From Power-Localized to Extended Quasi-Energy Eigenstates in a Quantum Periodically Driven System

Oliveira, César R. de; Guarneri, Italo; Casati, Giulio

doi:10.1209/0295-5075/27/3/003

Cited by 23 publications

(33 citation statements)

References 9 publications

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“…This system is known as the Pustylnikov model [3] (or, alternatively, the "gravitational bouncer", or the "bubblon model" [42,[155][156][157]) and represents a standard example of chaotic motion. Moreover, despite its simplicity, it may find possible applications in the dynamical manipulation of cold atoms [158].…”

Section: A Simple Example In 1d: the Gravitational Bouncermentioning

confidence: 99%

Non-dispersive wave packets in periodically driven quantum systems

2002

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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

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Section: A Simple Example In 1d: the Gravitational Bouncermentioning

confidence: 99%

Non-dispersive wave packets in periodically driven quantum systems

2002

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“…At this critical value the spectrum of the system undergoes a phase transition and changes from point spectrum to a continuum spectrum [18][19][20][21], and as a consequence, we find quantum diffusion. We can identify this transition of the spectrum by noting that the quantum revivals disappear completely as the modulation strength exceeds the critical modulation strength.…”

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confidence: 74%

Quantum recurrences: Probe to study quantum chaos

Saif

2000

Phys. Rev. E

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We study the phase space of periodically modulated gravitational cavity by means of quantum recurrence phenomena. We report that the quantum recurrences serve as a tool to connect phase space of the driven system with spectrum in quantum domain. With the help of quantum recurrences we investigate the quasi-energy spectrum of the system for a certain fixed modulation strength. In addition, we study transition of spectrum from discrete to continuum as a function of modulation strength.

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“…More precisely, the classical evolution of the Fermi accelerator displays the onset of global diffusion above a critical modulation strength λ l = 0.24 4 , while the quantum evolution remains localized until a larger value λ u of the modulation 9,12,13 . Above that point both the classical and the quantum dynamics are diffusive.…”

Section: Accelerated Dynamicsmentioning

confidence: 99%

Coherent Acceleration of Material Wave Packets

Saif

Meystre

2009

From Quantum to Cosmos

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We study the quantum dynamics of a material wavepacket bouncing off a modulated atomic mirror in the presence of a gravitational field. We find the occurrence of coherent accelerated dynamics for atoms. The acceleration takes place for certain initial phase space data and within specific windows of modulation strengths. The realization of the proposed acceleration scheme is within the range of present day experimental possibilities.

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From Power-Localized to Extended Quasi-Energy Eigenstates in a Quantum Periodically Driven System

Cited by 23 publications

References 9 publications

Non-dispersive wave packets in periodically driven quantum systems

Non-dispersive wave packets in periodically driven quantum systems

Quantum recurrences: Probe to study quantum chaos

Coherent Acceleration of Material Wave Packets

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