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arXiv · quant-ph/0512086

Arnol'd Tongues and Quantum Accelerator Modes

Italo Guarneri·Laura Rebuzzini·Shmuel Fishman
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Abstract

The stable periodic orbits of an area-preserving map on the 2-torus, which is formally a variant of the Standard Map, have been shown to explain the quantum accelerator modes that were discovered in experiments with laser-cooled atoms. We show that their parametric dependence exhibits Arnol'd-like tongues and perform a perturbative analysis of such structures. We thus explain the arithmetical organisation of the accelerator modes and discuss experimental implications thereof.

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Italo Guarneri, Laura Rebuzzini, Shmuel Fishman. 2005-12-12. Arnol'd Tongues and Quantum Accelerator Modes. https://doi.org/10.1088/0951-7715/19/5/006

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