dorsal/arxiv
View SchemaNon-dispersive wave packets in periodically driven quantum systems
| Authors | Andreas Buchleitner, Dominique Delande, Jakub Zakrzewski |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0210033 |
| URL | https://arxiv.org/abs/quant-ph/0210033 |
| DOI | 10.1016/S0370-1573(02)00270-3 |
| Journal | Physics Reports 368(5), 409-547 (2002) |
Abstract
With the exception of the harmonic oscillator, quantum wave-packets usually spread as time evolves. We show here that, using the nonlinear 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 nonlinear 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 wavepackets 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. We also discuss other related phenomena in atomic and molecular physics as well as possible further extensions of the theory.
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"abstract": "With the exception of the harmonic oscillator, quantum wave-packets usually\nspread as time evolves. We show here that, using the nonlinear resonance\nbetween an internal frequency of a system and an external periodic driving, it\nis possible to overcome this spreading and build non-dispersive (or\nnon-spreading) wave-packets which are well localized and follow a classical\nperiodic orbit without spreading. From the quantum mechanical point of view,\nthe non-dispersive wave-packets are time periodic eigenstates of the Floquet\nHamiltonian, localized in the nonlinear resonance island. We discuss the\ngeneral mechanism which produces the non-dispersive wave-packets, with emphasis\non simple realization in the electronic motion of a Rydberg electron driven by\na microwave field. We show the robustness of such wavepackets for a model\none-dimensional as well as for realistic three dimensional atoms. We consider\ntheir essential properties such as the stability versus ionization, the\ncharacteristic energy spectrum and long lifetimes. The requirements for\nexperiments aimed at observing such non-dispersive wave-packets are also\nconsidered. We also discuss other related phenomena in atomic and molecular\nphysics as well as possible further extensions of the theory.",
"arxiv_id": "quant-ph/0210033",
"authors": [
"Andreas Buchleitner",
"Dominique Delande",
"Jakub Zakrzewski"
],
"categories": [
"quant-ph",
"nlin.CD"
],
"doi": "10.1016/S0370-1573(02)00270-3",
"journal_ref": "Physics Reports 368(5), 409-547 (2002)",
"title": "Non-dispersive wave packets in periodically driven quantum systems",
"url": "https://arxiv.org/abs/quant-ph/0210033"
},
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