Synthesis of a classical atom: Wavepacket analogues of the Trojan asteroids

Abstract

he reason w hy atomic physicists are i nterested i n celestial m echani cs is simple: the gravi tati ona l and C oulom bic potenti als are mathemati cally i denti cal and a one-electron atom is, therefore, governed by the same Hami ltoni an as is the Kepler problem . However, once one goes beyon d the two-bod y Kepler problem the connecti ons between atomi c physi cs and celesti al mechanics become less di rect. For exam ple, the three-body problem , arguab ly the raison d' eà tre of celestial mechani cs for several centuries, has recei ved relatively little attenti on from atomic physi cists because i t does not have a direct quantu m counterpart: three quantu m parti cles canno t m utually attract one anothe r and at the same ti me interact throug h a purely Coulombi c force law . Nevertheless, i n the last ® ve years several research groups have di scovered that quantu m analogues of a parti cular limi t of the three-bod y problem, the restricted three-body problem , not only exist but contain dramati cally new physics. Thi s arti cle will describe this work and in parti cular will demonstrate the possibi lity of producing locali zed electroni c states in atom s that are di rect analog s of the coherent states of the harm oni c osci llator. These coherent wavepackets behave i n a simi lar way to the coherent states of the harmonic osci llator and the resulti ng atom mi mi cs a`classi cal' or Bohr atom althoug h external ® elds must be used to m aintain thei r i ntegri ty. Such w avepacket states are of as much funda mental interest i n laser chemi stry as they are i n atomi c, m olecular, opti cal, and soli d state physi cs. T he potenti al applicati ons of ti me-evolving quantu m wavepackets seem limi tless; some exam ples of thei r uses i nclude: the explorati on of the bounda ry between classi cal and quantu m m echani cs, the i nvesti gation of the i nterpretati on of quantu m mechanics by creating experi mental reali zations of such classi c experim ents as SchroÈ di nger' s Cat, the control of chemi cal reacti on dynam ics to achieve laser i sotope separation, the storage of coherence for quantu m computational or com municati ons purposes, and the constructi on of opti cal switches and m odulato rs.

Microcanonical initial distribution strategy for classical simulations in strong field physics

“…From the atomic physics point of view, the very same models that explain recollision with linear polarization so well predict its suppression as the ellipticity is increased, and that it would be completely eliminated for circular polarization [14,18]. On the other hand, from the celestial mechanics point of view, the persistence of recollisions is not much of a surprise since asteroid capture -the counterpart of recollision -is well known and understood by now [1][2][3]. As a consequence, the question of recollision with CP fields was left open with apparently contradictory experimental results until that is the absence of a knee shape for He and Xe [19,20], which tends to validate the absence of recollision, while a knee shape has been observed for the double ionization of Mg [21] and nitrogen oxide [22] in CP fields.…”

“…It is remarkable that in the almost hundred years that have passed since the inception of this model, analogies between celestial and atomic systems continue to be discovered and exploited. For example, the Restricted Three-Body problem (RTBP) (made up of Sun-Jupiter-Asteroid), is closely related to Rydberg atom ionization in microwave fields [1][2][3]. The basic theory of chemical reactions, Transition State Theory [4][5][6], has turned out to be relevant for asteroid capture [7][8][9] and may one day be useful for the design of spacecraft missions [10].…”

Squeezing of electromagnetic field in a cavity by electrons in Trojan states

“…The possibility of creating stationary, nondispersive, localized, wave packets describing a highly excited electron in a hydrogen atom strongly driven by circularly polarized microwave radiation was predicted theoretically several years ago [1] and confirmed in numerous publications [2][3][4] (for recent reviews of the subject see [5][6][7]). Such electronic states are called Trojan wave packets by analogy with the cloud of Trojan asteroid in the SunJupiter system.…”

Nondispersive Two-Electron Wave Packets in a Helium Atom

“…Equilibria of the classical Hamiltonian can most easily be found by constructing a zero-velocity surface (ZVS) [11], which shares some properties with a potential energy surface (PES), but contains addition terms due to the centrifugal and Lorentz forces [10,11]. An extended discussion of the construction of the ZVS in atomic systems is given in [10,20]-briefly the ZVS is obtained by rewriting the Hamiltonian in terms of velocities rather than momenta. This gives…”

“…(2) vanishes. As with a PES equilibria of the motion are then obtained as extrema of the ZVS (maxima, minima, and saddles) [10,20]. We find three possible types of equilibrium point whose stability depends on the particular values of the parameters.…”