Non-dispersive wave packets in periodically driven quantum systems

Abstract

With the exception of the harmonic oscillator, quantum wave packets usually spread as time evolves. This is due to the non-linear character of the classical equations of motion which makes the various components of the wave packet evolve at various frequencies. We show here that, using the non-linear resonance between an internal frequency of a system and an external periodic driving, it is possible to overcome this spreading and build non-dispersive (or non-spreading) wave packets which are well localized and follow a classical periodic orbit without spreading. From the quantum mechanical point of view, the non-dispersive wave packets are time periodic eigenstates of the Floquet Hamiltonian, localized in the non-linear resonance island. We discuss the general mechanism which produces the non-dispersive wave packets, with emphasis on simple realization in the electronic motion of a Rydberg electron driven by a microwave field. We show the robustness of such wave packets for a model one-dimensional as well as for realistic three-dimensional atoms. We consider their essential properties such as the stability versus ionization, the characteristic energy spectrum and long lifetimes. The requirements for experiments aimed at observing such non-dispersive wave packets are also considered. The analysis is extended to situations in which the driving frequency is a multiple of the internal atomic frequency. Such a case allows us to discuss non-dispersive states composed of several, macroscopically separated wave packets communicating among themselves by tunneling. Similarly we briefly discuss other closely related phenomena in atomic and molecular physics as well as possible further extensions of the theory. (C) 2002 Elsevier Science B.V. All rights reserved

Characterizing high-nquasi-one-dimensional strontium Rydberg atoms

“…As demonstrated in earlier studies using n ∼ 300 potassium Rydberg atoms, the production of strongly polarized quasi-one-dimensional (quasi-1D) Rydberg states provides a valuable gateway to studies of nonlinear dynamics and chaos in the ultrafast, ultraintense regime [1][2][3] and to the control and manipulation of excited electronic states, including the creation of states in which the electron moves about the nucleus in a near-circular "Bohr-like" orbit [4][5][6]. Notwithstanding the wealth of new insights obtained using alkali metals, the alkaline-earth elements offer the opportunity to explore new aspects of Rydberg atom physics [7][8][9].…”

Adiabatic quantum transport in a spin chain with a moving potential

“…Translating this pendulum language back to the spin chain case, one anticipates that a slowly moving parabolic magnetic field (with slowly increasing n 0 ) should result in a robust scenario for transferring quantum population along the spin chain. During this process the dispersion of the spin wave should also be bounded by the separatrix structure, i.e., a moving but non-spreading wavepacket [22] of the spin wave can be expected. The main remaining task of this paper is devoted to detailed aspects of this adiabatic control scheme.…”

Inelastic Multiple Scattering of Interacting Bosons in Weak Random Potentials

“…The proposed possible application of Rydberg physics to realize quantum information processing [190,191], together with the experimental ability to control center of mass and electronic degrees of freedom simultaneously, has revived the field. This allows, on the one side, to investigate novel collective dynamics of interacting Rydberg gases [188,192,193], and to explore the potential of Rydberg physics for robust and fault-tolerant quantum control [194,195] and engineering [196].…”

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