Classical and Quantum Chaos in Atom Optics Farhan Saif Department of Electronics, Quaid-i-Azam University, Islamabad, Pakistan. Department of Physics, University of Arizona, Tucson 85721, Arizona, USA.
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[email protected] The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum arXiv:quant-ph/0604066v1 10 Apr 2006 chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits dynamical localization and quantum recurrences. I Introduction Two hundred years ago, G¨ottingen physicist George Christoph Lichtenberg wrote “I think it is a sad situation in all our chemistry that we are unable to suspend the constituents of matter free”. Today, the possibilities to store atoms and to cool them to temperatures as low as micro kelvin and nano kelvin scale, have made atom optics a fascinating subject. It further provides a playground to study the newer effects of quantum coherence and quantum interference. In atom optics we take into account the internal and external degrees of freedom of an atom. The atom is considered as a de Broglie matter wave and these are optical fields which provide components, such as, mirrors, cavities and traps for the matter waves (Meystre 2001, Dowling and Gea-Banacloche 1996). Thus, we find a beautiful manifestation of quantum duality.