title: Quantum accelerator modes from the Farey tree.
abstract: We show that mode locking finds a purely quantum nondissipative 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.
authors.affiliation: Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany.
authors.forename: A
authors.initials: A
authors.lastname: Buchleitner
authors.forename: M B
authors.initials: MB
authors.lastname: d'Arcy
authors.forename: S
authors.initials: S
authors.lastname: Fishman
authors.forename: S A
authors.initials: SA
authors.lastname: Gardiner
authors.forename: I
authors.initials: I
authors.lastname: Guarneri
authors.forename: Z-Y
authors.initials: ZY
authors.lastname: Ma
authors.forename: L
authors.initials: L
authors.lastname: Rebuzzini
authors.forename: G S
authors.initials: GS
authors.lastname: Summy