the nonperturbative regime, helping clarify some of the differences between the perturbative and the nonperturbative regimes of excitation. We also show that our solution is nonunique, and the quantum controller has a multiplicity of solutions to chose from.
Localized wavepackets are created in high- n ( n ~ 300) Rydberg atoms which travel in near-circular orbits around the nucleus. Application of carefully tailored electric fields to quasi-1D Rydberg atoms creates coherent superpositions of Stark states with near extreme values of one of the components of the angular momentum. Half-cycle electric field pulses (HCPs) probe the dynamics of the circular states producing signature oscillations in survival probability that correspond to the expected wavepacket evolution. Although these wavepackets slowly dephase and lose their localization, their motion can be followed for several orbits and provides an analog of the original Bohr model, i.e., an electron in circular classical orbit around the nucleus. Measurements of the asymmetry in survival probability with increasing probe strength at different phases of the orbit confirm orbital motion of the wavepacket. Classical trajectory Monte-Carlo simulations (CTMC) agree with experimental results, and provide promising leads for future studies.
High angular momentum Rydberg wave packets are studied. Application of carefully tailored electric fields to low angular momentum, high- n ( n ∼ 300) Rydberg atoms creates coherent superpositions of Stark states with near extreme values of angular momentum, [cursive l]. Wave packet components orbit the parent nucleus at rates that depend on their energy, leading to periods of localization and delocalization as the components come into and go out of phase with each other. Monitoring survival probability signals in the presence of position dependent probing leads to observation of characteristic oscillations based on the composition of the wave packet. The discrete nature of electron energy levels is observed through the measurement of quantum revivals in the wave packet localization signal. Time-domain spectroscopy of these signals allows determination of both the population and phase of individual superposition components. Precise manipulation of wave packets is achieved through further application of pulsed electric fields. Decoherence effects due to background gas collisions and electrical noise are also detailed. Quantized classical trajectory Monte-Carlo simulations are introduced and agree remarkably well with experimental results.