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Journal of Physics B Atomic Molecular and Optical Physics

Non-circular Trojan-like wavepackets: quantum theory and application to quantum control

E A Shapiro, Maciej Kaliński, Joseph H. Eberly

Published Aug 3, 2000• 3 citations
Publisher

Abstract

We develop a fully quantum-mechanical theory to describe non-circular Trojan-like wavepackets. These correspond to nonlinear resonances in Rydberg hydrogen dressed in a circularly polarized microwave field. The theory is applied to describe adiabatic quantum control of Rydberg states via the wavepackets. The possibility of such quantum control is demonstrated in numerical experiments.

DOI
10.1088/0953-4075/33/16/311

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We develop a fully quantum-mechanical theory to describe non-circular Trojan-like wavepackets. These correspond to nonlinear resonances in Rydberg hydrogen dressed in a circularly polarized microwave field. The theory is applied to describe adiabatic quantum control of Rydberg states via the wavepackets. The possibility of such quantum control is demonstrated in numerical experiments.
This article demonstrates that coherent states in Rydberg atoms can be produced and stabilized by combining a circularly polarized microwave field with a static, perpendicular magnetic field. These electronic wavepackets owe their stability to atomic analogs of the Lagrange equilibria which confine Jupiter's Trojan asteroids. While these “Trojan” wavepackets may slowly decay due to tunneling, a more significant source of dispersion will arise if the tails of the wavepacket penetrate appreciably into the non-linear or chaotic parts of phase space. In the laboratory frame, if these dispersive factors can be minimized — and this may be accomplished using magnetic fields — the electronic wavepacket will travel along a circular Kepler orbit while remaining localized radially and angularly for a finite — but large — number of Kepler periods. In this sense, the system is a classical Bohr atom.
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 an experimental method of producing circular Rydberg states using a circularly polarized microwave field. A Na sss state is excited in the circularly polarized microwave field, and as the field is turned off, it makes an adiabatic rapid passage through a multiphoton resonance and evolves adiabatically into the circular state. Minimal optical selectivity is required and the field can be turned off quickly.