dorsal/arxiv
View SchemaSemiclassical catastrophes and accumulative angular squeezing of a kicked quantum rotor
| Authors | M. Leibscher, I. Sh. Averbukh, P. Rozmej, R. Arvieu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306146 |
| URL | https://arxiv.org/abs/quant-ph/0306146 |
| DOI | 10.1103/PhysRevA.69.032102 |
| Journal | Phys. Rev. A 69, 032102 (2004) |
Abstract
We present a detailed theory of spectacular semiclassical catastrophes happening during the time evolution of a kicked quantum rotor (Phys.Rev. Lett. {\bf 87}, 163601 (2001)). Both two- and three-dimensional rotational systems are analyzed. It is shown that the wave function of the rotor develops a {\em cusp} at a certain delay after a kick, which results in a sharply focused rotational wave packet. The {\em cusp} is followed by a fold-type catastrophe manifested in the {\em rainbow}-like moving angular singularities. In the three-dimensional case, the rainbows are accompanied by additional singular features similar to {\em glory} structures known in wave optics. These catastrophes in the time-dependent angular wave function are well described by the appropriate tools of the quasiclassical wave mechanics, i.e. by Airy and Bessel approximations and Pearcey's functions. A scenario of "accumulative squeezing" is also presented in which a specially designed train of short kicks produces an unlimited narrowing of the rotor angular distribution. This scenario is relevant for the molecular alignment by short laser pulses, and also for atom lithography schemes in which cold atoms are focused by an optical standing wave.
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"abstract": "We present a detailed theory of spectacular semiclassical catastrophes\nhappening during the time evolution of a kicked quantum rotor (Phys.Rev. Lett.\n{\\bf 87}, 163601 (2001)). Both two- and three-dimensional rotational systems\nare analyzed. It is shown that the wave function of the rotor develops a {\\em\ncusp} at a certain delay after a kick, which results in a sharply focused\nrotational wave packet. The {\\em cusp} is followed by a fold-type catastrophe\nmanifested in the {\\em rainbow}-like moving angular singularities. In the\nthree-dimensional case, the rainbows are accompanied by additional singular\nfeatures similar to {\\em glory} structures known in wave optics. These\ncatastrophes in the time-dependent angular wave function are well described by\nthe appropriate tools of the quasiclassical wave mechanics, i.e. by Airy and\nBessel approximations and Pearcey\u0027s functions. A scenario of \"accumulative\nsqueezing\" is also presented in which a specially designed train of short kicks\nproduces an unlimited narrowing of the rotor angular distribution. This\nscenario is relevant for the molecular alignment by short laser pulses, and\nalso for atom lithography schemes in which cold atoms are focused by an optical\nstanding wave.",
"arxiv_id": "quant-ph/0306146",
"authors": [
"M. Leibscher",
"I. Sh. Averbukh",
"P. Rozmej",
"R. Arvieu"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.69.032102",
"journal_ref": "Phys. Rev. A 69, 032102 (2004)",
"title": "Semiclassical catastrophes and accumulative angular squeezing of a kicked quantum rotor",
"url": "https://arxiv.org/abs/quant-ph/0306146"
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