Observation of fractional revivals in the evolution of a Rydberg atomic wave packet

Yeazell, John A.; Stroud, C. R.

doi:10.1103/physreva.43.5153

Cited by 188 publications

(138 citation statements)

References 12 publications

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“…This implies that the temporal dynamics is built from exactly the same frequencies; thus, the 3D dynamics is essentially the same as the 1D dynamics. 5 Indeed, collapses and revivals of the wave-packet were also observed, under various experimental conditions, in the laboratory [5,11,25,26]. Fig.…”

Section: A Simple Example: the One-dimensional Hydrogen Atommentioning

confidence: 89%

“…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%

“…There have been several experimental realizations of electronic wave-packets in atoms [4,5,11,25,27,28], either along the pure radial coordinate or even along angular coordinates too. However, all these wave-packets dispersed rather quickly.…”

Section: A Simple Example: the One-dimensional Hydrogen Atommentioning

confidence: 99%

“…(85) are trivial: E = E n − khω, which is nothing but the unperturbed energy spectrum modulohω. 11 In the presence of a small perturbation, only quasi-degenerate states with values close to E n − khω will be efficiently coupled. In the semiclassical limit, see section 2, eq.…”

Section: The Mathieu Approachmentioning

confidence: 99%

“…On the other hand, given a localized wave-packet at time t = 0, a decomposition |ψ(t = 0) = n c n |φ n (10) with coefficients c n = φ n |ψ(t = 0) (11) in unperturbed energy eigenstates…”

Section: What Is a Wave Packet?mentioning

confidence: 99%

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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: the One-dimensional Hydrogen Atommentioning

confidence: 89%

“…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%

Section: A Simple Example: the One-dimensional Hydrogen Atommentioning

confidence: 99%

Section: The Mathieu Approachmentioning

confidence: 99%

Section: What Is a Wave Packet?mentioning

confidence: 99%

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Non-dispersive wave packets in periodically driven quantum systems

2002

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Wave Packets Can Factorize Numbers

Mack

Bienert

Haug

et al. 2002

phys. stat. sol. (b)

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We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new, promising and effective method to factorize numbers. IntroductionInterference of waves instead of Newton's light corpuscles --what a revolutionary idea of Thomas Young pronounced in his famous talk at the Royal Society in 1801 [1]. The opposite idea --particles as waves --proposed by Louis de Broglie and cast into the appropriate mathematical form by Erwin Schrö dinger more than 100 years later opened a new realm in atomic physics with more applications today than ever. ''Can a quantum-mechanical description of physical reality be considered complete?" This famous question raised by Albert Einstein, Boris Podolsky and Nathan Rosen in their seminal paper [2] brought out most clearly the importance of entanglement [3] as the basic ingredient of quantum theory. Interference, wave mechanics and entanglement are the three ideas on which Peter Shor could build his factorization algorithm [4] with a polynomial rather than exponential speed. This discovery gave birth to the new field of quantum information [5]. Guided by the same three central ideas we show in the present paper that the time evolution of elementary quantum systems carries intrinsically the tools to factorize numbers [6].Stationary states have played an important role in the development of quantum mechanics. For this reason the time evolution of wave packets has for many years taken a back seat even in textbooks on quantum theory. In this context it is interesting to recall that already in 1927 Kennard [7] studied the time evolution of wave packets in simple potentials [8]. Recently, sophisticated techniques to create short laser pulses have opened a new era for a controlled creation and observation of wave packets in atoms [9], molecules [10] and cavities [11]. Even wave packet dynamics of cold atoms [12] and Bose-Einstein condensates [13] has been observed. These examples illustrate convincingly that today's technology allows to promote this gedankenexperiment of factorization to a real implementation in a quantum system.The use of wave packet dynamics to factorize numbers has been recognized for special examples. Clauser and Dowling [14] uses a N-slit Young interference setup. Hence, the number to be factorized is encoded in the number of slits. The indicator of a factor is the interference pattern on a screen as a function of the wavelength of the light or matter wave. Whenever the intensity across the screen is constant, the appropriately scaled wavelength provides a factor. Similarly, Harter [15] considers the time evolution of a particle in a box. In contrast to these contributions we provide a general framework for factorization and moreover, exhaust the potential of interference by capitalizing on properties of quadratic phase factors.

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