Coherence and decay of Rydberg wave Packets

Parker, Johathan; Stroud, C. R.

doi:10.1103/physrevlett.56.716

Cited by 329 publications

(236 citation statements)

References 9 publications

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“…A refined estimation of the revival time actually shows that this analysis overestimates the revival time by a factor two. 2 The correct result is [8][9][10][11]:…”

Section: What Is a Wave Packet?mentioning

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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“…A refined estimation of the revival time actually shows that this analysis overestimates the revival time by a factor two. 2 The correct result is [8][9][10][11]:…”

Section: What Is a Wave Packet?mentioning

confidence: 99%

Non-dispersive wave packets in periodically driven quantum systems

2002

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“…For one-dimensional problems, this Return Probability manifests interesting recurrences very close to 1, as time evolves. This phenomenon was studied in the physics literature to understand time evolution of Rydberg atoms and their quantum beats, with decay and reformation of the wave packet (see for example [23,20], [32] and references herein contained). In this section we want to give a flavour of results obtained by physicists in the last twenty years, concerning revivals for the quantum return probability ( [32] for a very clear and detailed review) and show how to put them in a more rigorous mathematical framework.…”

Section: Revivals For 1-d Systemsmentioning

confidence: 99%

“…In Section 3, we consider the (integrable) d = 1 case, and consider the "return probability" in the semiclassical limit. We give a mathematical rigorous presentation of beautiful results on "quantum revivals" obtained by physicists twenty years ago (see [23], [32], [20]). In Section 4 we consider the general d-dimensional case and give a semiclassical calculus of the "return probability" and of the quantum fidelity, with precise error estimates.…”

Section: Introductionmentioning

confidence: 99%

A Phase-Space Study of the Quantum Loschmidt Echo in the Semiclassical Limit

Combescure

Robert

2006

Ann. Henri Poincaré

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The notion of Loschmidt echo (also called "quantum fidelity") has been introduced in order to study the (in)-stability of the quantum dynamics under perturbations of the Hamiltonian. It has been extensively studied in the past few years in the physics literature, in connection with the problems of "quantum chaos", quantum computation and decoherence. In this paper, we study this quantity semiclassically (as → 0), taking as reference quantum states the usual coherent states. The latter are known to be well adapted to a semiclassical analysis, in particular with respect to semiclassical estimates of their time evolution. For times not larger than the so-called "Ehrenfest time" C| log |, we are able to estimate semiclassically the Loschmidt Echo as a function of t (time), (Planck constant), and δ (the size of the perturbation). The way two classical trajectories merging from the same point in classical phase-space, fly apart or come close together along the evolutions governed by the perturbed and unperturbed Hamiltonians play a major role in this estimate. We also give estimates of the "return probability" (again on reference states being the coherent states) by the same method, as a function of t and .

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“…We remark that such kind of sums have been studied in the context of fractional revivals [Par86,Ave89] in wavepacket dynamics in anharmonic potentials [Lei96a,Lei96b,Sch01]. Here the autocorrelation function is defined as the overlap of a time-evolved wavepacket with the initial wavepacket and is accessible in pump-probe experiments.…”

Section: Organization Of the Present Workmentioning

confidence: 99%

Factorization of numbers with physical systems

Merkel

Averbukh

Girard

et al. 2006

Fortschritte der Physik

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The periodicity properties of Gauss sums allow us to factor integer numbers. We show that the excitation probability amplitudes of appropriate quantum systems interacting with specific laser fields are determined by Gauss sums. The resulting probabilities are experimentally accessible by measuring the fluorescence from this level. In particular, we discuss a two‐photon transition in a ladder system driven by a chirped laser pulse. In addition, we consider two realizations of laser driven one‐photon transitions. For each quantum system we demonstrate the power of this factorization scheme using numerical examples.

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Coherence and decay of Rydberg wave Packets

Cited by 329 publications

References 9 publications

Non-dispersive wave packets in periodically driven quantum systems

Non-dispersive wave packets in periodically driven quantum systems

A Phase-Space Study of the Quantum Loschmidt Echo in the Semiclassical Limit

Factorization of numbers with physical systems

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