Quantum Accelerator Modes from the Farey Tree

Details Quantum Accelerator Modes from the Farey Tree Quantum Accelerator Modes from the Farey Tree

2005-01-27

arxiv.org/abs/physics/0501146v3

Phys. Rev. Lett. 96, 164101 (2006)

Physics

Atomic Physics

Final published version

Scientific paper

10.1103/PhysRevLett.96.164101

We show that mode-locking finds a purely quantum non-dissipative counterpart in atom-optical quantum accelerator modes. These modes are formed by exposing cold atoms to periodic kicks in the direction of the gravitational field. They are anchored to generalized Arnol'd tongues, parameter regions where driven nonlinear classical systems exhibit mode-locking. A hierarchy for the rational numbers known as the Farey Tree provides an ordering of the Arnol'd tongues and hence of experimentally observed accelerator modes.

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